https://en.wikipedia.org/w/api.php?action=feedcontributions&feedformat=atom&user=CasteiswrongWikipedia - User contributions [en]2024-11-20T15:39:12ZUser contributionsMediaWiki 1.44.0-wmf.3https://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223491085Talk:Snell's law2024-05-12T14:00:00Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated and the manuscript had no conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)<br />
::If you look at the rest of the comment after his first line of observation, there are two massive errors as is common with these so-called medieval "mathematicians". Firstly, he discards the JH portion of the length of the incident ray (CH) without reducing the refracted ray (CE or CI) by the same percentage. Secondly, he sets; <math>\frac{longline(AK)}{shortline(AB)} = \frac{shortline(CI)}{longline(CJ)}<br />
\Rrightarrow longline^2 = shortline^2 <br />
\Rrightarrow long = short </math> <br />
::Essentially, he has no understanding of ratios with his math concluding that the lengths are equal, or no refraction had occurred, while his diagram proves otherwise. Looks like he was playing around with pencils and geometry. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 05:10, 12 May 2024 (UTC)<br />
:::@[[User:Casteiswrong|Casteiswrong]]Please see [[WP:OR]]. You can't add your own POV or challange the works of authors here. [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4|talk]]) 08:31, 12 May 2024 (UTC)<br />
::::Sorry, I should have been specific. My second reply is not in the book, and it is unrelated to my edit because it is clearly WP:OR. I was trying to open an entirely different discussion from the edit I had made because I was wondering if we should include this finding as well, however, as I said before Selin explicitly states that the ratio was '''postulated by Ibn Sahl but never calculated and with no conceptual comment'''. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 09:30, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Wikipedia:Administrators%27_noticeboard/Edit_warring&diff=1223488603Wikipedia:Administrators' noticeboard/Edit warring2024-05-12T13:41:33Z<p>Casteiswrong: user comment</p>
<hr />
<div>{{Short description|Noticeboard for edit warring}}<br />
<!--Adds protection template automatically if semi-protected--><noinclude>{{#if:{{PROTECTIONLEVEL:edit}}|{{pp|small=yes}}}}__NEWSECTIONLINK__{{no admin backlog}}{{/Header}}[[Category:Non-talk pages that are automatically signed]] [[Category:Wikipedia edit warring]]<br />
{{pp-move|small=yes}}<br />
{{User:MiszaBot/config<br />
|archiveheader = {{Administrators' noticeboard navbox all}} <br />
|maxarchivesize = 250K<br />
|counter = 482<br />
|algo = old(2d)<br />
|key = 0a3bba89e703569428f2aab1add75bd7d7d1583d2d1f397783aee23fda62b06f<br />
|archive = Wikipedia:Administrators' noticeboard/3RRArchive%(counter)d<br />
}}</noinclude><!--<br />
<br />
NOTE: THE *BOTTOM* IS THE PLACE FOR NEW REPORTS. --><br />
<br />
== [[User:Affinepplan]] reported by [[User:Closed Limelike Curves]] (Result: EC protection, warning) ==<br />
<br />
'''Page:''' {{pagelinks|Later-no-harm criterion}}<br />
<br />
'''User being reported:''' {{userlinks|Affinepplan}}<br />
<br />
'''Previous version reverted to:''' <br />
<br />
'''Diffs of the user's reverts:'''<br />
# {{diff2|1222975543|02:48, 9 May 2024 (UTC)}} "Undid revision [[Special:Diff/1222974899|1222974899]] by [[Special:Contributions/Aydoh8|Aydoh8]] ([[User talk:Aydoh8|talk]])"<br />
# {{diff|oldid=1222965636|diff=1222969242|label=Consecutive edits made from 01:48, 9 May 2024 (UTC) to 01:51, 9 May 2024 (UTC)}}<br />
## {{diff2|1222968836|01:48, 9 May 2024 (UTC)}} "removed irrelevant and unrigorous political commentary"<br />
## {{diff2|1222969242|01:51, 9 May 2024 (UTC)}} "removed irrelevant and unrigorous speculation about election strategy"<br />
<br />
'''Diffs of edit warring / 3RR warning:'''<br />
# {{diff2|1222971525|02:06, 9 May 2024 (UTC)}} "Warning: You are a suspected [[WP:SOCK|sockpuppet]]."<br />
<br />
'''Diffs of attempt to resolve dispute on article talk page:'''<br />
# {{diff2|1222972855|02:18, 9 May 2024 (UTC)}} "/* This article needs serious revision */"<br />
<br />
<u>'''Comments:'''</u><br />
<br />
Likely use of anonymous IP edits in attempt to evade 3RR. –Sincerely, [[User:Closed Limelike Curves|A Lime]] 05:44, 9 May 2024 (UTC)<br />
<br />
:Pinging @[[User:Aydoh8|Aydoh8]] who warned @[[User:Affinepplan|Affinepplan]]. Sorry you got dragged into this :(<br />
:I believe users @[[User:64.112.229.118|64.112.229.118]], @[[User:47.230.61.20|47.230.61.20]], @[[User:Affinepplan|Affinepplan]] are the same person.<br />
:Short timeline:<br />
:# @[[User:64.112.229.118|64.112.229.118]] attempts to delete portions of article. Reverted by @[[User:Ankermast|Ankermast]].<br />
:# @[[User:64.112.229.118|64.112.229.118]] responds by adding a disparaging [[Template:Multiple issues]] message insulting authors of the page. Reverted by me @[[User:Closed Limelike Curves|Closed Limelike Curves]].<br />
:# @[[User:Affinepplan|Affinepplan]] (believed to be same user as above) reverts to restore the template. (1st revert.)<br />
:# ~1 week passes, with intervening edits from unrelated users.<br />
:# I notice the restored template and revert.<br />
:# @[[User:47.230.61.20|47.230.61.20]] (believed to be same user) reverts to restore the template. (Second revert, first in 24 hour period.)<br />
:# I notice the unusual activity and request page protection, as well as warning @[[User:Affinepplan|Affinepplan]]. I do not restore.<br />
:# @[[User:Aydoh8|Aydoh8]] takes notice and restores the previous version of the page. @[[User:Affinepplan|Affinepplan]] restores (Third revert.)<br />
:# @[[User:Aydoh8|Aydoh8]] reverts again and informs @[[User:Affinepplan|Affinepplan]] their actions may constitute edit warring. @[[User:Affinepplan|Affinepplan]] nevertheless '''reverts a fourth time, ignoring warning.'''<br />
:–Sincerely, [[User:Closed Limelike Curves|A Lime]] 06:11, 9 May 2024 (UTC)<br />
::@[[User:Closed Limelike Curves|Closed Limelike Curves]] I was going to bring this to AN3 anyway if they kept going. Looks like they've stopped. I also recommend you file a sockpuppet report at [[WP:SPI]] as well. [[User:Aydoh8|Aydoh8]] ([[User talk:Aydoh8|talk]] &#124; [[Special:Contributions/Aydoh8|contribs]]) 11:18, 9 May 2024 (UTC)<br />
*'''Result:''' Since [[User:Affinepplan]] and [[User:Closed Limelike Curves]] have both edited the artice on May 11 I conclude that the edit war is not over. So I have put [[WP:ECP|extended confirmed protection]] on the article for one month. That will exclude the main warring parties (and any IPs) from editing the article directly. Please try to reach agreement on the talk page and see [[WP:DR]] if you are stuck. [[User:Affinepplan]] may have been editing logged-out and they are warned not to continue that. [[User:EdJohnston|EdJohnston]] ([[User talk:EdJohnston|talk]]) 03:06, 12 May 2024 (UTC)<br />
<br />
== [[User:서아7]] reported by [[User:Btspurplegalaxy]] (Result: Blocked 72 hours) ==<br />
<br />
'''Page:''' {{pagelinks|Weverse}}<br />
<br />
'''User being reported:''' {{userlinks|서아7}}<br />
<br />
'''Previous version reverted to:''' <br />
<br />
'''Diffs of the user's reverts:'''<br />
# {{diff2|1222995990|06:47, 9 May 2024 (UTC)}} "Wikipedia pages with editing battles are unreliable articles. It was a correct point that it was mostly remanded, and the history remains.Controlling speech just because it's a new account damages Wikipedia's credibility.You should stop remanding and creating stupid articles. Wikipedia loses its value if it posts incorrect information."<br />
# {{diff2|1222985213|04:30, 9 May 2024 (UTC)}} "현재는 돈을 weverse에게 지불하면 사무소 소속자 이외에도 누구나 개설할 수 있다"<br />
# {{diff2|1222884538|14:43, 8 May 2024 (UTC)}} "나는 사실을 지적하고 있다<br />
kpop에 익숙해져라<br />
나도 BTS는 좋아해"<br />
# {{diff2|1222883819|14:38, 8 May 2024 (UTC)}} "낡은 정보를 싣지 마라<br />
원래 한국의 기사는 틀린것이 있기 때문에 소스에는 불충분<br />
원래 영어 원어민은 거의 한국 콘텐츠 안봐"<br />
# {{diff2|1222876268|13:36, 8 May 2024 (UTC)}} "-"<br />
# {{diff|oldid=1222467043|diff=1222848435|label=Consecutive edits made from 08:01, 8 May 2024 (UTC) to 08:10, 8 May 2024 (UTC)}}<br />
## {{diff2|1222847677|08:01, 8 May 2024 (UTC)}} "o"<br />
## {{diff2|1222847814|08:03, 8 May 2024 (UTC)}} "o"<br />
## {{diff2|1222848241|08:08, 8 May 2024 (UTC)}} "The organizer pays weverse"<br />
## {{diff2|1222848435|08:10, 8 May 2024 (UTC)}} "It is currently being used by people other than hybe members, so it has been removed."<br />
<br />
'''Diffs of edit warring / 3RR warning:'''<br />
<br />
<br />
'''Diffs of attempt to resolve dispute on article talk page:'''<br />
<br />
<br />
<u>'''Comments:'''</u><br />
*{{AN3|b|72 hours}} [[User:Aoidh|Aoidh]] ([[User talk:Aoidh|talk]]) 13:59, 9 May 2024 (UTC)<br />
<br />
== [[User:Reywas92]] reported by [[User:PaulGamerBoy360]] (Result: Stale) ==<br />
<br />
'''Page:''' {{pagelinks|Buchanan Corner, Indiana}}<br />
<br />
'''User being reported:''' {{userlinks|Reywas92}}<br />
<br />
'''Previous version reverted to:''' <br />
<br />
'''Diffs of the user's reverts:'''<br />
<br />
<br />
'''Diffs of edit warring / 3RR warning:'''<br />
<br />
<br />
'''Diffs of attempt to resolve dispute on article talk page:'''<br />
<br />
<br />
<u>'''Comments:'''</u><br />
<br />
This User Has Been Edit waring With Me, I Have Tried to Keep it Civil, & I Am No Longer Editing The Page Due To It, I Need Administrator Intervention to Stop This User From Undoing Constructive Edits, A Source is Still A Source Wether it Is One Sentence or Multiple Pages. [[User:PaulGamerBoy360|😎😎PaulGamerBoy360😎😎]] ([[User talk:PaulGamerBoy360|talk]]) 15:14, 9 May 2024 (UTC)<br />
<br />
@[[User:Reywas92|Reywas92]] - Why are you reverting when [[WP:3RRNO]] does not apply? Poor sources are not vandalism.<br/><br />
*Two of these edits were removing copyrighted content copied and pasted from findagrave.com. These others were of his readding of unreliable and inappropriate sources, but I understand I should have just let them stand until Paul actually understood [[WP:RS]]. [[User:Reywas92|Reywas92]]<sup>[[User talk:Reywas92|Talk]]</sup> 15:54, 9 May 2024 (UTC)<br />
<br />
::they were not copyrighted, i used quill bot to change them, if you did a side by side comparison you will se that they are not the same. also i have just found more sources for the cemeteries, but im just going to post them in the afd not the article because aparently we are going to make up guidelines stating that family cemeteries cannot be listed. [[User:PaulGamerBoy360|😎😎PaulGamerBoy360😎😎]] ([[User talk:PaulGamerBoy360|talk]]) 16:01, 9 May 2024 (UTC)<br />
:::Using a tool to paraphrase would still seem to be in violation of [[WP:PARAPHRASE]] [[User:EvergreenFir|'''<span style="color:#8b00ff;">Eve</span><span style="color:#6528c2;">rgr</span><span style="color:#3f5184;">een</span><span style="color:#197947;">Fir</span>''']] [[User talk:EvergreenFir|(talk)]] 16:31, 9 May 2024 (UTC)<br />
::::I compared them. The first passage was identical to the entire findagrave.com text, the second consisted only of the first sentences of its findagrave.com entry. I have requested revdel. [[User:NebY|NebY]] ([[User talk:NebY|talk]]) 16:57, 9 May 2024 (UTC)<br />
<br />
@[[User:PaulGamerBoy360|PaulGamerBoy360]] - You are in the wrong here. Reywas92 is correct regarding your sources and edits. A sources it not "still a source" if that source is not reliable. Why are you edit warring with Reywas92? [[User:EvergreenFir|'''<span style="color:#8b00ff;">Eve</span><span style="color:#6528c2;">rgr</span><span style="color:#3f5184;">een</span><span style="color:#197947;">Fir</span>''']] [[User talk:EvergreenFir|(talk)]] 15:22, 9 May 2024 (UTC)<br />
<br />
:No, I have read the guidlines & it says you may still use an "unreliable source" as long as you can find more sources to support the facts, there were more sources to support the fact on the intro paragraph, and only one of the sources on the intro paragraph was "unreliable" all the other were reliable, i was in the proccess of finding more sources to support the cemetaries, no guidelines state that family cemeteries cant be listed, I have stopped editing that page. besides even the small "generally unreliable" sources add up with the same information shows that the information is most likely true, they all support eachother, i am in the proccess of finding more sources, but for ofline sources to be found, people need to see that the offline sources are needed. Removing the paragraphs from the article will prevent others from finding the needed sources. (And it seems the discussion about the reliablitiy of Find-a-Grave revolved areoud the people side, and not the Cemetery Side of the Site) [[User:PaulGamerBoy360|😎😎PaulGamerBoy360😎😎]] ([[User talk:PaulGamerBoy360|talk]]) 15:54, 9 May 2024 (UTC)<br />
::@[[User:PaulGamerBoy360|PaulGamerBoy360]] where on [[WP:RS]] or [[WP:V]] does it say that you can use unreliable sources? At [[WP:USERGENERATED]] on [[WP:RS]] it specifically lists FindAGrave as one of the "{{tq|[e]xamples of unacceptable user-generated sources}}". [[User:EvergreenFir|'''<span style="color:#8b00ff;">Eve</span><span style="color:#6528c2;">rgr</span><span style="color:#3f5184;">een</span><span style="color:#197947;">Fir</span>''']] [[User talk:EvergreenFir|(talk)]] 16:29, 9 May 2024 (UTC)<br />
*I'll close this as stale, but I wouldn't object to the discussion above continuing a bit. Not excessively, though, as it's no longer about edit warring. {{u|PaulGamerBoy360}}, if something remains unclear about copyright or verifiability, the [[WP:Teahouse|Teahouse]] is a good place to ask. [[User:ToBeFree|&#126; ToBeFree]] ([[User talk:ToBeFree|talk]]) 19:35, 9 May 2024 (UTC)<br />
*{{AN3|s}} [[User:ToBeFree|&#126; ToBeFree]] ([[User talk:ToBeFree|talk]]) 19:35, 9 May 2024 (UTC)<br />
<br />
== [[User:Skibidi36]] reported by [[User:Escape Orbit]] (Result: Blocked 2 weeks) ==<br />
<br />
'''Page:''' {{pagelinks|Ail al-Kahiay Campaign (1798)}}<br />
<br />
'''User being reported:''' {{userlinks|Skibidi36}}<br />
<br />
'''Previous version reverted to:''' <br />
<br />
'''Diffs of the user's reverts:'''<br />
# {{diff2|1223030642|13:06, 9 May 2024 (UTC)}} "I'm reverting this edit for vandalism again, majority of historians as well as the arab wikipedia agree that this is a Saudi victory."<br />
<br />
'''Diffs of edit warring / 3RR warning:'''<br />
<br />
<br />
'''Diffs of attempt to resolve dispute on article talk page:'''<br />
<br />
<br />
<u>'''Comments:'''</u><br />
<br />
Resuming same edit-warring that's been going on for weeks after previous block [[User:Escape_Orbit|<span style="color: green;">Escape Orbit</span>]] <sup>[[User_talk:Escape_Orbit|(Talk)]]</sup> 16:34, 9 May 2024 (UTC)<br />
*{{AN3|b|2 weeks}} [[User:EvergreenFir|'''<span style="color:#8b00ff;">Eve</span><span style="color:#6528c2;">rgr</span><span style="color:#3f5184;">een</span><span style="color:#197947;">Fir</span>''']] [[User talk:EvergreenFir|(talk)]] 16:43, 9 May 2024 (UTC)<br />
<br />
== [[User:عبدالرحمن عراق]] reported by [[User:Escape Orbit]] (Result: Blocked indefinitely) ==<br />
<br />
'''Page:''' {{pagelinks|Ail al-Kahiay Campaign (1798)}}<br />
<br />
'''User being reported:''' {{userlinks|عبدالرحمن عراق}}<br />
<br />
'''Previous version reverted to:''' <br />
<br />
'''Diffs of the user's reverts:'''<br />
<br />
<br />
'''Diffs of edit warring / 3RR warning:'''<br />
<br />
<br />
'''Diffs of attempt to resolve dispute on article talk page:'''<br />
<br />
<br />
<u>'''Comments:'''</u><br />
<br />
Resuming same edit-warring that's been going on for weeks, after previous block [[User:Escape_Orbit|<span style="color: green;">Escape Orbit</span>]] <sup>[[User_talk:Escape_Orbit|(Talk)]]</sup> 16:35, 9 May 2024 (UTC)<br />
*{{AN3|b|indefinitely}} [[User:EvergreenFir|'''<span style="color:#8b00ff;">Eve</span><span style="color:#6528c2;">rgr</span><span style="color:#3f5184;">een</span><span style="color:#197947;">Fir</span>''']] [[User talk:EvergreenFir|(talk)]] 16:44, 9 May 2024 (UTC)<br />
<br />
== [[User:Delores Hilll]] reported by [[User:Myrealnamm]] (Result: No violation) ==<br />
<br />
'''Page:''' {{pagelinks|Godzilla x Kong: The New Empire}}<br />
<br />
'''User being reported:''' {{userlinks|Delores Hilll}}<br />
<br />
'''Previous version reverted to:''' <br />
<br />
'''Diffs of the user's reverts:'''<br />
# {{diff2|1223356147|15:43, 11 May 2024 (UTC)}} "Undid revision [[Special:Diff/1223356038|1223356038]] by [[Special:Contributions/109.76.198.112|109.76.198.112]] ([[User talk:109.76.198.112|talk]])"<br />
# {{diff2|1223355653|15:39, 11 May 2024 (UTC)}} "Undid revision [[Special:Diff/1223355380|1223355380]] by [[Special:Contributions/109.76.198.112|109.76.198.112]] ([[User talk:109.76.198.112|talk]])"<br />
<br />
'''Diffs of edit warring / 3RR warning:'''<br />
# {{diff2|1223355953|15:42, 11 May 2024 (UTC)}} "/* Reverting Edits */ new section"<br />
<br />
'''Diffs of attempt to resolve dispute on article talk page:'''<br />
<br />
<br />
<u>'''Comments:'''</u><br />
<br />
Reverting "good faith" edits by IP users, and only giving them uw4s. Please check. If I'm wrong, and the IPs are vandalising, then that's a trout for me [[User:Myrealnamm|<span style="color:#0085BD">My</span><span style="color:#ED7700">real</span><span style="color:#2A7E19">namm</span>]] ([[User talk:Myrealnamm|💬talk]] · [[Special:Contributions/Myrealnamm|✏️contribs]]) at 15:51, 11 May 2024 (UTC)<br />
<br />
:Sorry for the inaccurate information for this notice. I wasn't familiar with the Edit Warring section in Twinkle. [[User:Myrealnamm|<span style="color:#0085BD">My</span><span style="color:#ED7700">real</span><span style="color:#2A7E19">namm</span>]] ([[User talk:Myrealnamm|💬talk]] · [[Special:Contributions/Myrealnamm|✏️contribs]]) at 15:51, 11 May 2024 (UTC)<br />
:: Hi. I cannot believe that anyone who has read the diffs or edit summaries of my changes can actually think my edits were vandalism. We all make mistakes sometimes but my edits were made in in a good faith effort to follow [[WP:UGC]] and I clearly explained as much in my edit summaries. Thanks. -- [[Special:Contributions/109.76.198.112|109.76.198.112]] ([[User talk:109.76.198.112|talk]]) 16:02, 11 May 2024 (UTC)<br />
*{{AN3|nv}} [[User:Bbb23|Bbb23]] ([[User talk:Bbb23|talk]]) 16:10, 11 May 2024 (UTC)<br />
<br />
The user also reverted my good faith edit [https://en.wikipedia.org/w/index.php?title=Arianism&diff=prev&oldid=1223356601 here] (I removed a link from a word that was literally linked in the previous section) and gave me a uw4 [https://en.wikipedia.org/w/index.php?title=User_talk:2001:BB6:47ED:FA58:ADC9:2C9F:7B0:FC19&oldid=1223356617 here]. This is not edit-warring, of course. This should be moved to ANI. [[Special:Contributions/2001:BB6:47ED:FA58:ADC9:2C9F:7B0:FC19|2001:BB6:47ED:FA58:ADC9:2C9F:7B0:FC19]] ([[User talk:2001:BB6:47ED:FA58:ADC9:2C9F:7B0:FC19|talk]]) 16:12, 11 May 2024 (UTC)<br />
<br />
== [[User:Unfriendnow]] reported by [[User:108.35.216.149]] (Result: Blocked one week) ==<br />
<br />
'''Page:''' Multiple (see below) <br /><br />
'''User being reported:''' {{userlinks|Unfriendnow}}<br />
<br />
<br />
<br />
'''Diffs of the user's reverts:'''<br />
# [https://en.wikipedia.org/w/index.php?title=Agnelli_family&diff=prev&oldid=1223083622] is a partial revert of [https://en.wikipedia.org/w/index.php?title=Agnelli_family&diff=prev&oldid=1222196929] at {{pagelinks|Agnelli family}}<br />
# [https://en.wikipedia.org/w/index.php?title=Andrew_Cavendish,_11th_Duke_of_Devonshire&diff=prev&oldid=1223239673] is a revert of [https://en.wikipedia.org/w/index.php?title=Andrew_Cavendish,_11th_Duke_of_Devonshire&diff=prev&oldid=1222195663] at {{pagelinks|Andrew Cavendish, 11th Duke of Devonshire}}<br />
# [https://en.wikipedia.org/w/index.php?title=William_Cavendish,_Marquess_of_Hartington&diff=prev&oldid=1223296238] is a revert of [https://en.wikipedia.org/w/index.php?title=William_Cavendish,_Marquess_of_Hartington&diff=prev&oldid=1222883295] at {{pagelinks|William Cavendish, Marquess of Hartington}}<br />
# [https://en.wikipedia.org/w/index.php?title=Rose_Hanbury&diff=prev&oldid=1223368095] is a revert of [https://en.wikipedia.org/w/index.php?title=Rose_Hanbury&diff=prev&oldid=1222196496] at {{pagelinks|Rose Hanbury}}<br />
<br />
<br />
<br />
<br />
'''Diff of edit warring / 3RR warning:''' [https://en.wikipedia.org/w/index.php?title=User_talk:Unfriendnow&diff=prev&oldid=1220919712]<br />
<br />
'''Diff of ANEW notice posted to user's talk page:''' [https://en.wikipedia.org/w/index.php?title=User_talk:Unfriendnow&diff=prev&oldid=1223420350]<br />
<br />
<u>'''Comments:'''</u> <br /><br />
Since being unblocked (after using a sockpuppet [[User:Namenotimportant00]] to conduct a wide-ranging edit war), four of ten edits have been to continue these edit wars. Of the remaining six, [https://en.wikipedia.org/w/index.php?title=Patrick_J._Kennedy&diff=prev&oldid=1223275675 one] is a revert of precisely the same nature (but it is a first revert, not a repeat of an earlier reverted edit), [https://en.wikipedia.org/w/index.php?title=Talk:Charles_Wellesley,_9th_Duke_of_Wellington&diff=prev&oldid=1223069705 one] is inappropriate canvassing, and [https://en.wikipedia.org/w/index.php?title=Thomas_H._Shriver&diff=prev&oldid=1223105159 one] is the same kind of unsourced trivia that resulted in [https://en.wikipedia.org/w/index.php?title=User_talk:Unfriendnow&diff=prev&oldid=1222154687 the block in the first place]. [[Special:Contributions/108.35.216.149|108.35.216.149]] ([[User talk:108.35.216.149|talk]]) 00:38, 12 May 2024 (UTC)<br />
*{{AN3|b|one week}}. [[User:Bbb23|Bbb23]] ([[User talk:Bbb23|talk]]) 00:46, 12 May 2024 (UTC)<br />
<br />
== [[User:Abhishek0831996]] reported by [[User:Pharaoh496]] (Result: ) ==<br />
<br />
'''Page:''' {{pagelinks|Narendra Modi}} <br /><br />
'''User being reported:''' {{userlinks|Abhishek0831996}}<br />
<br />
'''Previous version reverted to:''' [https://en.wikipedia.org/w/index.php?title=Narendra_Modi&oldid=1223330057]<br />
<br />
'''Diffs of the user's reverts:'''<br />
# {{Diff|Narendra Modi|prev|1223342934|1}}<br />
# {{Diff|Narendra Modi|prev|1223449041|2}}<br />
<br />
<br />
<br />
'''Diff of attempt to resolve dispute on article talk page:''' [https://en.wikipedia.org/w/index.php?title=User_talk:Abhishek0831996&oldid=1223347526]<br />
<br />
'''Diff of ANEW notice posted to user's talk page:''' [https://en.wikipedia.org/w/index.php?title=User_talk:Abhishek0831996&oldid=1223460006]<br />
<br />
<u>'''Comments:'''</u> <br /><br />
<br />
* User is removing important edits on the PM of India's page, who is involved in an election currently.<br />
* He has a history of being biased towards editing.<br />
* He has reverted my edits twice, in which great care had been taken to ensure neutrality<br />
* I wrote a message on his talk page and the guy '''''simply removed it!'''''<br />
* This is the first time im filing such a complaint, so please excuse me if Im doing anything wrong; in which case I shall learn and adapt. I see someone disrupting the process and hence have filed this. [[User:Pharaoh496|Pharaoh496]] ([[User talk:Pharaoh496|talk]]) 11:55, 12 May 2024 (UTC)<br />
<br />
== [[User:I would be bias if it was allowed]] reported by [[User:TarnishedPath]] (Result: Indefinitely blocked) ==<br />
<br />
'''Page:''' {{pagelinks|Australian Labor Party}} <br /><br />
'''User being reported:''' {{userlinks|I would be bias if it was allowed}}<br />
<br />
'''Previous version reverted to:''' [[Special:Diff/1223227860]]<br />
<br />
'''Diffs of the user's reverts:'''<br />
# [[Special:Diff/1223337759]]<br />
# [[Special:Diff/1223438180]]<br />
# [[Special:Diff/1223455886]]<br />
# [[Special:Diff/1223458796]]<br />
<br />
'''Diff of edit warring / 3RR warning:''' [[Special:Diff/1223457507]]<br />
<br />
'''Diff of attempt to resolve dispute on article talk page:''' [[Talk:Australian_Labor_Party#Seeking_a_broad_consensus_to_re-situate_the_ALP's_ideology_in_accordance_to_reliable_sources.]]<br />
<br />
'''Diff of ANEW notice posted to user's talk page:''' [[Special:Diff/1223460616]]<br />
<br />
<u>'''Comments:'''</u> <br /><br />
<br />
There is longstanding consensus that the fields in the infobox that the editor is editing should not be modified unless broad consensus is obtained in talk. This is evident by another editor previously placing code in the infobox stating <nowiki><!-- It is important to seek and gain broad consensus on the article talk page before changing this --></nowiki>. Editor has ridiculously attempted to reverse the onus to obtain consensus in talk by claimed that others need to obtain consensus for why the editor's changes shouldn't happen. ''[[User:TarnishedPath|<b style="color:#ff0000;">Tar</b><b style="color:#ff7070;">nis</b><b style="color:#ffa0a0;">hed</b><b style="color:#420000;">Path</b>]]''<sup>[[User talk:TarnishedPath|<b style="color:#bd4004;">talk</b>]]</sup> 08:15, 12 May 2024 (UTC)<br />
<br />
:Notably after the editor was [[Special:Diff/1223465596|reverted by an admin]] after the editor's fourth revert, told to not continue, take it to talk and obtain consensus an IP has shown up and reverted three more times ([[Special:Diff/1223465905]], [[Special:Diff/1223468614]] and [[Special:Diff/1223476797]]). In the last edit by the IP they left the edit summary "I don't want an edit war, but Labor has a centrist faction" which is almost identical phrasing that the editor uses on the articles talk page in their edit at [[Special:Diff/1223479083]] when they wrote "Simply put, Labor has Centrist factions. I don't want an edit war". I'm not going to open a SPI between a single account and a single IP for obvious reasons but there certainly is some loud quaking. ''[[User:TarnishedPath|<b style="color:#ff0000;">Tar</b><b style="color:#ff7070;">nis</b><b style="color:#ffa0a0;">hed</b><b style="color:#420000;">Path</b>]]''<sup>[[User talk:TarnishedPath|<b style="color:#bd4004;">talk</b>]]</sup> 13:06, 12 May 2024 (UTC)<br />
*Indefinitely blocked.--[[User:Bbb23|Bbb23]] ([[User talk:Bbb23|talk]]) 13:31, 12 May 2024 (UTC)<br />
<br />
== [[User:Casteiswrong]] reported by [[User:Wikaviani]] (Result: ) ==<br />
<br />
'''Page:''' {{pagelinks|Snell's law}} <br /><br />
'''User being reported:''' {{userlinks|Casteiswrong}}<br />
<br />
'''Previous version reverted to:''' [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&oldid=1217236478]<br />
<br />
'''Diffs of the user's reverts:'''<br />
# [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223326135&oldid=1223300087]<br />
# [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=1223327866]<br />
# [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=prev&oldid=1223426994]<br />
# [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=1223427660]<br />
# [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=1223462235]<br />
<br />
<br />
<br />
<br />
'''Diff of edit warring / 3RR warning:''' [https://en.wikipedia.org/w/index.php?title=User_talk%3ACasteiswrong&diff=1223427185&oldid=1223419729]<br />
<br />
'''Diff of attempt to resolve dispute on article talk page:''' [https://en.wikipedia.org/w/index.php?title=Talk%3ASnell%27s_law&diff=1223427869&oldid=1223363220]<br />
<br />
'''Diff of ANEW notice posted to user's talk page:''' [https://en.wikipedia.org/w/index.php?title=User_talk%3ACasteiswrong&diff=1223471653&oldid=1223427278]<br />
<br />
<u>'''Comments:'''</u> <br /><br />
<br />
Reported user is actively edit-warring against several editors (includng me) to impose [[WP:OR|original research]] in the article and removes srongly sourced content that has been in the article for a quite long time. They have already been warned by an admin for edit warring and also by me, but they keep going on their disruptive path and made not less than 5 reverts within 24 hours.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 10:35, 12 May 2024 (UTC)<br />
<br />
Not fair, one user alone is charged with edit-warring while a team of editors with the same objective do not cumulatively break the same rule. This is a conflict between two scholars, Selin and Rashed, where the former is more objective while Rashed adds original research not even mentioned in the original manuscript translation. I am happy to remove all content and just stick the primary source, including my diagram derived from Selin's book and its translation. The readers will decide what to make out of it. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 13:40, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223467749Talk:Snell's law2024-05-12T09:41:59Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated and the manuscript had no conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)<br />
::If you look at the rest of the comment after his first line of observation, there are two massive errors as is common with these so-called medieval "mathematicians". Firstly, he discards the JH portion of the length of the incident ray (CH) without reducing the refracted ray (CE or CI) by the same percentage. Secondly, he sets; <math>\frac{longline(AK)}{shortline(AB)} = \frac{shortline(CI)}{longline(CJ)}<br />
\Rrightarrow longline^2 = shortline^2 <br />
\Rrightarrow long = short </math> <br />
::Essentially, he has no understanding of ratios with his math concluding that the lengths are equal, or no refraction had occurred, while his diagram proves otherwise. Looks like he was playing around with pencils and geometry. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 05:10, 12 May 2024 (UTC)<br />
:::@[[User:Casteiswrong|Casteiswrong]]Please see [[WP:OR]]. You can't add your own POV or challange the works of authors here. [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4|talk]]) 08:31, 12 May 2024 (UTC)<br />
::::Sorry, I should have been specific. My second reply is not in the book, and it is unrelated to my edit because it is clearly WP:OR. I was trying to open an entirely different discussion from the edit I had made because I was wondering if we should include this finding as well. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 09:30, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223467325Talk:Snell's law2024-05-12T09:36:21Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated and the manuscript had no conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)<br />
::If you look at the rest of the comment after his first line of observation, there are two massive errors as is common with these so-called medieval "mathematicians". Firstly, he discards the JH portion of the length of the incident ray (CH) without reducing the refracted ray (CE or CI) by the same percentage. Secondly, he sets; <math>\frac{longline(AK)}{shortline(AB)} = \frac{shortline(CI)}{longline(CJ)}<br />
\Rrightarrow longline^2 = shortline^2 <br />
\Rrightarrow long = short </math> <br />
::Essentially, he has no understanding of ratios with his math concluding that the lengths are equal, or no refraction had occurred, while his diagram proves otherwise. Looks like he was playing around with pencils and geometry. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 05:10, 12 May 2024 (UTC)<br />
:::@[[User:Casteiswrong|Casteiswrong]]Please see [[WP:OR]]. You can't add your own POV or challange the works of authors here. [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4|talk]]) 08:31, 12 May 2024 (UTC)<br />
::::Sorry, I should have been specific. My second reply is not in the book, and it is unrelated to my edit because it is clearly WP:OR. I was trying to open an entirely different discussion from the edit I had made. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 09:30, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223467057Snell's law2024-05-12T09:32:38Z<p>Casteiswrong: Put your sources on the talk page please. This is no place for an edit-war.</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref><br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. This means, although he doesn't say it, that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate any specific equation.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref>[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223466875Talk:Snell's law2024-05-12T09:30:06Z<p>Casteiswrong: /* Ibn Sahl's manuscript */ Reply</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated and the manuscript had no conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)<br />
::If you look at the rest of the comment after his first line of observation, there are two massive errors as is common with these so-called medieval "mathematicians". Firstly, he discards the JH portion of the length of the incident ray (CH) without reducing the refracted ray (CE or CI) by the same percentage. Secondly, he sets; <math>\frac{longline(AK)}{shortline(AB)} = \frac{shortline(CI)}{longline(CJ)}<br />
\Rrightarrow longline^2 = shortline^2 <br />
\Rrightarrow long = short </math> <br />
::Essentially, he has no understanding of ratios with his math concluding that the lengths are equal, or no refraction had occurred, while his diagram proves otherwise. Looks like he was playing around with pencils and geometry. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 05:10, 12 May 2024 (UTC)<br />
:::@[[User:Casteiswrong|Casteiswrong]]Please see [[WP:OR]]. You can't add your own POV or challange the works of authors here. [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4|talk]]) 08:31, 12 May 2024 (UTC)<br />
::::Sorry, I should have been specific. My second reply is not in the book, and it is unrelated to my edit because it is clearly WP:OR. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 09:30, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=User_talk:Gerard1453&diff=1223446712User talk:Gerard14532024-05-12T05:26:40Z<p>Casteiswrong: /* Ibn Sahl on refraction */ new section</p>
<hr />
<div>== Welcome ==<br />
<br />
<br />
{| width="100%" style="background:transparent"<br />
|style="width: 50%; border:1px solid <!-- Strange bug makes the number sign have to go in front of the parserfunction here-->#084080; background-color:<!-- Bug -->#F5FFFA; vertical-align:top"|<br />
{| width="100%" cellpadding="2" style="vertical-align:top; background-color:<!-- Bug -->#F5FFFA"<br />
| <div style="margin: 0; background-color:<br />
#CECEF2; font-family: sans-serif; border:1px solid <br />
#084080; text-align:left; color:black; padding-left:0.4em; padding-top: 0.2em; padding-bottom: 0.2em;"><p>Hello, Gerard1453, and '''[[Wikipedia:Welcoming committee/Welcome to Wikipedia|welcome to Wikipedia!]]'''</p><br />
<p>Thank you for [[Special:Contributions/Gerard1453|your contributions]] to this free encyclopedia. If you decide that you need help, check out ''Getting Help'' below, ask at the [[Wikipedia:Help desk|help desk]], or place '''{{Tlc|Help me}}''' on your talk page and ask your question there. Please remember to [[Wikipedia:Signatures|sign your name on talk pages]] by clicking [[File:Insert-signature.png|link=Wikipedia:How to sign your posts]] or [[File:Button sig.png|link=Wikipedia:How to sign your posts]] or by typing four tildes <nowiki>(~~~~)</nowiki>; this will automatically produce your username and the date. Also, please do your best to always fill in the [[m:Help:Edit summary|edit summary field]]. Below are some useful links to facilitate your involvement. Happy editing! [[User:Ninney|Ninney]] ([[User talk:Ninney|talk]]) 21:33, 10 August 2017 (UTC)</p></div><br />
|}<br />
{| width="100%" style="background-color:<!-- Bug -->#F5FFFA"<br />
|style="width: 50%; border:0; background-color:<!-- Bug -->#F5FFFA; vertical-align:top"|<br />
{| width="100%" cellpadding="2" style="vertical-align:top; background-color:<!-- Bug -->#F5FFFA;"<br />
|-<br />
! <div style="margin: 0; background-color:<br />
#084080; font-family: sans-serif; font-size:120%; font-weight:bold; border:1px solid <br />
#CEF2E0; text-align:left; color:<br />
#FFC000; padding-left:0.4em; padding-top: 0.2em; padding-bottom: 0.2em;">Getting started</div><br />
|-<br />
|style="color:#000"|<br />
* [[Wikipedia:Introduction|Introduction]]<br />
* [[Wikipedia:Contributing to Wikipedia|Contributing to Wikipedia]]<br />
* [[Wikipedia:Five pillars|The five pillars of Wikipedia]]<br />
* [[Help:Editing|How to edit a page]]<br />
* [[Help:Wikipedia: The Missing Manual/Introduction|Intuitive guide to Wikipedia]]<br />
|-<br />
! <div style="margin: 0; background:<br />
#084080; font-family: sans-serif; font-size:120%; font-weight:bold; border:1px solid <br />
#CEF2E0; text-align:left; color:<br />
#FFC000; padding-left:0.4em; padding-top: 0.2em; padding-bottom: 0.2em;">Finding your way around</div><br />
|-<br />
| style="color:#000"|<br />
* [[Portal:Contents|Table of contents]]<br />
* [[Wikipedia:Department directory|Department directory]]<br />
* [[Help:Directory|Help directory]]<br />
|-<br />
! <div style="margin: 0; background-color:<br />
#084080; font-family: sans-serif; font-size:120%; font-weight:bold; border:1px solid <br />
#CEF2E0; text-align:left; color:<br />
#FFC000; padding-left:0.4em; padding-top: 0.2em; padding-bottom: 0.2em;">Editing articles</div><br />
|-<br />
| style="color:#000"|<br />
* [[Wikipedia:Article development#How to develop an article|How to develop an article]]<br />
* [[Wikipedia:Simplified Manual of Style|Simplified Manual of Style]]<br />
|-<br />
|}<br />
|style="width: 50%; border:0; background-color:<!-- Bug -->#F5FFFA; vertical-align:top"|<br />
{| width="100%" cellpadding="2" style="vertical-align:top; background-color:<!-- Bug -->#F5FFFA"<br />
! <div style="margin: 0; background-color:<br />
#084080; font-family: sans-serif; font-size:120%; font-weight:bold; border:1px solid <br />
#CEF2E0; text-align:left; color:<br />
#FFC000; padding-left:0.4em; padding-top: 0.2em; padding-bottom: 0.2em;">Getting help</div><br />
|-<br />
|style="color:#000"|<br />
* [[Wikipedia:FAQ/Overview|Frequently asked questions]]<br />
* [[Help:Cheatsheet|Cheatsheet]]<br />
* [[WP:Teahouse|Our new user help forum, the Teahouse]]<br />
* [[Wikipedia:Questions|Where to ask a question]]<br />
* [[Help:Contents|Help pages]]<br />
* [[Wikipedia:New contributors' help page|New contributors' help page]]<br />
* [[Wikipedia:Article wizard|Article Wizard]] – a Wizard to help you create articles<br />
|-<br />
! <div style="margin: 0; background-color:<br />
#084080; font-family: sans-serif; font-size:120%; font-weight:bold; border:1px solid <br />
#CEF2E0; text-align:left; color:<br />
#FFC000; padding-left:0.4em; padding-top: 0.2em; padding-bottom: 0.2em;">How you can help</div><br />
|-<br />
|style="color:#000"|<br />
* [[Wikipedia:Community portal|Community Portal]]<br />
* [[WP:WikiProject|Join a WikiProject]]<br />
* Follow [[Wikipedia:Etiquette|Wikipedia etiquette]]<br />
* Practice [[Wikipedia:Civility|civility]]<br />
* [[Wikipedia:Wikipedia Signpost|Discover what's going on in the Wikimedia community]]<br />
|-<br />
|}<br />
|}<br />
|}<br />
==Important Notice==<br />
{{ivmbox | image = Commons-emblem-notice.svg |imagesize=50px | bg = #E5F8FF | text = This is a standard message to notify contributors about an administrative ruling in effect. ''It does '''not''' imply that there are any issues with your contributions to date.''<br />
<br />
You have shown interest in gender-related disputes or controversies or in people associated with them. Due to past disruption in this topic area, a more stringent set of rules called [[Wikipedia:Arbitration Committee/Discretionary sanctions|discretionary sanctions]] is in effect. Any administrator may impose [[Wikipedia:Arbitration Committee/Discretionary sanctions#Sanctions|sanctions]] on editors who do not strictly follow [[Wikipedia:List of policies|Wikipedia's policies]], or the [[Wikipedia:Arbitration Committee/Discretionary sanctions#Page restrictions|page-specific restrictions]], when making edits related to the topic.<br />
<br />
For additional information, please see the [[Wikipedia:Arbitration Committee/Discretionary sanctions#Guidance for editors|guidance on discretionary sanctions]] and the [[Wikipedia:Arbitration Committee|Arbitration Committee's]] decision [[Wikipedia:Arbitration/Requests/Case/Gender and sexuality|here]]. If you have any questions, or any doubts regarding what edits are appropriate, you are welcome to discuss them with me or any other editor.<br />
}}<!-- Derived from Template:Ds/alert --> ––[[User:FormalDude|<span style="color: #0151D2;font-size:100%">FormalDude </span>]] <span style="border-radius:7em;padding:1.75px 3.25px;background:#005bed;font-size:75%">[[User talk:FormalDude|<span style="color:#FFF">'''talk'''</span>]]</span> 14:50, 29 October 2021 (UTC)<br />
<br />
== Ibn Sahl on refraction ==<br />
<br />
I have got my hands on a translation from Ibn Sahl's manuscript, and it is utter nonsense. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 05:26, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223446577Talk:Snell's law2024-05-12T05:24:51Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated and the manuscript had no conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)<br />
::If you look at the rest of the comment after his first line of observation, there are two massive errors as is common with these so-called medieval "mathematicians". Firstly, he discards the JH portion of the length of the incident ray (CH) without reducing the refracted ray (CE or CI) by the same percentage. Secondly, he sets; <math>\frac{longline(AK)}{shortline(AB)} = \frac{shortline(CI)}{longline(CJ)}<br />
\Rrightarrow longline^2 = shortline^2 <br />
\Rrightarrow long = short </math> <br />
::Essentially, he has no understanding of ratios with his math concluding that the lengths are equal, or no refraction had occurred, while his diagram proves otherwise. Looks like he was playing around with pencils and geometry. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 05:10, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223446540Talk:Snell's law2024-05-12T05:24:25Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated and the manuscript had no conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)<br />
::If you look at the rest of the comment after his first line of observation, there are two massive errors as is common with these so-called medieval "mathematicians". Firstly, he discards the JH portion of the length of the incident ray (CH) without reducing the refracted ray (CE or CI) by the same percentage. Secondly, he sets; <math>\frac{longline(AK)}{shortline(AB)} = \frac{shortline(CI)}{longline(CJ)}<br />
\Rrightarrow longline^2 = shortline^2 <br />
\Rrightarrow long = short </math> <br />
Essentially, he has no understanding of ratios with his math concluding that the lengths are equal, or no refraction had occurred, while his diagram proves otherwise. Looks like he was playing around with pencils and geometry. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 05:10, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223446493Talk:Snell's law2024-05-12T05:23:47Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated and the manuscript had no conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)<br />
::If you look at the rest of the comment after his first line of observation, there are two massive errors as is common with these so-called medieval "mathematicians". Firstly, he discards the JH portion of the length of the incident ray (CH) without reducing the refracted ray (CE or CI) by the same percentage. Secondly, he sets; <math>\frac{longline(AK)}{shortline(AB)} = \frac{shortline(CI)}{longline(CJ)}<br />
::\Rrightarrow longline^2 = shortline^2 <br />
::\Rrightarrow long = short </math> <br />
::Essentially, he has no understanding of ratios with his math concluding that the lengths are equal, or no refraction had occurred, while his diagram proves otherwise. Looks like he was playing around with pencils and geometry. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 05:10, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223445621Talk:Snell's law2024-05-12T05:12:10Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated and the manuscript had no conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)<br />
::If you look at the rest of the comment after his first line of observation, there are two massive errors as is common with these so-called medieval "mathematicians". Firstly, he discards the JH portion of the length of the incident ray (CH) without reducing the refracted ray (CE or CI) by the same percentage. Secondly, he sets; <math>\frac{longline}{shortline} = \frac{shortline}{longline}<br />
::\Rrightarrow longline^2 = shortline^2 <br />
::\Rrightarrow long = short </math> <br />
::Essentially, he has no understanding of ratios with his math concluding that the lengths are equal, or no refraction had occurred, while his diagram proves otherwise. Looks like he was playing around with pencils and geometry. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 05:10, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223445491Talk:Snell's law2024-05-12T05:10:36Z<p>Casteiswrong: /* Ibn Sahl's manuscript */ Reply</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated and the manuscript had no conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)<br />
::If you look at the rest of the comment after his first line of observation, there are two massive errors as is common with these so-called medieval "mathematicians". Firstly, he discards the JH portion of the length of the incident ray (CH) without reducing the refracted ray (CE or CI) by the same percentage. Secondly, he sets; <math>\frac{longline}{shortline} = \frac{shortline}{longline}<br />
::\Rrightarrow longline^2 = shortline^2 <br />
::\Rrightarrow long = short </math> <br />
::Essentially, he has no understanding of ratios with his math concluding that the lengths are equal, or no refraction had occurred, while his diagram proves otherwise. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 05:10, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223431469Talk:Snell's law2024-05-12T02:32:51Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated and the manuscript had no conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223431394Talk:Snell's law2024-05-12T02:32:01Z<p>Casteiswrong: /* Ibn Sahl's manuscript */ Reply</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)<br />
<br />
:So what ? R. Rashed, a prominent expert of this topic credits Ibn Sahl with the discovery of this law and Selin does not denies that. This has been discussed several years ago, do not change again before reaching a consensus here, otherwise, you will be reported.<b><span style="color:orange">---Wikaviani </span></b><sup><small><b>[[User_talk:Wikaviani|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Wikaviani|<span style="color:black">(contribs)</span>]]</b></small></sup> 01:46, 12 May 2024 (UTC)<br />
::Selin says the ratio was postulated by Ibn Sahl but never calculated without a conceptual comment. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 02:32, 12 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223431137Snell's law2024-05-12T02:29:01Z<p>Casteiswrong: If you are not willing to come to the talk page, I will assume that's consensus achieved. The rule of consensus does not apply against POV pushers who have not even brought any recent tertiary sources to the table.</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref><br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. This means, although he doesn't say it, that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate any specific equation.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref>[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223426994Snell's law2024-05-12T01:40:53Z<p>Casteiswrong: Sorry tertiary source takes priority. There is a discussion open on the talk page if you want to participate</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref><br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. This means, although he doesn't say it, that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate any specific equation.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref>[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223365029Snell's law2024-05-11T16:54:09Z<p>Casteiswrong: /* History */</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref><br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. This means, although he doesn't say it, that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate any specific equation.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref>[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=User_talk:Hu741f4&diff=1223364236User talk:Hu741f42024-05-11T16:47:52Z<p>Casteiswrong: /* Snell's law */ new section</p>
<hr />
<div><br />
You have good friends up ur sleeve my brother, probs Hussein. Don't forget we have consensus in the parliament lol <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2405:6E00:B71:3000:81A1:CE20:EE4E:20C2|2405:6E00:B71:3000:81A1:CE20:EE4E:20C2]] ([[User talk:2405:6E00:B71:3000:81A1:CE20:EE4E:20C2#top|talk]]) 23:42, 1 November 2022 (UTC)</small> <!--Autosigned by SineBot--><br />
: What do you mean?<br />
[[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 14:09, 2 November 2022 (UTC)<br />
<br />
:Nice meeting you again old friend after a long time. I meant there is consensus amongst the general public about the etymology of the word "Sherwani" and since, the parliament is the peak representative body of the public, I used it instead. Thought you were smart enough to figure this out lol. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 07:33, 11 May 2024 (UTC)<br />
<br />
== Welcome! ==<br />
Hi Hu741f4! I noticed [[Special:Contributions/Hu741f4|your contributions]] and wanted to welcome you to the Wikipedia community. I hope you like it here and decide to stay.<br />
<br />
As you get started, you may find this short tutorial helpful:<br />
<br />
{{Clickable button 2|Help:Introduction|Learn more about editing|class=mw-ui-progressive|style=margin-left: 1.6em;}}<br />
<br />
Alternatively, the [[Wikipedia:Contributing to Wikipedia|contributing to Wikipedia]] page covers the same topics.<br />
<br />
If you have any questions, we have a friendly space where experienced editors can help you here:<br />
<br />
{{Clickable button 2|Wikipedia:Teahouse|Get help at the Teahouse|style=margin-left: 1.6em;}}<br />
<br />
If you are not sure where to help out, you can find a task here:<br />
<br />
{{Clickable button 2|Wikipedia:Task Center|Volunteer at the Task Center|style=margin-left: 1.6em;}}<br />
<br />
Happy editing! <!-- Template:Welcome--> [[User:I dream of horses|I dream of horses]] [[Special:Contribs/I dream of horses|(Contribs)]] [[User talk:I dream of horses|(Talk)]] 19:21, 30 July 2022 (UTC)<br />
<br />
Thank you! [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 19:23, 30 July 2022 (UTC)<br />
<br />
== October 2022 ==<br />
<br />
Per Wikipedia policity [[WP:BRD]] you should open a talk page thread on that page and garner a consensus as dictated. A new consensus takes time, usually several weeks. It is not a matter of simply posting your rationale and restoring that image. Best regards, [[User:Fowler&amp;fowler|<span style="color:#B8860B">Fowler&amp;fowler</span>]][[User talk:Fowler&amp;fowler|<span style="color:#708090">«Talk»</span>]] 22:13, 6 October 2022 (UTC)<br />
<br />
== Important ==<br />
<br />
{{ivmbox | image = Commons-emblem-notice.svg |imagesize=50px | bg = #E5F8FF | text = This is a standard message to notify contributors about an administrative ruling in effect. ''It does '''not''' imply that there are any issues with your contributions to date.''<br />
<br />
You have shown interest in '''[[India]], [[Pakistan]], and [[Afghanistan]].''' Due to past disruption in this topic area, a more stringent set of rules called [[Wikipedia:Arbitration Committee/Discretionary sanctions|discretionary sanctions]] is in effect. Any administrator may impose [[Wikipedia:Arbitration Committee/Discretionary sanctions#Sanctions|sanctions]] on editors who do not strictly follow [[Wikipedia:List of policies|Wikipedia's policies]], or the [[Wikipedia:Arbitration Committee/Discretionary sanctions#Page restrictions|page-specific restrictions]], when making edits related to the topic.<br />
<br />
To opt out of receiving messages like this one, place {{tlx|Ds/aware}} on your user talk page and specify in the template the topic areas that you would like to opt out of alerts about. For additional information, please see the [[Wikipedia:Arbitration Committee/Discretionary sanctions#Guidance for editors|guidance on discretionary sanctions]] and the [[Wikipedia:Arbitration Committee|Arbitration Committee's]] decision [[Wikipedia:Requests for arbitration/India-Pakistan|here]]. If you have any questions, or any doubts regarding what edits are appropriate, you are welcome to discuss them with me or any other editor.<br />
}}<!-- Derived from Template:Ds/alert --> [[User:Akshaypatill|Akshaypatill]] ([[User talk:Akshaypatill|talk]]) 08:09, 18 October 2022 (UTC)<br />
<br />
== Muhammad of Ghor ==<br />
<br />
I have reverted your last edit. The discussion is on the talk page. Please check the discussion. [[Talk:Muhammad_of_Ghor]] [[User:Akshaypatill|Akshaypatill]] ([[User talk:Akshaypatill|talk]]) 08:13, 18 October 2022 (UTC)<br />
<br />
Ok [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 08:29, 18 October 2022 (UTC)<br />
<br />
== WikiProject Medicine ==<br />
<br />
A [[WP:WikiProject]] is a group of editors who like to work together on articles. You're welcome to join us at [[Wikipedia:WikiProject Medicine]]. It's a good place to ask questions or to help each other out. If you'd like to, you're also welcome to join the informal, low-key contest about adding citations to articles: https://outreachdashboard.wmflabs.org/courses/Wikipedia/WikiProject_Medicine_reference_campaign_2023?enroll=qyoufwds (All you have to do is sign up at that link, and then edit normally. Everything else is automated.) [[User:WhatamIdoing|WhatamIdoing]] ([[User talk:WhatamIdoing|talk]]) 19:36, 15 February 2023 (UTC)<br />
<br />
== February 2023 ==<br />
<br />
{{{icon|[[File:Information orange.svg|25px|alt=Information icon]]}}} Please do not add your own point of view to Wikipedia articles, as you did to [[Mercury(II) chloride]]. Doing so violates Wikipedia's [[Wikipedia:Neutral point of view|neutral point of view policy]].<br />
<br />
I had already pointed out to you the second part of [https://en.wikipedia.org/w/index.php?title=Mercury(II)_chloride&diff=prev&oldid=1139912590 this] in our earlier interaction [https://en.wikipedia.org/w/index.php?title=Sulfuric_acid&diff=prev&oldid=1139181196 here]: there is only one Latin work attributed to [[Abu Bakr al-Razi|al-Razi]] scholars regard as partially authentic, which is the {{lang|la|Liber secretorum Bubacaris}}. If you had read that or Moureau 2020 p. 117 you would not have done [https://en.wikipedia.org/w/index.php?title=Mercury(II)_chloride&diff=prev&oldid=1139845572 this].<br />
<br />
Your continued editing with the clear [[WP:TE|tendency]] of attributing discoveries to Arabic-Islamic authors without reading up on the sources or by mispresenting them or by partially ignoring them (cf. [https://en.wikipedia.org/w/index.php?title=Sulfuric_acid&diff=prev&oldid=1139181196 what Needham actually says] vs what you made of that [https://en.wikipedia.org/w/index.php?title=Sulfuric_acid&diff=prev&oldid=1139117512 here], also completely ignoring [https://books.google.com/books?id=xrNDwP0pS8sC&pg=PA195 Needham's clear] {{grey|It is generally accepted that mineral acids were quite unknown both to the ancients in the West and to the Arabic alchemists}}) is getting to be disruptive.<br />
<br />
Please find another topic area which you have less strong personal views about and more appetite to read in full multiple recent sources. That would help us all at this point. <span style="text-shadow:#000 0em 0em 1em">☿&nbsp;[[User:Apaugasma|<span style="color:#6a0dad">Apaugasma</span>]] ([[User talk:Apaugasma|<span style="color:#000">talk</span>]]&nbsp;[[Special:Contributions/Apaugasma|☉]])</span> 14:54, 17 February 2023 (UTC)<br />
<br />
::: Please read Wikipedia policy regarding Original research [[WP:OR]]. The source cited doesn't mention that it is Falsely attributed to al-Razi. Other editors also disagree with you. https://en.m.wikipedia.org/wiki/Special:MobileDiff/1139913867 [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 15:08, 17 February 2023 (UTC)<br />
::::I gave a long quote from the source [[Talk:Mercury(II)_chloride#Attribution_of_De_aluminibus_et_salibus_to_al-Razi|on talk]] showing that scholars view it as [[pseudepigrapha|pseudepigraphical]]. The other editor can be excused for having been ignorant of this when they reverted, but you should have already known about what I quoted ''before'' you reverted, because I had already pointed it out to you. You clearly have no interest in reading sources in full and in representing what they are saying in a neutral way. This is, by itself, disruptive –even if you don't mean it that way. Please reconsider. <span style="text-shadow:#000 0em 0em 1em">☿&nbsp;[[User:Apaugasma|<span style="color:#6a0dad">Apaugasma</span>]] ([[User talk:Apaugasma|<span style="color:#000">talk</span>]]&nbsp;[[Special:Contributions/Apaugasma|☉]])</span> 15:16, 17 February 2023 (UTC)<br />
:::::Both are falsely attributed but you are specifically using falsely only for al-Razi and not for Hermes implying that it was indeed a work of Hermes[[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 15:25, 17 February 2023 (UTC)<br />
::::::Attributions to legendary figures like [[Hermes Trismegistus]] (see also: ''[[Hermetica]]'') are self-evidently false, which is why scholars do not dwell upon this.<br />
::::::The attribution of the ''De aluminibus et salibus'' to [[Abu Bakr al-Razi|al-Razi]], on the other hand, could be of crucial historical importance if authentic, and that is why scholars do write about this at some length (see, e.g., Ferrarrio 2009 pp. 42–43, and the older sources he cites which also discuss this question). In an actual article about the book, we would have an entire section devoted to the traditional attribution to al-Razi, while the attribution to Hermes would only be mentioned in the passing.<br />
::::::Because scholars pay more attention to the attribution to al-Razi and because recent experts explicitly argue that it is untenable, this deserves to be mentioned whenever we mention both the ''De aluminibus et salibus'' and al-Razi.<br />
::::::But my point here on your user talk is that ''you'' could have known all this if you just had read the sources with a neutral and inquisitive mind. By forcing me to explain all of this to you, you are wasting an enormous amount of my time, as well as of other Wikipedia editors like the patroller who reverted my edit on [[Mercury(II) chloride]] and then had to restore it after discussion on talk [https://en.wikipedia.org/w/index.php?title=Mercury(II)_chloride&diff=prev&oldid=1139913867][https://en.wikipedia.org/w/index.php?title=Mercury(II)_chloride&diff=next&oldid=1139913867].<br />
::::::This cannot continue like this, and I would like you to reflect upon that. Thanks, <span style="text-shadow:#000 0em 0em 1em">☿&nbsp;[[User:Apaugasma|<span style="color:#6a0dad">Apaugasma</span>]] ([[User talk:Apaugasma|<span style="color:#000">talk</span>]]&nbsp;[[Special:Contributions/Apaugasma|☉]])</span> 15:57, 17 February 2023 (UTC)<br />
<br />
== October 2023 ==<br />
<br />
[[File:Stop hand nuvola.svg|30px|left|alt=Stop icon]] Your recent editing history at [[:List_of_Muslim_Nobel_laureates]] shows that you are currently engaged in an [[Wikipedia:Edit warring|edit war]]; that means that you are repeatedly changing content back to how you think it should be, when you have seen that other editors disagree. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the [[Wikipedia:Talk page guidelines|talk page]] to work toward making a version that represents [[Wikipedia:Consensus|consensus]] among editors. The best practice at this stage is to discuss, not edit-war; read about [[WP:EPTALK|how this is done]]. If discussions reach an impasse, you can then post a request for help at a relevant [[Wikipedia:Noticeboards|noticeboard]] or seek [[Wikipedia:Dispute resolution|dispute resolution]]. In some cases, you may wish to request temporary [[Wikipedia:Protection policy|page protection]]. <br />
<br />
'''Being involved in an edit war can result in you being [[Wikipedia:Blocking policy|blocked from editing]]'''&mdash;especially if you violate the [[Wikipedia:Edit warring#The three-revert rule|three-revert rule]], which states that an editor must not perform more than three [[Help:Reverting|reverts]] on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring&mdash;'''even if you do not violate the three-revert rule'''&mdash;should your behavior indicate that you intend to continue reverting repeatedly.<!-- Template:uw-3rr --> – [[User:Dudhhr|dudhhr]]<small><sup>&nbsp;[[User talk:Dudhhr|talk]]</sup><sub>[[Special:Contribs/Dudhhr|contribs]]</sub><sup>she</sup><sub>her</sub></small> 18:42, 5 October 2023 (UTC)<br />
<br />
:I am cooperating The ip user has violated the the warning by reverting the edit recently after you warned the user. https://en.m.wikipedia.org/wiki/Special:MobileDiff/1178763465<br />
:Please revert his edit and ask him discuss it on talk page first [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 18:48, 5 October 2023 (UTC)<br />
<br />
== ArbCom 2023 Elections voter message ==<br />
<br />
<div class="ivmbox " style="margin-bottom: 1em; border: 1px solid #AAA; background-color: ivory; padding: 0.5em; display: flex; align-items: center; "><br />
<div class="ivmbox-image" style="padding-left:1px; padding-right:0.5em; flex: 1 0 40px; max-width: 100px">[[File:Scale of justice 2.svg|40px]]</div><br />
<div class="ivmbox-text"><br />
Hello! Voting in the '''[[WP:ACE2023|2023 Arbitration Committee elections]]''' is now open until 23:59 (UTC) on {{#time:l, j F Y|{{Arbitration Committee candidate/data|2023|end}}-1 day}}. All '''[[Wikipedia:Arbitration Committee Elections December 2023#Election timeline|eligible users]]''' are allowed to vote. Users with alternate accounts may only vote once.<br />
<br />
The [[WP:ARBCOM|Arbitration Committee]] is the panel of editors responsible for conducting the [[Wikipedia:Arbitration|Wikipedia arbitration process]]. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose [[WP:BAN|site bans]], [[WP:TBAN|topic bans]], editing restrictions, and other measures needed to maintain our editing environment. The [[Wikipedia:Arbitration/Policy|arbitration policy]] describes the Committee's roles and responsibilities in greater detail.<br />
<br />
If you wish to participate in the 2023 election, please review [[Wikipedia:Arbitration Committee Elections December 2023/Candidates|the candidates]] and submit your choices on the '''[[Special:SecurePoll/vote/{{Arbitration Committee candidate/data|2023|poll}}|voting page]]'''. If you no longer wish to receive these messages, you may add {{tlx|NoACEMM}} to your user talk page. <small>[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|talk]]) 00:55, 28 November 2023 (UTC)</small><br />
<br />
</div><br />
</div><br />
<!-- Message sent by User:Illusion Flame@enwiki using the list at https://en.wikipedia.org/w/index.php?title=Wikipedia:Arbitration_Committee_Elections_December_2023/Coordination/MM/08&oldid=1187132475 --><br />
<br />
== Snell's law ==<br />
<br />
Hi, I have removed your content and opened a discussion on the talk page. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:47, 11 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223363220Talk:Snell's law2024-05-11T16:39:10Z<p>Casteiswrong: /* Ibn Sahl's manuscript */ new section</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl's study on refraction.jpg|border|200px|]]<br />
[[File:Ibn Sahl manuscript.jpg|border|231px]]<br />
<br />
'''Translation''': The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326}}</ref> [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 16:39, 11 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223359674Snell's law2024-05-11T16:11:34Z<p>Casteiswrong: /* History */</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref><br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. This means, although he doesn't say it, that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate any specific equation using angles and sine functions.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref>[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223347592Talk:Snell's law2024-05-11T14:32:40Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223347498Talk:Snell's law2024-05-11T14:32:03Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|Translation: The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223347452Talk:Snell's law2024-05-11T14:31:44Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn Sahl manuscript.jpg|frameless|Translation: The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223340627Talk:Snell's law2024-05-11T13:36:49Z<p>Casteiswrong: /* Ibn Sahl's manuscript */</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn-sahl-manuscript-J3M6J2.jpg|thumb|Translation: The straight line CE (refracted ray) is therefore smaller than CH (incident ray). We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.]] [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 13:35, 11 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Snell%27s_law&diff=1223340416Talk:Snell's law2024-05-11T13:35:02Z<p>Casteiswrong: /* Ibn Sahl's manuscript */ new section</p>
<hr />
<div>{{Talk header}}<br />
{{WikiProject banner shell|class=B|vital=yes|1=<br />
{{WikiProject Physics|importance=High}}<br />
{{WikiProject Scuba diving |importance=Low}}<br />
}}<br />
<br />
==Old thread==<br />
Consistency problem: <br />
<br />
In the top explanatory figure '''n2>n1''' is explicitly stated.<br />
In section "Total internal reflection and critical angle", however, the following must hold true (see also the corresponding figure): '''n1>n2'''. As in the text there is no indication of this inversion, this leads to confusion. We should either make the relationship consistent throughout, or use different names for the refractive indices in the different examples.<br />
<br />
[[Special:Contributions/145.64.134.221|145.64.134.221]] ([[User talk:145.64.134.221|talk]]) 11:53, 1 October 2009 (UTC)<br />
<br />
-----<br />
<br />
It would be nice to spell Snel's name correctly (i.e., with a single "l").<br />
His name is "Snel" in his native language, or "Snellius" in Latin. The common spelling "Snell" is a solecism committed by people who know neither Dutch nor Latin.<br />
<br />
Perhaps it would also be wise to point out that Snel was not the *original* discoverer; the law was first found by Thomas Harriot, about 1600 -- two decades before Snel's work.<br />
<br />
I have some information about this at<br />
<br />
http://mintaka.sdsu.edu/GF/explain/optics/discovery.html<br />
<br />
----<br />
<br />
An experimental paragraph added. See a short article by Kwan, Dudley and Lantz about this in Physics World in 2003 or 2002. This article says that Thomas Harriot (Hariot may be his preferred spelling) was actually not the first.<br />
*I've improved the history section with information from that article, and incorporated the references in it. Hope that's clearer. I'm not sure what to do with the external link, which contradicts those articles (says Harriot was first). -- [[User:DrBob|Bob Mellish]] 17:36, 30 September 2005 (UTC)<br />
<br />
Snell may be a solecism, but it's English, and it's the English name of the law, even if not how the man wrote his own name. Given how fluid spelling could be in the 17th century, it could be that Snell spelt his name in several different ways. Can someone check this?<br />
<br />
== Image wrong? ==<br />
<br />
The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, <math>\theta_1</math> and <math>\theta_2</math> are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [http://scienceworld.wolfram.com/physics/SnellsLaw.html] for how the image should be corrected.<br />
<br />
The image is misleading and confusing, and should be rectified as soon as possible; however, as I lack experience with graphics, I request someone to upload a corrected version as soon as possible.<br />
<br />
*Um, no. The image is correct, and correctly labelled. The image in the article has the two media on the left and right sides of the diagram; the interface runs vertically. The image at Scienceworld has the two media at the top and bottom of their diagram; their interface runs horizontally. Try rotating one of the diagrams by 90&deg;, and you'll see how they match. -- [[User:DrBob|Bob Mellish]] 18:25, 26 September 2005 (UTC)<br />
<br />
==Snell's law spelling ==<br />
<br />
I agree it is Snel and not Snell's law. Also in English. The 'discoverer' (not getting in the historical issue here, just the spelling bit) of the quantitative law of refraction was 'Willebrord Snel van Royen', thus one l, and there is no fluidity to this spelling as far as I know. The two-l-spelling has nothing to do with 'Snel' spelled differently in the English language but with incorrect de-latinazation of Snellius.<br />
<br />
:FWIW, in the Netherlands, up to the present, the person has always been known as Snellius, not Snel. I think, most Dutchmen who have heard about him would be surprised to learn that he wasn't born as Snellius. [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 05:29, 11 July 2007 (UTC)<br />
<br />
:Also FWIW, the Dutch encyclopedia [[Winkler Prins]], under "Snellius", shows "Snell van Royen" as the original family name - with two l's. Finally, with Snellius goes "Willebrordus", not "Willebrord." This is all you're going to get from me on the name of Snellius! [[User:Iterator12n|Iterator12n]] <span style="color: Blue;"><span style="font-size: 0.8em;"><sup>[[User Talk:Iterator12n|<span style="color: Blue;">Talk</span>]] </sup></span></span> 20:07, 14 July 2007 (UTC)<br />
<br />
His name was Willebrod Snel van Royen. The sine law carries his name which is snel and not snell. As mentioned above the double l is due to incorrect de-latinazation.<br />
<br />
== Other formulae ==<br />
<br />
I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...<br /><br />
<br />
<math>\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}</math><br /><br /> to...<br />
<math>\lambda_1 sin\theta_1 = \lambda_2 sin\theta_2</math><br /><br />
<br />
[[User:JSpudeman|James S]] 00:12, 11 December 2006 (UTC)<br />
<br />
:Those ratios of velocities, wavelengths, indices of refraction, etc. are fine, but they are not Snell's law. Snell's law needs to have the sines of the angles in it. We seem to have forgotten to state the law near the top of the article anywhere. I'm working on it... [[User:Dicklyon|Dicklyon]] 20:04, 22 December 2006 (UTC)<br />
:OK, I fixed the lead, putting the law equation and illustration into it; and I added a book page of history. I don't really understand the point of what someone was trying to do with these relations in the Explanation section, so I'll leave it for now. But as I said, without the angles, or some measurement proportional to their sines, it's not Snell's law. [[User:Dicklyon|Dicklyon]] 20:40, 22 December 2006 (UTC)<br />
<br />
==Merge from Angle of refraction?==<br />
<br />
I propose to merge [[Angle of refraction]] into Snell's law, since it covers exactly the same material. Please support, oppose, or otherwise comment here. [[User:Dicklyon|Dicklyon]] 08:36, 23 December 2006 (UTC)<br />
:'''support''' [[User:The Photon|The Photon]] 03:46, 24 December 2006 (UTC)<br />
:Expecting no objection, I went ahead and incorporated a few bits from there that we didn't have here, and converted it to a redirect. [[User:Dicklyon|Dicklyon]] 05:30, 24 December 2006 (UTC)<br />
<br />
==Reverting JCraw's extensive uncommented changes==<br />
<br />
JCRaw, that's a lot of changes to do all at once without even any change comments. You've de-linked the references from what they refer to, and made them into a very hard-to-maintain form (because the numbers don't track automatically). And you've introduced non-words (e.g. ''constance'') and grammatical errors into the lead. I haven't reviewed most of the changes yet, but on these bases alone I'm going to revert, and we can make the changes you want more slowly and carefully, giving other editors a chance to collaborate on them, please. [[User:Dicklyon|Dicklyon]] 17:00, 4 January 2007 (UTC)<br />
<br />
JSpudeman, the way you've put it back is really no better. You still have the hard-to-maintain ref style, grammatical errors in the lead, and unclear what point you're trying to make there. The statement about "it's [sic] original form" is probably wrong, since the constant ratio of sines was articulated before velocities or indices of refraction were known. [[User:Dicklyon|Dicklyon]] 23:24, 4 January 2007 (UTC)<br />
<br />
Point noted; i know of the application Fermat's principle to Snell's Law, but i was unaware of the history linking them together. However -- what was the original formula that was used before the inclusion of least-time? It would be interesting to know how the original formula was developed. On that note, do you own that book? I presume that from your reference to it's contents that you do? If so, why not reference it? [[User:JSpudeman|James S]] 23:23, 7 January 2007 (UTC)<br />
<br />
::Which book are you referring to? I have Huygens. The others I mostly just find on books.google.com. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:<br />
<br />
:''In optics and physics, Snell's law (also known as Descartes' Law or the law of refraction) is a formula that relates the angles where a ray of light crosses a boundary between different media, such as air and glass.''<br />
<br />
Although it's fine, it doesn't quite explain the reason for the relation of the angles, or what is being related other than "angles" (i.e incidence/refraction). <br />
<br />
::The law was determined before a reason for it could be found, if by reason you mean the underlying physical basis. When Descartes and Fermat articulated the law as being based on a "principle of least time," they still didn't have an underlying physical reason to explain that principle. Huygens explained it with his wave theory, but it took another 120 years and rediscovery of that approach for that reason to begin to be accepted. In the mean time, Snell's law served geometric optics admirably, even without any "reason" behind it. So, I think the reason can come later, or can remain divorced from the law. In fact, all that's being related is angles. The law just says the ratio of sines is constant, just like [[Ibn Sahl]] said with a geometric relationship in his construction. [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
Similarly, i was just taking a glance at the [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=96133490&oldid=95512206 edit history] and noticed that apart from a slight change in grammar, some of the explanations were removed. Again, i'm staying well away from this one, but i'm wondering why that is exactly. Although practically the same information is there, it makes it more difficult for those who are reading the article as an impartial/non-informed user, i think, to [[Wikipedia:Manual_of_Style#Big.2C_little.2C_long.2C_short|pick up on the article]]. <br />
<br />
::The explanations that ended up in footnotes are removed until someone takes the time to incorporate them better. The "ref" mechanism was already in use, keeping a list of numbered refs in sync with numbers in the text, when it was taken over to use for footnotes instead, leaving the numbered references with no automatic way to stay synchronized. That's why I reverted it. If there's stuff in there that was useful, why not help incorporate it? [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) [[User:JSpudeman|James S]] 23:36, 7 January 2007 (UTC)<br />
<br />
::Not if you don't hijack the "ref" mechansim again ;^} [[User:Dicklyon|Dicklyon]] 01:14, 8 January 2007 (UTC)<br />
<br />
::'''JCraw''', I looked over your notes again, and I'm having trouble getting the point of them, or why you added them. It looks like you have a couple of useful references with derivations and applications, but what you said about them in the footnotes was difficult to understand. Please join the discussion here to tell us what issue you are trying to address. [[User:Dicklyon|Dicklyon]] 06:51, 8 January 2007 (UTC)<br />
<br />
Where did the idea that it was ever known as "Descartes's Law" come from? I have never heard of it under that name. Out of 5 different books on E&M/Optics(Frankel, Feynmann, Jackson, Ditchburn, Stratton) handy for me to check, not '''one''' uses this term.<br />
<br />
It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.<br />
<br />
On a side note: "optics and physics" is redundant, since optics by definition is a branch of physics. Slighly more informative would have been "optics and wave theory", since that makes it clearer that Snell's Law applies to radio waves as well. But it would have made even more sense (following Jackson's hints) to rephrase the whole sentence as:<br />
<br />
:''In optics and wave theory, Snell's law (also known as Descartes' Law or the law of refraction) is a kinematical formula that relates the angle of incidence and that of refraction where a ray of light crosses a boundary between transparent media with differing optical characteristics, such as air and glass.''<br />
<br />
[[Special:Contributions/68.166.188.143|68.166.188.143]] ([[User talk:68.166.188.143|talk]]) <small>—Preceding [[Wikipedia:Signatures|undated]] comment was added at 18:39, 1 September 2008 (UTC)</small><!--Template:Undated--> <!--Autosigned by SineBot--><br />
<br />
==The original form of the law==<br />
<br />
Here's [http://books.google.com/books?vid=OCLC13466184&id=ZwIAAAAAQAAJ&pg=RA4-PA295&lpg=RA4-PA295&dq=snell+sines+ratio+date:0-1820#PRA4-PA295,M1 an 1803 book] that explains that Snel did the same thing that [[Ibn Sahl]] had done. Nowhere does the velocity of propagation or the index of refraction enter into his observation that the ratio of sines is a constant for a given pair of media. Later, when it was realized that light speed varies in different media, it was realized that the law of sines was in agreement with a principle of least time, or [[Fermat's principle]]; that's where velocity and index started to come into the equation, via their ratio. Let's not get the cart before the horse on this. [[User:Dicklyon|Dicklyon]] 01:42, 5 January 2007 (UTC)<br />
<br />
:This 1803 book nowhere mentions Ibn Sahl. It does discuss though, p. 295, that Snellius conducted ''"a series of numerous and delicate experiments."''. Roshdi Rashed in his discussion of Ibn Sahl's work nowhere mentions ''any'' experiment conducted - he simply ''relabels'' the sin/sin-ratio. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:51, 24 October 2017 (UTC)<br />
<br />
== Applicability to sound waves ==<br />
Snell's law is not just limited to propagation of light but can also be used to explain the propagation of sound waves across different medium where the speed of sound changes. The article fails to mention this. <br />
I think this law can be used for explaining other kind of wave propagation too, though I am not sure. But at least we sound waves should be mentioned in the introduction of the article. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 05:50, 16 April 2007 (UTC)<br />
<br />
:It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? [[User:Dicklyon|Dicklyon]] 06:05, 16 April 2007 (UTC)<br />
<br />
:: I agree, but the article focuses heavily on propagation of light waves and the importance is not evident in relation to other kinds of waves. A reader not aware of the applicability of the law in other cases, won't realize it easily. -- [[User:Mythealias|Myth]] ([[User talk:Mythealias|Talk]]) 06:21, 16 April 2007 (UTC)<br />
<br />
::: That's because light is the usual application. Sound diffracts so much that Snell's law is seldom a useful approximation to sound wave behavior. If you have other applications, or relevant sources, please do bring them up. [[User:Dicklyon|Dicklyon]] 14:58, 16 April 2007 (UTC)<br />
<br />
:::: Snell's law is very important in the study of underwater sound. See, for example: Robert J. Urick, "Principles of Underwater Sound (2nd edition)." New York: McGraw-Hill, 1975, p.116. [[User:Ephesians 2:10|Ephesians 2:10]] ([[User talk:Ephesians 2:10|talk]]) 23:10, 8 September 2009 (UTC)<br />
<br />
<br />
==How to reach consensus==<br />
<br />
See [[WP:BRD]]. If you make a change (e.g. adding "by scientists") and someone reverts it, bring it up on the talk page if you care; don't just make it again. [[User:Dicklyon|Dicklyon]] 05:26, 1 August 2007 (UTC)<br />
<br />
== Proposal to rotate the image ==<br />
<br />
[[Image:Snells law.svg|right|thumb|250px]]<br />
[[Image:Snells law2.svg|right|thumb]]<br />
The image on the right ([[:Image:Snells law.svg]]) is quite nice, but I think in the literature the interface between media is usually horizontal (like between air and water). I have rotated the image, see [[:Image:Snells law2.svg]] (also on the lower right). I propose to replace the original with this rotated version. Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 00:58, 25 December 2007 (UTC)<br />
:In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 01:59, 25 December 2007 (UTC)<br />
:: Done. Rotated, the image shows the details better while taking less real estate. [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:54, 1 January 2008 (UTC)<br />
<br />
== Explanation for section removal ==<br />
<br />
I [http://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=183335661&oldid=183335577 removed] a section from the article, for the following reasons:<br />
# The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram<br />
# Then name of the section is misleading, that section is not about calculating refractive indeces<br />
# The analogy with the car going from highway to the mud causing it to change angle is I think misleading, it is not as if a ray is a pair of parallel waves and one of them reaches the seconc medium first and forces the second wave to turn. Besides, is mud denser than asphalt?<br />
Comments? [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 04:34, 10 January 2008 (UTC)<br />
<br />
== Formula confusion ==<br />
<br />
I'm confused about the formula. If the angle of incidence is 0, then how does the formula work? Or does it not work for maxima and minima of the sine wave? [[User:Styrofoam1994|<strong><span style="color: DarkBlue; font-family: Times New Roman;">STYROFOAM☭1994</span></strong>]][[User talk:Styrofoam1994|<sup><span style="color: black;">TALK</span></sup>]] 22:58, 29 January 2008 (UTC)<br />
<br />
:The equation <math>n_1\sin\theta_1 = n_2\sin\theta_2</math> is satisfied with &theta;<sub>1</sub> = 0 and &theta;<sub>2</sub> = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:09, 30 January 2008 (UTC)<br />
<br />
== Vector Form Inconsistency ==<br />
<br />
The "vector form" example calculates cos(theta_1) incorrectly. The dot product of -l and n is clearly positive, but the example shows that the result is negative. When I calculate the reflected angle, I only get the correct answer if I define cos(theta_1) as the dot product of l and n (instead of -l and n).<br />
<br />
The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/71.235.123.252|71.235.123.252]] ([[User talk:71.235.123.252|talk]]) 03:03, 30 January 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot--><br />
<br />
<br />
<br />
I had difficulty with this formula in 3D vector mode:<br />
<br />
Note: <math>\mathbf{n}\cdot(-\mathbf{l})</math> must be positive. Otherwise, use<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.</math><br />
<br />
I got results to agree with Breault ASAP raytrace results by modifying the first formula:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}</math><br />
<br />
to the more general:<br />
:<math>\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}</math><br />
<br />
This worked for both cases.<br />
<br />
[[User:Palmeroo|Palmeroo]] ([[User talk:Palmeroo|talk]]) 17:34, 28 February 2008 (UTC)<br />
<br />
Are there any reasons why this hasn't been corrected?<br />
<br />
Anyway, I've updated it, so please check if it is correct now.<br />
[[User:Anders Ytterström|Anders Ytterström]] ([[User talk:Anders Ytterström|talk]]) 20:26, 2 May 2008 (UTC)<br />
<br />
<br />
Is the formula still wrong? it disagrees with this webpage:<br />
http://www.nationmaster.com/encyclopedia/Snell's-law<br />
and it doesnt even make sense... how can refraction depend on the position of the light? It has nothing to do with lighting... Someone has to fix this.<br />
[[Special:Contributions/128.100.32.72|128.100.32.72]] ([[User talk:128.100.32.72|talk]]) 00:19, 30 November 2008 (UTC)<br />
<br />
:That web page is just an old copy of this article. If there's an actual source that disagrees, that would be more interesting. The light vector is just the direction of travel of a light ray to be analyzed; don't think of its source as a lighting source, just where a ray is coming from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 00:58, 30 November 2008 (UTC)<br />
<br />
Does anyone know why Ibuwan edited the second formula for v_refract on Feb 14, 2012? I believe this to be wrong; the formula worked before, (with two additions) and is broken now (with two subtractions).<br />
(171.66.163.219)<br />
<br />
:I changed the formula for a better understanding for symmetry. it used to read <math>+ \left(-A + B\right)</math> and i changed it to<math>- \left(A - B\right)</math>so both are actually equal. It would be interesting to see it work with only two additions, because i carefully verified my result. (not for this article, but for my work) so please feel free to correct if im wrong. [[User:Ibuwan|Ibuwan]] ([[User talk:Ibuwan|talk]]) 01:37, 8 May 2012 (UTC)<br />
<br />
== Metamaterials? ==<br />
<br />
Um, Snell's law has been disproven/broken/shattered for the better part of a year now... when is this article going to be updated to reflect that? Light can be bent at left angles using [[metamaterials]], and the light traveling "backwards" in a vacuum exceeds the "normal" limit of light speed (the only thing (other than [[tachyons]])) that travels faster than light is still light... just light traveling backwards). [[Special:Contributions/68.185.167.117|68.185.167.117]] ([[User talk:68.185.167.117|talk]]) 15:02, 26 November 2008 (UTC)<br />
<br />
:That work has not bothered Snell's law at all, but if you'd like to add a bit about it, citing a good source, that might be useful. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:44, 4 December 2008 (UTC)<br />
<br />
==Al Haythem, A.I.Sabra and the Sine Law of Refraction==<br />
<br />
I have removed a sentence from the main text in which it was claimed that Al Haythem had known the sine law of refraction and which gave A.I. Sabra's <i>Theories of Light From Descartes to Newton</i> as source for this claim. This is not true Al Haythem did not have knowledge of the sine law of refraction and this is clear from the following passage from Sabra(page97): <blockquote>Now let us suppose that Ibn al-Haythem moved one step further and assumed the increase... (there follow a series of mathematical deductions)... In other words the sines of the angles of incidence and refraction are in a constant ratio, which is the geometrical statement of the law of refraction .(...) He did not, however, take that step...</blockquote> Sabra then goes on to argue that this might have been the route taken by Descarte who knew Al Haythem's work in discorvering the law of refraction. What we have here is a hypothetical argument concerning the possible route of discovery taken by Descarte and not the claim that Al Haythem had discovered the law himself, which he had not.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:12, 4 December 2008 (UTC)<br />
<br />
==Snell's Law Obsolete?==<br />
<br />
This was from the [[Faster-Than-Light]] article: <blockquote>This is influenced by man-made metamaterials, which allow light to be bent backwards; the discovery of these shattered the now defunct Snell's Law, an old "law of physics".</blockquote><br />
<br />
Shouldn't something to that effect be added to this article, then? [[User:SineSwiper|SineSwiper]] ([[User talk:SineSwiper|talk]]) 01:52, 18 December 2008 (UTC)<br />
<br />
:Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. [[User:Stevenj|— Steven G. Johnson]] ([[User talk:Stevenj|talk]]) 04:41, 5 August 2009 (UTC)<br />
<br />
== Finding the speed of light ==<br />
<br />
I think the formula for finding the actual speed of light (<math>n=c/v</math>) should be added into the section. This is the only appropriate place on Wikipedia to put it on. However, I cannot find a reliable source to cite. If someone can find this, I think it will help a great many people. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:14, 3 January 2009 (UTC)<br />
<br />
I just found it on [[Refractive index]], but I think it should also be added here. [[User:Fireedud|Fireedud]] ([[User talk:Fireedud|talk]]) 18:21, 3 January 2009 (UTC)<br />
<br />
== "Today's Featured Picture" for 9/23/2009 incorrect !! ==<br />
<br />
The image, in the article at "Explanation#Derivations", is incorrect in the lower part, below the interface. It shows the wavefronts as becoming hyperbolic, so that the portions at large distances from the central axis asymptotically become straight lines. However, the refracted rays below the interface would then not appear to diverge from a point, and that is not the case in reality. The point source position is shifted (upwards, in the figure), but the light source seen from below the interface still appears as a point. These means the wavefronts must continue to diverge from a point, and thus remain segments of a sphere, with only the center of the sphere being shifted. The figure needs to be corrected by someone with a facility in graphics animation. A few other editors should verify and confirm my conclusion, but it is really quite obvious, and easily apparent visually so that it needs to be fixed quickly. Thanks, [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 15:53, 23 September 2009 (UTC)<br />
<br />
:I believe it is correct. The refracted rays will NOT appear to come from a point, as is well known; there will be spherical and chromatic aberrations, as is the case when putting a prism behind a lens that's designed to image through air. The rays far from the source will approach the critical angle. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:02, 23 September 2009 (UTC)<br />
<br />
:I'm going to have to disagree with you as well. According to Snell's Law, <math>\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin\theta_1\right)</math>. Note that n<sub>1</sub> (air) = 1 and n<sub>2</sub> (water) = 1.33 (and thus n<sub>2</sub>/n<sub>1</sub> = 0.75), and that <math>\sin\theta_1 = \sin\left(\arctan\frac{x}{h}\right)</math>, where ''x'' is the horizontal distance from the central axis and ''h'' is the height of the source over the water. For my purposes, I'll just say h=2 meters (the height and the units are arbitrary and unimportant). So we get that <math>\theta_2 = \arcsin\left(0.75\sin\left(\arctan\frac{x}{2}\right)\right)</math>. Due to some lovely trigonometry, <math>\theta_2</math> is not just the angle of refraction from vertical; it's also the angle of the underwater wave (which is perpendicular to the angles of refraction) from horizontal (i.e. the angle of inclination of the wave). So, we can plot <math>\theta_2</math>, as defined above, in [http://www.wolframalpha.com/input/?i=Plot%5bArcSin%5b0.75*Sin%5bArcTan%5bx%2F2%5d%5d%5d%2C+{x%2C+-20%2C+20}%5d WolframAlpha]. You'll see that <math>\theta_2</math> changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant <math>\theta_2</math> (angle of inclination) far from the central axis means (near-)straight line. That's what the image depicts, so I think the image is correct. Tell me if you think I made an error in my calculations and explanation; they were hastily done. -- '''[[User:Tariqabjotu|<span style="color: black;">tariq</span><span style="color: gray;">abjotu</span>]]''' 20:38, 23 September 2009 (UTC)<br />
<br />
::Your argument seems plausible to me at the moment, though I need to verify it when I have more time. The fact that objects under water appear sharp and unblurred led me to believe that the refraction of a plane surface does not affect the spherical character of the waveform of light from a point source, but I see now that the small-angles approximation may indeed account for this, and the existence of critical refraction supports your argument. Thanks for (probably) correcting me, and apologies for the false alarm. [[User:Wwheaton|Wwheaton]] ([[User talk:Wwheaton|talk]]) 14:25, 25 September 2009 (UTC)<br />
<br />
:::If you look at objects underwater, or embedded in glass or plastic, from an angle, they actually appear with significant blur and color fringing. See [http://www.google.com/patents?id=xi4SAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q=&f=false my patent] on how such aberrations can be approximately corrected, in the case of an optical system designed to focus in air being used through glass. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 03:46, 26 September 2009 (UTC)<br />
<br />
== Is it really a law? ==<br />
About 20 years ago, I remember being told in college that Snell's Law is not a law because<br />
# It can be derived (which has since made me wonder about the nature of laws)<br />
# It is an approximation<br />
If there's any truth to this, I think it would be good to include. (If there's wide misconception about this, I think it'd be even better to attend to it) Googling for '"snell's law" "not a law"' has been inconclusive. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 23:35, 13 June 2010 (UTC)<br />
<br />
:Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:25, 15 June 2010 (UTC)<br />
<br />
There is no categorical definition as to what constitutes a law in physics and Snell's Law is known as Snell's Law and that's that. As to your objections what has being derived got to do with it? All of the mathematical laws of physics are derived from raw empirical experimental data. Finally in what sense is Snell's Law an approximation? Please elucidate?[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 13:23, 15 June 2010 (UTC)<br />
<br />
::I can't. I haven't seen that teacher in 20 years. I don't even remember his name, which is fortunate, because he was a jackass. But he seemed to know what he was talking about. [[User:AngusCA|AngusCA]] ([[User talk:AngusCA|talk]]) 02:39, 16 June 2010 (UTC)<br />
Actually is a rule derived from Fermat principle.This principle does not explains underwater refraction if the point Q is at the bottom of the sea and sunlight cannot reach it.Be carefull about math:it is not a trick!You cannot put Q on a "ray" because O & Q define the ray!It is exactly the Q point whitch defines the ray. <small><span class="autosigned">([[User talk:El662009|talk]])10:28, 8 January 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Wolf's paper ==<br />
<br />
Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? [[User:Tkuvho|Tkuvho]] ([[User talk:Tkuvho|talk]]) 11:08, 3 June 2011 (UTC)<br />
<br />
== Second Picture is Incorrect ==<br />
<br />
The second picture in the article(the one that shows the incident, refracted and reflected wave) has an inaccuracy in the Refracted Wave. The inaccuracy occurs where the angle of reflection is labeled. I have already made an image that I believe contains more relevant information to the less informed and does not contain the inaccuracy in the only two angles that are relevant to Snell's Law and will be uploading it as the successor shortly. <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Chapin J|Chapin J]] ([[User talk:Chapin J|talk]] • [[Special:Contributions/Chapin J|contribs]]) 21:07, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
<br />
== Vector form ==<br />
<br />
Every few months, we get an uncommented edit or two to change a sign or two in the "Vector form" section. I tried to check the source but the relevant pages aren't showing up in gbs. The ref came in in [https://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=next&oldid=275435983 this uncommented edit], which didn't change the equations, so I don't really know if the equations came from there, or were consistent with the ref at that time, or what. Someone should check, and put a comment in the wikisource about staying true to the ref. Or work it out and make sure it's right. Part of the problem is that the direction of the surface normal is not defined, so people may be trying it different ways. An appropriate figure would help. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:33, 26 January 2014 (UTC)<br />
<br />
I reworked the presentation considerably, making sure it is understandable and self-consistent. If someone has the source and wants to make sure I didn't say anything that it doesn't supprot, please let us know so we can adjust. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 19:35, 26 January 2014 (UTC)<br />
<br />
== Elaborate on Ibn Sahl's authorship of the law ==<br />
<br />
It is claimed in this article (and in the article on Ibn Sahl) that Ibn Sahl was the first to understand the law of refraction correctly, namely in the following way (text under image):<br />
<br />
[[File:Lommni zakon konstrukcija.svg|thumb|center|upright=2.5|'''Image 1''': For any given angle <math>\theta_\mathrm{i}</math> of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle <math>\theta_\mathrm{r}</math> with the surface normal) by keeping the ratio of the two hypothenuses <math>b/a</math> constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index <math>n_\mathrm{rel} = n_\mathrm{i}/n_\mathrm{r}</math> .]]<br />
<br />
[[File:Ibn Sahl manuscript.jpg|thumb|upright=1|'''Image 2:''' An excerpt from Ibn Sahl's manuscript]]<br />
<br />
I am not convinced by the material I have found on the internet so far. Here are a few reasons:<br />
# '''The articles on Wikipedia provide insufficient justification.''' Image 2 is presented in each of them, yet no translation of the surrounding arabic text is given. It seems very important to me, what the text is about. If the text is explaining the construction of a refracted ray on the plano-convex lens in the sketch (lower right) with the aid of the two right triangles (upper left), then that is concrete evidence of Sahl's understanding of the law. However, if he is talking about something unrelated (if the two right triangles have no corelation with refraction), then that is quite a substantial reason to doubt his understanding. If the person who posted this image to support the claim of Sahl's authorship knew of the meaning of the text and did not provide a translation because it has no relation to refraction, I would consider that very dishonest.<br />
# '''There is only one article containing original research on the subject and it is hard to come by.''' That is the article by Roshdi Rashed, ''A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses'', a free version of which I have not been able to find. All of the other cited references (and all literature I have been able to find) do not provide any justification for Sahl's authorship. They simply assume it, citing Rashed's article. If somebody has a full english version of Rashed's article, please give me a link. It's the only reason I'm still on the fence about this and haven't completely dismissed the claim.<br />
# [[File:Rekons1.svg|thumb|300px|'''Step 0:''' I have renamed the points with Latin letters so it's easier for me to reference them. I have also colored the plano-convex lens gray.]] '''On image 2, I see no construction of the refracted ray on the plano-convex lens itself.''' I would expect Ibn Sahl to use the two right triangles as an aid in constructing the refracted ray. Perhaps he did and it's just not immediately evident from the sketch, let's investigate. It's claimed that one of the notches on the optical axis is supposed to be the focal point. Quote from the article about Ibn Sahl: "''The curvature of the convex part of the lens brings all rays parallel to the horizontal axis (and approaching the lens from the right) to a focal point on the axis at the left.''" The lens is a thick spherical lens and so does not have a well defined focal point, but let's not hold this against the explanation. Let's instead assume that one of the notches on the optical axis is where the parallel ray from the right, refracted at the point marked on the upper right part of the lens' surface intersects the optical axis. I have tried reconstructing the refracted ray using vector graphics (Inkscape). Here's what I did:<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons2.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' I have tried fitting a yellow semicircle to the semicircle going through points A, B and F as a test. This is the best fit I could achieve. It's not great, also the center is in point N, which is not marked on the original picture. Could be that the aspect ratio of the original is off. Let's forget about this for now.<br />
<!--image 2--><br />
| image2 = Rekons3.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' We'll try to construct a refracted ray through point R following instructions from image 1. First, we need to find the surface normal in R. For this we fit a red circle to the semicircle going through A, P, B. The best fit is achieved with the center in M (not marked on the original). Clearly, the line MP is now the surface normal of the imaginary right half of the lens in P and thus also of the real lens in R.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 300 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = Rekons4.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' We now take the blue line XY, rotate it (preserving length) and fit it through M and O, so that one end is in M. We mark the other end with L. Now we need to move the green line XZ with one end in L and fit the other end to the red surface normal MP we found in the previous step. This gives us the direction of the refracted ray LN.<br />
<!--image 2--><br />
| image2 = Rekons5.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' Finally, we draw a line parallel to LN through R (our refracted ray). We also draw a blue incoming ray through R. As we can see, the ray is not refracted much and so does not go through any of the origally marked points. This is perhaps not surprising, since the relative refractive index calculated from the ratio of the blue (XY) and green (XZ) lines is only about 1.26. For example, the relative refractive index for a glass-air interface is about 1.5.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
I interpret this as a negative result for the corelation between the original image and Snell's law. A very positive result would be if the refracted ray went through one of the points marked on the optical axis. I didn't want to give up yet, so I changed the aspect ratio of the original image (suspecting that the original was wrong) so that the blue line XY was a perfect fit between C and H. Specifically, I squished the image horizontally to 78% of its original width. I think H was intended (in the original) to be the point on the optical axis, closest to P (thus directly above P). The procedure in the following pictures is the same as above so I will only comment on important differences.<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header = Refracted ray reconstruction with a modified aspect ratio<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod1.svg <!-- filename only --><br />
| caption1 = '''Step 1:''' The test fit of a yellow circle is now much better. Also, the center of the yellow circle is now actually in point O.<br />
<!--image 2--><br />
| image2 = RekonsMod2.svg <!-- filename only --><br />
| caption2 = '''Step 2:''' The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer =<br />
}}<br />
<br />
{{multiple image|caption_align=left<br />
<!-- Essential parameters --><br />
| align = center <!-- right (default), left, center, none --> <br />
| direction = horizontal <!-- horizontal (default), vertical --><br />
| background color = <!-- box background --><br />
<br />
<!-- Header --><br />
| header_background =<br />
| header_align = center <!-- center (default), left, right --><br />
| header =<br />
<br />
<!-- Images --><br />
| width = 250 <!-- image width in pixels, overrides "width[n]"s --><br />
<!--image 1--><br />
| image1 = RekonsMod3.svg <!-- filename only --><br />
| caption1 = '''Step 3:''' The blue line of the incoming ray now stretches from H (a point present in the original image) to C. This is not surprising, since the image was resized based on this criterion.<br />
<!--image 2--><br />
| image2 = RekonsMod4.svg <!-- filename only --><br />
| caption2 = '''Step 4:''' However, the ray is now refracted even less, the relative refractive index being around 1.18.<br />
<br />
<!-- Footer --><br />
| footer_background = <br />
| footer_align = left <!-- left (default), center, right --><br />
| footer = <br />
}}<br />
Again, a negative result. You can try to tinker with these .svg files yourself, all you need is Inkscape. Somebody please refute or confirm my doubts. I am writing the history section of the article on light on sl.wikipedia and I want to present the truth, not speculation.<br />
<br />
Marko Petek 00:05, 15 July 2015 (UTC) <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Marko Petek|Marko Petek]] ([[User talk:Marko Petek|talk]] • [[Special:Contributions/Marko Petek|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--><br />
: Here's the actual supporting passage:<br />
: {{Quote|text="'''''The hyperbola as a conic section: The law of refraction.'''''<p>Ibn Sahl first considers refraction on a plane surface. Defining <math>GF</math> as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index <math>n</math> of this crystal in relation to air.<sup>19</sup></p><blockquote>'Let <math>DC</math> be a light ray in the crystal, which is refracted [see figure] in the air along <math>CE</math>. The perpendicular to the plane surface <math>GF</math> at <math>G</math> intersects line <math>CD</math> at <math>H</math> and the refracted ray at <math>E</math>.'</blockquote><p>The ratio <math>CE/CH < 1</math>, which Ibn Sahl uses throughout his study, is the reciprocal of <math>n</math>:</p><blockquote>'Let <math>i_1</math> and <math>i_2</math> be the angles formed by <math>CD</math> and <math>CE</math>, respectively, with the normal; we have <blockquote><math>\frac{CE}{CH}=\frac{CE}{CG}\cdot\frac{CG}{CH}=\frac{\sin i_1}{\sin i_2} =\frac{1}{n}</math>.</blockquote>Let <math>I</math> be a point on segment <math>CH</math> such that <math>CI = CE</math>, and let point <math>J</math> be the middle of <math>IH</math>. We have <math>CI/CH = 1/n</math>. Therefore <math>C, I, J, H</math> characterize the crystal for any refraction.'</blockquote><p>This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.</p><p><sup>19</sup>[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."</p>|author=Rashed (1990), p. 478}}<br />
: According to Rashed, the plate with the Arabic text comes from page 7 of the manuscript, and the geometric references are to the triangle on that page. The sketches themselves, I admit, are too vague to be considered on their own. Nevertheless, if the translation that Rashed gives is faithful to the original work (especially the last sentence, suggesting that the relative location of those collinear points are a ''material property of crystals'' that determine an ''invariant quantity for refraction experiments''), I think it's fair to say that ibn Sahl gets priority for the law of refraction. [[User:Conformancenut347|Conformancenut347]] ([[User talk:Conformancenut347|talk]]) 19:01, 29 July 2016 (UTC)<br />
<br />
I share the doubts aired by user @Marko Petek on 15 July 2015, who righfully complains that ''“no translation of the surrounding arabic text is given”'' and ''“There is only one article containing original research on the subject (...)”''. The article by [[Roshdi Rashed]] can be found in the [https://www.jstor.org/ JSTOR archives], ref. [1] and runs from p. 464 - 491. JSTOR allows up to 3 free items on your personal shelf. If you do so, you will have the full article at hand/on your JSTOR-shelf and on p. 478 of the ''Isis''-issue you will find the 'derivation' by ibn Sahl which is also quoted by user @Conformancenut347. <br />
<br />
Now, there is something strange: Rashed/ibn Sahl nowhere ''proves'' that the ratio sin i_1/ sin i_2 is constant, he simply ''relabels'' it to be (the inverse of) the [[refractive index]] ''n'' for the denser medium! (Presumably the boundary air/glass or air/water is studied, the refractive index for air assumed to be 1, which is not obvious). What we want is an ''empirical'' proof that the ''ratio'' of the two sinuses is constant, i.e. that the value of ''n'' is constant.<br />
<br />
Ibn Sahl didn't have a concept of the velocity of light in a medium, nor the theoretical apparatus of the scholars of the Enlightement (Huygens) and later. And even if he had, he would still have to turn to experiment to check the theoretical claims.<br />
<br />
Again: he only could have arrived at his result by experiment - we want to see ''tables'' with angles (see ref. [2] for an example) and the ratio sin/sin for each angle. There is no description of the measurement set up, the refracting medium [http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/indrf.html (various kinds of glass, water, other)], no mention of the light source and its [[Dispersion_(optics)|colour]] and how he created a bundle of (almost) monochromatic light. <br />
<br />
Rashed concludes his 'derivation' on p. 478 with: ''“This result of considerable importance, encountered here for the first time, enabled Ibn Sahl to utilize the law of inverse return [?] in the case of refraction, which is essential for the study of biconvex lenses, as we shall see later.”''<br />
<br />
On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine): <br />
<br />
:''“Some years ago, I discovered and began to reconstruct a treatise on burning instruments written around 984 by a mathematician connected with the court of Baghdad, Abu Saʿd al-ʿAlaʾ ibn Sahl, whose work was known to Ibn al-Hayhtam and was even sometimes copied in hiw own hand (see Fig. 1). ['Fig. 1' is the first figure appearing in wiki [[Ibn Sahl]]]. Ibn Sahl (...) went further than he [Ptolemy] in the study of refraction. This treatise ''On the Burning Instruments'' (...) he succeeded in stating Snellius'law long before Snellius himself (...) these results come as a surprise (...) Libraries in both Damascus and Teheran contain a manuscript bearing this title. It was thought (...) that these were two copies of one and the same manuscript (...) the manuscripts contain[ing] different texts (...) [with] no passages in common (...) My first task was to discern the latent [?] structure (...) I then determined where to insert it [the Damascus fragment in the Tehran fragment] and filled in some other gaps [Oh oh!] (...) provide a definitive reconstruction of what has survived (...) it is quite easy [oh?] to surmise what their contents were.”''<br />
<br />
Rashed commits [[mortal sin]]: he single-handedly tinkers with the original manuscript, which we do not get to see, and fills in the gaps as he sees fit, as he ''thinks'' it ''should '' be. But a good historian of science ''never'' fiddles with the original, he tries to authenticate, tries to guess the provenance, the year it was written, in fact let loose on the document the whole array of [[Palaeography|paleographic]], [[Philology|philologic]] and physical analyses (including carbon dating), as is done by specialized institutes like the [http://www.bodleian.ox.ac.uk/ Bodleian libaries]; see for example the analysis of the [http://www.bodleian.ox.ac.uk/news/2017/sep-14 Bakhshali manuscript] that ''“contains the oldest recorded origins of the symbol 'zero'”''.<br />
<br />
Because we do not have the original manuscripts in their 'pristine' form, we cannot judge how far Rashed went in 'reconstructing' the text, we can do so only by visiting the libraries where the medieval manuscripts are stored. They should be placed on line. Failing that, we must leave open the possibility that much of the missing fragments were 'resurrected' with the aid of the fantasy of Roshdi Rashed.<br />
<br />
It will be very difficult to reconstruct anything: when one is familiar with modern developments in optics since Snellius, one is bound to see in the old manuscripts things that are not really there, but which are artefacts of one's own cultural baggage.<br />
<br />
Skimming over the publication, I do not quite understand what Rashed/Ibn Sahl are doing; apparently Ibn Sahl wanted to design devices for 'burning', presumably for military purposes. Using a lens of glass to ignite, say, a wooden ship at some distance will require a lens of considerable diameter: a hugh amount of molten glass will have to poored in a large mould with the right geometry. It is not clear if this ever was tried out, if glass with the right optical properties could be found, and if the construct succeeded in its goal to incinerate an object. Cooling down of the molten disc is a challenge, and there is always the possibility that the disc fractures somwehere along the cooling traject. Did Ibn-Sahl ever grind some of his own lenses?<br />
<br />
Curiously, nowhere the classical [[Lens_(optics)#Imaging_properties|imaging peoperties and lens formulae]] are considered. <br />
<br />
On the last page (491) of the treatise, Rashed points out the possibility of using a lens for imaging but, ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. [[Astigmatism]] is a defect of eye and [[Spherical aberration|aberrations]] are that of lenses. However the lens errors, which would be corrected only much later in the 18-th and 19-th century, would have hindered the practical application of ''burning'' lenses too, so I do not see the point. Apart from that, these imperfections didn't hamper the West from inventing [[glasses|spectacles]] in the 13-th century or the [[telescope]] in the 17-th century.<br />
<br />
In fact I find it most puzzling that it didn't occur to the Arabs, with all their knowledge of optics, to simply to hold two lenses in front of their eyes (eye glasses) or hold one behind the other (telescope). <br />
<br />
Finally, no serious scholar ever refers to the work by Roshdi Rashed. But inspect his treatise yourself on JSTOR, see [1] and form your own opinion.<br />
<br />
Summarizing:<br />
* Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.<br />
* Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar<br />
* No table with numerical results of the experiments, i.e. sin/sin-ratio vs incident angle, is provided. Nor details of the experimental setup (type of medium, colour of the light, etc.)<br />
* Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?<br />
<br />
References:<br />
<br />
[1] Roshdi Rashed, ''[http://www.jstor.org/stable/233423 , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses]'', ''Isis'' Vol. 81, No. 3 (Sep., 1990), pp. 464-491<br />
<br />
[2] ''[https://schoolworkhelper.net/lab-refraction-of-light-air-into-glass/ Lab: Refraction of Light- Air into Glass Answers]'', Schoolworkhelper.net (2016)<br />
<br />
-- [[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:32, 13 October 2017 (UTC)<br />
<br />
::The text of the wiki-article says in section ''History'': ''“In the manuscript ''On Burning Mirrors and Lenses'', Sahl used the law to derive lens shapes that focus light '''with no geometric aberrations.''' ”'' This conflicts with Rashed on p.491 of his article: ''“when attention is paid to the problems raised by the image of an object observed through a lens, the situation becomes quite different; in this case it is impossible to avoid difficulties as astigmatism and aberration”''. I think the wiki-text should be repaired. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::Agreed, that's very suspect and should be fixed. You can look at the history to figure out who originally put that, based or what source, and how it evolved, and perhaps invite relevant editors to comment. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::Now that I have the ISIS areticle by Rashid, I think this is less suspect, but needs to be clarified. In the "burning" case he's only talking about aberration at a single on-axis point, and contrasting to the imaging case, where it's impossible to avoid aberrations with a single lens. And of course chromatic aberration is not part of what's being considered. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:38, 14 October 2017 (UTC)<br />
<br />
:Interesting discussion. But it seems to me to be too much [[WP:OR]] to be acted on. The source by the respected historian [[Roshdi Rashed]] seems clear enough, along with the original sketch, in establishing that Ibn Sahl discovered an empirical/geometrical way to describe refracted rays, in a way that is consistent with the law now done with trig functions and known as Snell's law, even if not in its full generality. I don't know about the rest of the figure, and even whether that's a plano-convex lens being depicted or not. Doesn't much matter. And doesn't much matter that Ibn Sahl didn't present either a proof or a table of experimental data. If Roshdi Rashed's interpretation is to be challenged, that should be done in a peer-reviewed venue, then we can talk about that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:06, 14 October 2017 (UTC)<br />
:By the way, the "burning lenses" being referred to were more likely small lenses, a few inches in diameter, enough to concentrate sun rays enough to burn wood surfaces; possibly the theory was being looked at for big lenses, but nobody was able to make big lenses, so the theory wasn't much good for that. Lenses were not made well enough at that time to use for imaging, and that's why no telescopes and such. That didn't happen until the making of glass and lenses was good enough to use for eye-glasses. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:13, 14 October 2017 (UTC)<br />
:Also, as I pointed out above, over 10 years ago ([[#The original form of the law]]), Snel's original version was no more general, and no more like the current law, than Ibn Sahl's; it sounds like it was about the same. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 05:19, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanx for your comments. Have you read the article on JSTOR by Rashed carefully? Then you will see that he freely rewrote and added to the original. This means that we cannot exclude he invented things or misinterpreted. Rashed is supposed to make the original available to other scholars (on-line preferably) so it can be authenticated - how can you otherwise exclude that Rashed constructed the sketches himself?? Everything else you add to it is of secondary importance - you can never 'sell' it as being the original work by ibn-Sahl, as Rashed does, certainly not given that all of Rashed's comments are given 1000 years after ibn-Sahl: they will always bear the imprint of conscious knowledge of later developments and your own ideological and personal stance. Peer-reviewed venue: Rashed's treatise was published 17 years ago - no scholar has since took a careful look at it contents. No serious scientist ever refers to it in textbooks, in say introductory courses in physics - for good reason. An early discovery of 'Snell' would have been a small scientific sensation - it has so fare been eerily silent. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 14:51, 14 October 2017 (UTC)<br />
:::No, I haven't got the article yet. It's OK if you want to question his authority, methods, accuracy, or whatever, but until you get your alternative analysis published, we're stuck with this one [[WP:RS]]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
<br />
:: Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 15:15, 14 October 2017 (UTC)<br />
:::Good idea. I look forward to hearing what you get from him. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 15:52, 14 October 2017 (UTC)<br />
:::OK, I got the paper now. First thing I notice is that he says Ibn Sahl's manuscript is coming out soon in a book (that was 1990); and it did come out, in 1993, and you can invest in a copy if you want: [https://www.abebooks.com/servlet/SearchResults?sts=t&an=Roshdi+Rashed&tn=sahl&kn=&isbn= here]. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 16:28, 14 October 2017 (UTC)<br />
:::Another thing to note: Rashed says the section of the document on the plano-convex lens is "complete". I haven't read in detail yet, but I'm thinking that means your thought that he extrapolated too much content is more applicable to other sections, not this part where the refraction law is shown. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 17:28, 14 October 2017 (UTC)<br />
:::Also, Google Scholar says Rashed's paper has been cited 153 times. Why do you say nobody cites it? Also note that "Professor Rashed obtained the 1990 Prize of the Third World Academy of Sciences for this work." according to a source I found. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:02, 14 October 2017 (UTC)<br />
:::I updated the image from the JSTOR PDF. You are right that the aspect ratio was stretched more than 10%. It should be closer to the original now, I think. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 18:18, 14 October 2017 (UTC)<br />
<br />
::@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby [https://www.library.universiteitleiden.nl/ Leiden University Libraries]. '''Alas, even if a team of experts''' managed to determine provenance and date of creation of the fragments found by Rashed, we are not out of the woods yet. The 'primal' manuscript originates with Ibn Sahl, around 1000 AD. Scribes then copy this document manifold, each transciption again the source for more copies and so on. This way a '''family tree of related documents''' arises, each 'generation' differing more of less from its predecessor: by way of simple transcription errors ([3], p. 105: ''“Murphyʼs Law of Textual Criticism: If you can imagine an error, a scribe has probably made it”''), scribes who do not quite understand the subject matter or language/style/idiom of the document, or think they can 'improve' on it. A perfect example of this is Rashed himself, who doesn't quite understand the essential ''physics'' of 'Snell' (the constancy of the sin/sin-ratio, within the limitations of experimental set-up) and rewrote (partially?) the document and 'improved' on the extant fragments. <br />
<br />
::It is '''very improbable that Rashed discovered (fragments of) the 1000 year old 'trunk' ''' of the tree; it is much more likely that the extant fragments are of a (much) later date. This then means that the handwriting is not Ibn Sahl's and even if it carried a signature purporting to be Ibn Sahl's, it must be a forgery - by definition. It is not uncommon for authors to use not their own name/signature, but that of great personality of the past to lend their own work more authority - or as tribute to the Master ([3], pp. 166 - 167, section ''Detecting Forged Manuscripts''). An example is the [[First Epistle of Peter]] which was not written by the Apostle Peter himself but was written under pseudonym: ''“Although the text identifies Peter as its author, the language, dating, style, and structure of this letter have led many scholars to conclude that this letter is pseudonymous.”''.<br />
<br />
::All the problems related to old manuscripts are even more pronounced in the Islamic world where the printing press - which 'freezes' a document - was introduced centuries later; the first Qu'ran was printed in the 19-th century if I am not mistaken.<br />
<br />
::The related manuscripts are potentially scattered among as many physical locations (libraries, other public or private collections), so it is paramount to collect as many texts as possible, so one can compare and '''try to identify a core text common to ''all'' transcriptions''', see [4]. If there is only one authenticated manuscript (date of creation, region, etc.), it becomes next to impossible to say anything about the primal original by Ibn Sahl - assuming he ever wrote about what is now Snell's law.<br />
<br />
::Until such time that the results of paleographical, philological and physical (carbon dating, chemical analysis of ink etc.) inquiry are published in the relevant journal(s) together with the translation of the fragments, making explicitly clear where Ibn Sahl 'ends' and the interpretation by Rashed begins, I strongly suggest to '''delete the sections of the lemma referring to the find (?) by Roshdi Rashed'''; in the Rashed/Ibn-Sahl manuscript not a single experiment is conducted, let alone the experimental confirmation of Snell's law convincingly demonstrated.<br />
<br />
::[3] [https://mnheritagesongbook.files.wordpress.com/2013/07/encyclopedia_nt_tc_final.pdf Robert B. Waltz, ''The Encyclopedia of New Testament Textual Criticism'', (Last Preliminary Edition, June 16, 2013)]<br />
<br />
::[4] [[Roger Collins]], ''Caliphs and Kings: Spain, 796-1031 (A History of Spain)'', (2012)<br />
<br />
::p. 17: ''“As the study of better preserved texts shows, the process of copying results in the introduction of new errors each time it occurs, and a modern edition would normally rely on many or all of the extant manuscripts in attempting to reconstruct the author's original version. Where a work only survives in a single late manuscript, it can be assumend that its text will have been corrupted by several generations of scribal errors (...) we cannot be confident that we posses the most authoritative version of it.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 17:20, 24 October 2017 (UTC)<br />
<br />
<br />
Might I politely suggest that instead of filling this talk page with your theories that your publish a peer reviewed article on the subject in a recognised journal for the topic, as Rashed has done, and then the article can be changed according to the rules of Wikipedia.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:16, 25 October 2017 (UTC)<br />
<br />
:May I suggest you address the ''substance'' of my arguments? Please read all of this talk-section ''Elaborate on Ibn Sahl's authorship of the law'' and then refute blow-by-blow the comments, made by me and others, which you do not endorse. Here are some sayings to think over, by historian [[Roger Collins]] in his ''The Arab Conquest of Spain 710 -797'' (1989): ''“Source criticism precedes analysis, let alone narrative. If it does not, the result can be mere fiction”'' (p. 1) and ''“(...) hyper-criticism, as its opponents like to call it, is preferable to the writing of romance (...)”'' (p. 5). Finally, remember that all claims of a physical nature must be backed-up by [[Experimental physics|experiment]]: full details of the experimental set-up and '''numerical''' results confirming or refuting the claim; there is no such thing as a 'geometrical proof' in physics.--[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 16:50, 25 October 2017 (UTC)<br />
<br />
::I Surprise, surprise, I have read this talk-section, a large part of your so-called substance has answered by Dicklyon, which you ride rough shot over or ignore. You accuse Rashed of speculation but indulge in widespread unsubstantiated speculation yourself. As I said publish a well founded criticism of Rashed's work in a peer reviewed journal article and then we can consider changing the Wikipedia article.[[User:Thony C.|Thony C.]] ([[User talk:Thony C.|talk]]) 05:49, 26 October 2017 (UTC)<br />
<br />
:::Hi Thony congrats. Did you read the [http://www.jstor.org/stable/233423 complete article by Rashed on JSTOR]? Have also you seen the comments by user @Marko Petek 00:05, 15 July 2015 (UTC), at the far beginning of this section? And you haven't refuted my remarks on say the problem of the authenticity of the (transcribed) fragments found (?) by Rashed, which he doesn't disclose and which he freely augmented without us ever allowing to check where the ''fragments'' end and ''Rashed'' begins? [https://www.mamamia.com.au/is-it-okay-to-cry-at-work-depends-on-so-many-things/ But I give up]; I wish you all the best of luck with a 'proof' in the guise of a silly drawing of a triangle and some untranslated scribbles in (medieval?/modern?) Arabic. --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 08:41, 26 October 2017 (UTC)<br />
<br />
The '''French wiki has the following''' in the section [[:fr:Lois_de_Snell-Descartes#Historique]]:<br />
<br />
:''“Cependant, le traité d'Ibn Sahl [in the article by Roshdi Rashed]] reste énigmatique, car la relation apparait sans donnée expérimentale, ni fondement théorique. De plus, aucune constante équivalente à l'indice optique n'est définie. En outre, Il est difficile de croire qu'Ibn al-Haytham (Alhazen) n'ait pas repris la découverte fondamentale de son maitre Ibn Sahl. La loi semble simplement avoir été oubliée. Une interprétation possible est qu'il s'agisse d'un exercice de conception de lentille, considéré dans le domaine purement géométrique, sans que la loi physique soit établie.”''<br />
<br />
Which means: <br />
:''“That said, '''the treatise by Ibn Sahl''' [in the publication by Roshdi Rashed] '''is enigmatic, because the relation''' [between the sinuses] '''appears without experimental underpinning and lacks foundation in theory'''. Moreover, no constant is defined equivalent to the index of refraction. Furthermore it is difficult to believe that Ibn al-Haytham (Alhazen) didn't utilize the fundamental discovery of his tutor. The law seems simply to have been forgotten. Another possibility is that it concerned solely an exercise in thinking about lenses, an exercise purely of geometric nature without any attempt to establish a physics law.”'' ('''Bold''' by me.)<br />
<br />
The editor of the French lemma uses source [5] (below) by physicist [https://www.army.mil/article/154037/army_researchers_build_partnerships_through_international_assignments Dr. Gorden Videen] as his source. Unfortunately, I only got hold of the abstract, see below, and I need all of the article to complement the history-section.<br />
<br />
To conclude a word by [[Richard Feynman]], in his famous [http://www.feynmanlectures.caltech.edu/I_toc.html The Feynman Lectures on Physics, Volume I, chapter 26, section26-2]:<br />
<br />
:''“(...) what is the relation of one angle to the other? This also puzzled the ancients for a long time (...) It is, however, one of the few places in all of Greek physics that one may find any experimental results listed. Claudius Ptolemy made a list of the angle in water for each of a number of different angles in air. Table 26–1 shows (...) This, then, is '''one of the important steps in the development of physical law: first we observe an effect, then we measure it and list it in a table'''; then we try to find the rule by which one thing can be connected with another.”''<br />
<br />
[5] Dr. Gorden Videen, ''[https://www.researchgate.net/publication/279669748_Whose_law_of_refraction Whose Law of Refraction?]'', [https://www.osa-opn.org/home/articles/volume_19/issue_5/ Optics & Photonics News (May 2008)]<br />
<br />
:''“Abstract. (...) Sameen Khan claims that Ibn Sahl discovered the sine law of refraction in the 10th century. The case is based on a figure showing a pair of triangles on a page depicting a plano-convex lens. Researchers both performed and recorded the results of their experiments in texts and provided insights into their theories. The claim of presedence for Ibn Sahl leaves [us] in a conundrum. '''Fundamental laws of physics do not just appear without any physical basis or observations'''. '''It is believed that the Battle for Snell's law is being waged under false pretenses''', and its casualties are victims of an overambitious translation.”'' --[[User:Gerard1453|Gerard1453]] ([[User talk:Gerard1453|talk]]) 18:32, 5 November 2017 (UTC)<br />
<br />
I read your arguments and opinions, but as far as i know, Rashed is a recognized expert on this topic, so if he says that Ibn Sahl invented this law then that's enough for me.<br />
[[User:Wikaviani|Wikaviani]] ([[User talk:Wikaviani|talk]]) 02:24, 10 January 2018 (UTC)<br />
<br />
The work of Wikipedians is to add information and see if the information is supported by a reliable source or not. It is not the duty of Wikipedia editors to examine the work of authors. A reliable source is saying that snells' law was given earlier by ibn sahl.That is enough.<br />
<br />
== Popular media ==<br />
<br />
Most Wikipedia pages reference the use of their subject in popular media, this one is referenced in the game Simpsons Tapped Out, specifically when the new Lard Lad statue is unveiled. It should at least get a small mention. [[Special:Contributions/47.32.35.106|47.32.35.106]] ([[User talk:47.32.35.106|talk]]) 06:31, 1 October 2016 (UTC)<br />
<br />
== Huygens derivation ==<br />
<br />
I don´t quite see how Huygens derivation acts. Why choosing this propation direction and not others in each wavelet? According to Doctor Lincoln from Fermilab [https://www.youtube.com/watch?v=NLmpNM0sgYk&t=683s Why does light bend when it enters glass?], this is not a good explanation. Fermat's approach seems more the description of what happens rather than why. --[[User:Xareu bs|Xareu bs]] ([[User talk:Xareu bs|talk]]) 11:49, 30 August 2019 (UTC)<br />
<br />
== Ibn Sahl's manuscript ==<br />
<br />
[[File:Ibn-sahl-manuscript-J3M6J2.jpg|thumb|Translation: The straight line CE is therefore smaller than CH. We separate from the straight line CH the straight line CI equal to the straight line CE; we divide HI in half at point J; we set the ratio of the straight line AK to the straight line AB equal to the ratio of the straight line CI to the straight line CJ; we extend the straight line BL along AB and set it equal to the straight line BK.]] [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 13:35, 11 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223337453Snell's law2024-05-11T13:07:06Z<p>Casteiswrong: /* History */ grammar made it precise</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref><br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. This implies, although he doesn't say it, that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate a specific law using angles and sine functions.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref>[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223336522Snell's law2024-05-11T12:57:03Z<p>Casteiswrong: fixed the law</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref><br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. This implies, although he doesn't explicitly state it, that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate a specific law using angles and sine functions.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref>[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223335678Snell's law2024-05-11T12:48:36Z<p>Casteiswrong: /* History */ tertiary source error removed.</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2}= n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref><br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. This implies, although he doesn't explicitly state it, that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate a specific law using angles and sine functions.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3rd |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref>[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223335517Snell's law2024-05-11T12:47:02Z<p>Casteiswrong: /* History */ minor grammar</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2}= n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref><br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. This implies, although he doesn't explicitly state it, that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate a specific law using angles and sine functions.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3. edition |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref>[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223335367Snell's law2024-05-11T12:45:22Z<p>Casteiswrong: /* History */ adjust image</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2}= n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref><br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. Although he doesn't explicitly state it, this implies that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate a specific law using angles and sine functions.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3. edition |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref>[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223335261Snell's law2024-05-11T12:44:16Z<p>Casteiswrong: Ibn Sahl did not discover any law, all credit goes to Lord Willebrord Snel van Royen.</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''', and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2}= n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Image:Ibn Sahl manuscript.jpg|thumbnail|left|Reproduction of a page of [[Ibn Sahl (mathematician)|Ibn Sahl]]'s ''On Burning Instruments'']]<br />
<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref> <br />
<br />
[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
In his work, ''On Burning Instruments'', [[Ibn Sahl (mathematician)|Ibn Sahl]] describes a method to understand the refraction of light through a crystal. He draws a line perpendicular to the plane of refraction at a specific distance from the point of refraction. He also draws the refracted ray and extends the incident ray beyond the plane of refraction until both rays intersect the perpendicular line. From this geometric construction, Ibn Sahl concludes that the length of the refracted ray is shorter than that of the incident ray. Although he doesn't explicitly state it, this implies that the ratio of the length of the refracted ray to the length of the incident ray is less than one, which would correspond to the inverse of the refractive index of the crystal. However, Ibn Sahl does not calculate this ratio, nor does he formulate a specific law using angles and sine functions.<ref>{{Cite book |title=Encyclopaedia of the history of science, technology and medicine in non-western cultures |date=2016 |publisher=Springer |isbn=978-94-007-7746-0 |editor-last=Selin |editor-first=Helaine |edition=3. edition |series=Springer reference |location=Dordrecht |pages=2326-2327}}</ref><br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
The law was rediscovered by [[Thomas Harriot]] in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> who however did not publish his results although he had corresponded with [[Kepler]] on this very subject. In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626)—Snell—derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Snell%27s_law&diff=1223326135Snell's law2024-05-11T10:52:32Z<p>Casteiswrong: /* History */ Ibn Sahl did not discover the law. I will add details about what he did discover.</p>
<hr />
<div>{{Short description|Formula for refraction angles}}<br />
<br />
[[Image:Snells law2.svg|thumb|[[Refraction]] of light at the interface between two media of different [[refractive index | refractive indices]], with n<sub>2</sub> > n<sub>1</sub>. Since the velocity is lower in the second medium (v<sub>2</sub> < v<sub>1</sub>), the angle of refraction θ<sub>2</sub> is less than the angle of incidence θ<sub>1</sub>; that is, the ray in the higher-index medium is closer to the normal.]]<br />
<br />
'''Snell's law''' (also known as the '''Snell–Descartes law''' and the '''law of refraction''') is a [[formula]] used to describe the relationship between the [[angle of incidence (optics)|angles of incidence]] and [[refraction]], when referring to [[light]] or other [[wave]]s passing through a boundary between two different [[isotropic]] [[medium (optics)|media]], such as water, glass, or air.<br />
In optics, the law is used in [[Ray tracing (physics)|ray tracing]] to compute the angles of incidence or refraction, and in experimental optics to find the [[refractive index]] of a material. The law is also satisfied in [[Metamaterials#Negative refractive index|meta-materials]], which allow light to be bent "backward" at a negative angle of refraction with a [[Refractive index#Negative refractive index|negative refractive index]].<br />
<br />
The law states that, for a given pair of media, the ratio of the sines of [[Angle of incidence (optics)|angle of incidence]] (<math>\theta_1 </math>) and angle of refraction (<math>\theta_2 </math>) is equal to the refractive index of the second medium with regard to the first (<math>n_{21}</math>) which is equal to the ratio of the [[refractive indices]] (<math>\tfrac{n_2}{n_1}</math>) of the two media, or equivalently, to the ratio of the [[phase velocities]] (<math>\tfrac{v_1}{v_2}</math>) in the two media.<ref>{{Cite book |title=[[Principles of Optics]]|last=Born and Wolf|publisher=Pergamon Press INC.|year=1959|location=New York, NY|page=37}}</ref><br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{n_2}{n_1} = \frac{v_1}{v_2} </math><br />
<br />
The law follows from [[Fermat]]'s [[Fermat's principle|principle of least time]], which in turn follows from the propagation of light as waves.<br />
<br />
==History==<br />
[[Ptolemy]], in [[Alexandria]], Egypt,<ref>David Michael Harland (2007). "''[https://books.google.com/books?id=ScORNbV0E8wC&pg=PA1 Cassini at Saturn: Huygens results]''". p.1. {{ISBN|0-387-26129-X}}</ref> had found a relationship regarding refraction angles, but it was inaccurate for angles that were not small. Ptolemy was confident he had found an accurate empirical law, partially as a result of slightly altering his data to fit theory (see: [[confirmation bias]]).<ref>{{cite web |title=Ptolemy (ca. 100-ca. 170) |work=Eric Weinstein's World of Scientific Biography |url=http://scienceworld.wolfram.com/biography/Ptolemy.html}}</ref> <br />
<br />
[[Image:Snell Law of Sines 1837.png|thumb|right|An 1837 view of the history of "the Law of the Sines"<ref>William Whewell, ''History of the Inductive Science from the Earliest to the Present Times'', London: John H. Parker, 1837.</ref>]]<br />
<br />
The law is named after a Dutch [[mathematician]] and [[astronomer]], [[Willebrord Snellius]] (1580–1626), who discovered the law of refraction and wrote down its mathematical form.<ref>{{Cite book |url=https://www.google.nl/books/edition/Elements_of_Classical_Physics/fZU3BQAAQBAJ?hl=nl&gbpv=1&dq=willebrord+snell+physics+law&pg=PA39&printsec=frontcover|title=Elements of Classical Physics |last=Martin |first=Martin|date=2013 |publisher=Elsevier |isbn= 1483148602|page=39}}</ref> <br />
<br />
[[Alhazen]], in his ''[[Book of Optics]]'' (1021), came close to rediscovering the law of refraction, but he did not take this step.<ref>[[A. I. Sabra]] (1981), ''Theories of Light from Descartes to Newton'', [[Cambridge University Press]]. ([[cf.]] Pavlos Mihas, [https://web.archive.org/web/20120527202345/http://www.ihpst2005.leeds.ac.uk/papers/Mihas.pdf Use of History in Developing ideas of refraction, lenses and rainbow], p. 5, Demokritus University, [[Thrace]], [[Greece]].)</ref><br />
<br />
[[Thomas Harriot]] claimed to know the law in 1602,<ref>{{cite journal |last1=Kwan |first1=A. |last2=Dudley |first2=J. |last3=Lantz |first3=E. |year=2002 |title=Who really discovered Snell's law? |journal=[[Physics World]] |volume=15 |issue=4 |page=64 |doi=10.1088/2058-7058/15/4/44}}</ref> but did not publish his results as he claimed ill health prevented him from putting it explicitly into a form suitable for publication (although he had corresponded with [[Kepler]] on the subject). In 1621, the Dutch astronomer [[Willebrord Snellius]] (1580–1626) — Snell — derived a mathematically equivalent form, that remained unpublished during his lifetime. [[René Descartes]] independently derived the law using heuristic momentum conservation arguments in terms of sines in his 1637 essay ''[[Dioptrique]]'', and used it to solve a range of optical problems. Rejecting Descartes' solution, [[Pierre de Fermat]] arrived at the same solution based solely on his [[Fermat's principle|principle of least time]]. Descartes assumed the [[speed of light]] was infinite, yet in his derivation of Snell's law he also assumed the denser the medium, the greater the speed of light. Fermat supported the opposing assumptions, i.e., the speed of light is finite, and his derivation depended upon the speed of light being slower in a denser medium.<ref>[[Florian Cajori]], [https://books.google.com/books?id=XNtUAAAAYAAJ ''A History of Physics in its Elementary Branches: Including the Evolution of Physical Laboratories''] (1922)</ref><ref>Ferdinand Rosenberger, [https://books.google.com/books?id=hxsAAAAAQAAJ ''Geschichte der Physik''] (1882) Part. II, p.114</ref> Fermat's derivation also utilized his invention of [[adequality]], a mathematical procedure equivalent to differential calculus, for finding maxima, minima, and tangents.<ref>[[Carl Benjamin Boyer]], ''The Rainbow: From Myth to Mathematics'' (1959)</ref><ref>[[Florian Cajori]], "Who was the First Inventor of Calculus" ''The American Mathematical Monthly'' (1919) [https://books.google.com/books?id=5wxLAAAAYAAJ Vol.26]</ref><br />
<br />
In his influential mathematics book [[La Géométrie|''Geometry'']], Descartes solves a problem that was worked on by [[Apollonius of Perga]] and [[Pappus of Alexandria]]. Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD. When the lines are not all parallel, Pappus showed that the loci are conics, but when Descartes considered larger n, he obtained cubic and higher degree curves. To show that the cubic curves were interesting, he showed that they arose naturally in optics from Snell's law.<ref>The Geometry of Rene Descartes (Dover Books on Mathematics) by Rene Descartes, David Eugene Smith and Marcia L. Latham (Jun 1, 1954).</ref><br />
<br />
According to Dijksterhuis,<ref>{{cite book |last=Dijksterhuis |first=Fokko Jan |year=2004 |title=Lenses and Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century |publisher=Springer |isbn=1-4020-2697-8 |url=https://books.google.com/books?id=cPFevyomPUIC&q=Descartes-had-seen-Snel%27s+intitle:Lenses+intitle:and+intitle:Waves+intitle:Christiaan&pg=PA135}}</ref> "In ''De natura lucis et proprietate'' (1662) [[Isaac Vossius]] said that Descartes had seen Snell's paper and concocted his own proof. We now know this charge to be undeserved but it has been adopted many times since." Both Fermat and Huygens repeated this accusation that Descartes had copied Snell. In [[French language|French]], Snell's Law is sometimes called "la loi de Descartes" or more frequently "''[[:fr:loi de Snell-Descartes|loi de Snell-Descartes]]''".<br />
<br />
[[Image:Huygens Refracted Waves.png|left|thumb|[[Christiaan Huygens]]' construction]]<br />
<br />
In his 1678 ''[[Traité de la Lumière]]'', [[Christiaan Huygens]] showed how Snell's law of sines could be explained by, or derived from, the wave nature of light, using what we have come to call the [[Huygens–Fresnel principle]].<br />
<br />
With the development of modern optical and electromagnetic theory, the ancient Snell's law was brought into a new stage. In 1962, [[Nicolaas Bloembergen]] showed that at the boundary of nonlinear medium, the Snell's law should be written in a general form.<ref>{{cite journal |last1=Bloembergen |first1=N. |last2=Pershan |first2=P. S. |date=1962 |title=Light waves at the boundary of nonlinear media |journal=Physical Review |bibcode=1962PhRv..128..606B |doi=10.1103/PhysRev.128.606 |volume=128 |issue=2 |page=606|hdl=1874/7432 |url=https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://dspace.library.uu.nl/bitstream/1874/7432/1/1962-bloembergen-ligtwaves.pdf |archive-date=2022-10-09 |url-status=live }}</ref> In 2008 and 2011, [[Electromagnetic metasurface|plasmonic metasurfaces]] were also demonstrated to change the reflection and refraction directions of light beam.<ref>{{cite journal |last1=Xu |first1=T. |display-authors=etal |date=2008 |title=Plasmonic deflector |journal=Opt. Express |volume=16 |issue=7 |pages=4753–9 |doi=10.1364/oe.16.004753|pmid=18542573 |bibcode=2008OExpr..16.4753X |doi-access=free }}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–7 |pmid=21885733|s2cid=10156200 |url=http://metaconferences.org/ocs/index.php/META12/META12/paper/view/808 |doi-access=free }}</ref><br />
<br />
{{clear}}<br />
<br />
== Explanation ==<br />
[[File:SnelliusLeiden1.jpg|thumb|Snell's law on a wall in Leiden]]<br />
Snell's law is used to determine the direction of light rays through refractive media with varying indices of refraction. The indices of refraction of the media, labeled <math>n_1</math>, <math>n_2</math> and so on, are used to represent the factor by which a light ray's speed decreases when traveling through a refractive medium, such as glass or water, as opposed to its velocity in a vacuum.<br />
<br />
As light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one. These angles are measured with respect to the ''normal line'', represented perpendicular to the boundary. In the case of light traveling from air into water, light would be refracted towards the normal line, because the light is slowed down in water; light traveling from water to air would refract away from the normal line.<br />
<br />
Refraction between two surfaces is also referred to as ''reversible'' because if all conditions were identical, the angles would be the same for light propagating in the opposite direction.<br />
<br />
Snell's law is generally true only for isotropic or specular media (such as [[glass]]). In [[anisotropic]] media such as some [[crystal]]s, [[birefringence]] may split the refracted ray into two rays, the ''ordinary'' or ''o''-ray which follows Snell's law, and the other ''extraordinary'' or ''e''-ray which may not be co-planar with the incident ray.<br />
<br />
When the light or other wave involved is monochromatic, that is, of a single frequency, Snell's law can also be expressed in terms of a ratio of wavelengths in the two media, <math>\lambda_1</math> and <math>\lambda_2</math>:<br />
<br />
:<math>\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{\lambda_1}{\lambda_2}</math><br />
<br />
==Derivations and formula==<br />
[[Image:Snells law wavefronts.gif|right|frame|[[Wavefronts]] from a [[point source]] in the context of Snell's law. The region below the grey line has a higher [[index of refraction]], and proportionally lower [[speed of light]], than the region above it.]]<br />
Snell's law can be derived in various ways.<br />
===Derivation from Fermat's principle===<br />
Snell's law can be derived from [[Fermat's principle]], which states that the light travels the path which takes the least time. By taking the [[derivative]] of the [[optical path length]], the [[stationary point]] is found giving the path taken by the light. (There are situations of light violating Fermat's principle by not taking the least time path, as in reflection in a (spherical) mirror.) In a classic analogy, the area of lower [[refractive index]] is replaced by a beach, the area of higher [[refractive index]] by the sea, and the fastest way for a rescuer on the beach to get to a [[drowning]] person in the sea is to run along a path that follows Snell's law.<br />
<br />
[[File:Snells law Diagram B vector.svg|right|thumb|250px|Light from medium 1, point Q, enters medium 2, refraction occurs, and finally the light reaches point P.]]<br />
As shown in the figure to the right, assume the refractive index of medium 1 and medium 2 are <math>n_1</math> and <math>n_2</math> respectively. Light enters medium 2 from medium 1 via point O.<br />
<br />
<math>\theta_1</math> is the angle of incidence, <math>\theta_2</math> is the angle of refraction with respect to the normal.<br />
<br />
The phase velocities of light in medium 1 and medium 2 are<br />
:<math>v_1=c/n_1</math> and<br />
:<math>v_2=c/n_2</math> respectively.<br />
<br />
<math>c</math> is the speed of light in vacuum.<br />
<br />
Let T be the time required for the light to travel from point Q through point O to point P. <br />
:<math>T=\frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + (l - x)^2}}{v_2} = \frac{\sqrt{x^2 + a^2}}{v_1} + \frac{\sqrt{b^2 + l^2 -2lx + x^2}}{v_2}</math><br />
where a, b, l and x are as denoted in the right-hand figure, x being the varying parameter.<br />
<br />
To minimize it, one can differentiate :<br />
:<math>\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0</math> (stationary point)<br />
<br />
Note that<br />
<math>\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1</math><br />
<br />
and <math>\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2</math><br />
<br />
Therefore, <br />
<br />
:<math>\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0</math><br />
<br />
:<math>\frac{\sin\theta_1}{v_1}=\frac{\sin\theta_2}{v_2}</math><br />
<br />
:<math>\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}</math><br />
<br />
:<math>n_1\sin\theta_1=n_2\sin\theta_2</math><br />
<br />
===Derivation from Huygens's principle===<br />
{{further|Huygens–Fresnel principle}}<br />
Alternatively, Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths.<br />
<br />
===Derivation from Maxwell's equations===<br />
{{further|Fresnel equations}}<br />
Another way to derive Snell's Law involves an application of the general [[boundary conditions]] of [[Maxwell equations]] for [[electromagnetic radiation]] and [[Electromagnetic induction|induction]].<br />
<br />
===Derivation from conservation of energy and momentum===<br />
Yet another way to derive Snell's law is based on translation symmetry considerations.<ref>{{cite book |last1=Joannopoulos |first1=John D |url=http://ab-initio.mit.edu/book/ |title=Photonic Crystals: Molding the Flow of Light |last2=Johnson |first2=SG |last3=Winn |first3=JN |last4=Meade |first4=RD |publisher=Princeton University Press |year=2008 |isbn=978-0-691-12456-8 |edition=2nd |location=Princeton NJ |pages=31}}</ref> For example, a homogeneous surface perpendicular to the z direction cannot change the transverse momentum. Since the [[Wave vector|propagation vector]] <math>\vec{k}</math> is proportional to the photon's momentum, the transverse propagation direction <math>(k_x,k_y,0)</math> must remain the same in both regions. Assume without loss of generality a plane of incidence in the <math>z,x</math> plane <math>k_{x\text{Region}_1} = k_{x\text{Region}_2}</math>. Using the well known dependence of the [[wavenumber]] on the [[refractive index]] of the medium, we derive Snell's law immediately.<br />
<br />
:<math>k_{x\text{Region}_1} = k_{x\text{Region}_2} \, </math><br />
<br />
:<math> n_1 k_0\sin\theta_1 = n_2 k_0\sin\theta_2 \, </math><br />
<br />
:<math> n_1\sin\theta_1 = n_2\sin\theta_2 \, </math><br />
<br />
where <math>k_0=\frac{2\pi}{\lambda_0}=\frac{\omega}{c}</math> is the wavenumber in vacuum. Although no surface is truly homogeneous at the atomic scale, full translational symmetry is an excellent approximation whenever the region is homogeneous on the scale of the light wavelength.<br />
<br />
===Vector form===<br />
{{see also|Specular reflection#Direction of reflection}}<br />
<br />
Given a normalized light vector <math>\vec{l}</math> (pointing from the light source toward the surface) and a normalized plane normal vector <math>\vec{n}</math>, one can work out the normalized reflected and refracted rays, via the cosines of the angle of incidence <math>\theta_1</math> and angle of refraction <math>\theta_2</math>, without explicitly using the sine values or any trigonometric functions or angles:<ref>{{cite book |last=Glassner |first=Andrew S. |year=1989 |title=An Introduction to Ray Tracing |publisher=Morgan Kaufmann |isbn=0-12-286160-4 |url=https://books.google.com/books?id=YPblYyLqBM4C}}</ref><br />
<br />
:<math>\cos\theta_1 = -\vec{n}\cdot \vec{l}</math><br />
<br />
Note: <math>\cos\theta_1</math> must be positive, which it will be if <math>\vec{n}</math> is the normal vector that points from the surface toward the side where the light is coming from, the region with index <math>n_1</math>. If <math>\cos\theta_1</math> is negative, then <math>\vec{n}</math> points to the side without the light, so start over with <math>\vec{n}</math> replaced by its negative.<br />
<br />
:<math>\vec{v}_{\mathrm{reflect}}=\vec{l} + 2\cos\theta_1 \vec{n}</math><br />
This reflected direction vector points back toward the side of the surface where the light came from.<br />
<br />
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector:<br />
:<math>\sin\theta_2 = \left(\frac{n_1}{n_2}\right) \sin\theta_1 = \left( \frac{n_1}{n_2} \right) \sqrt{ 1 - \left(\cos\theta_1 \right)^2 }</math><br />
:<math>\cos\theta_2 = \sqrt{1-(\sin\theta_2)^2} = \sqrt{1 - \left( \frac{n_1}{n_2} \right)^2 \left( 1 - \left( \cos\theta_1 \right)^2 \right)}</math><br />
:<math>\vec{v}_{\mathrm{refract}} = \left( \frac{n_1}{n_2} \right) \vec{l} + \left( \frac{n_1}{n_2} \cos\theta_1 - \cos\theta_2 \right) \vec{n}</math><br />
<br />
The formula may appear simpler in terms of renamed simple values <math> r = n_1 / n_2 </math> and <math> c = -\vec{n}\cdot \vec{l}</math>, avoiding any appearance of trig function names or angle names:<br />
:<math>\vec{v}_{\mathrm{refract}} = r \vec{l} + \left( r c - \sqrt{1 - r^2 \left( 1 - c^2 \right)} \right) \vec{n}</math><br />
<br />
Example:<br />
:<math>\vec{l} = \{0.707107, -0.707107\}, ~ \vec{n} = \{0,1\}, ~ r = \frac{n_1}{n_2} = 0.9</math><br />
:<math>c = \cos\theta_1=0.707107, ~ \sqrt{1 - r^2 \left( 1 - c^2 \right)} = \cos\theta_2 = 0.771362</math><br />
:<math>\vec{v}_{\mathrm{reflect}}=\{0.707107, 0.707107\}<br />
,~\vec{v}_{\mathrm{refract}}=\{0.636396, -0.771362\}</math><br />
<br />
The cosine values may be saved and used in the [[Fresnel equations]] for working out the intensity of the resulting rays.<br />
<br />
[[Total internal reflection]] is indicated by a negative [[radicand]] in the equation for <math>\cos\theta_2</math>, which can only happen for rays crossing into a less-dense medium (<math> n_2 < n_1</math>).<br />
<br />
==Total internal reflection and critical angle==<br />
[[File:Refraction internal reflection diagram.svg|thumb|250px|right|Demonstration of no refraction at angles greater than the critical angle]]<br />
{{Main|Total internal reflection}}<br />
When light travels from a medium with a higher refractive index to one with a lower refractive index, Snell's law seems to require in some cases (whenever the angle of incidence is large enough) that the sine of the angle of refraction be greater than one. This of course is impossible, and the light in such cases is completely reflected by the boundary, a phenomenon known as [[total internal reflection]]. The largest possible angle of incidence which still results in a refracted ray is called the '''critical angle'''; in this case the refracted ray travels along the boundary between the two media.<br />
<br />
[[Image:RefractionReflextion.svg|thumb|center|650px|Refraction of light at the interface between two media]]<br />
<br />
For example, consider a ray of light moving from water to air with an angle of incidence of 50°. The refractive indices of water and air are approximately 1.333 and 1, respectively, so Snell's law gives us the relation<br />
<br />
:<math>\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.333}{1}\cdot\sin\left(50^\circ\right) = 1.333\cdot 0.766 = 1.021,</math><br />
<br />
which is impossible to satisfy. The critical angle θ<sub>crit</sub> is the value of θ<sub>1</sub> for which θ<sub>2</sub> equals 90°:<br />
<br />
:<math>\theta_\text{crit} = \arcsin\left(\frac{n_2}{n_1}\sin\theta_2\right) = \arcsin\frac{n_2}{n_1} = 48.6^\circ.</math><br />
<br />
==Dispersion==<br />
{{Main|Dispersion (optics)}}<br />
<br />
Note that the law does not account for different wavelengths but the differences are usually miniscule enough. In many wave-propagation media, wave velocity changes with frequency or wavelength of the waves; this is true of light propagation in most transparent substances other than a vacuum. These media are called dispersive. The result is that the angles determined by Snell's law also depend on frequency or wavelength, so that a ray of mixed wavelengths, such as white light, will spread or disperse. Such dispersion of light in glass or water underlies the origin of [[rainbow]]s and other [[optical phenomena]], in which different wavelengths appear as different colors.<br />
<br />
In optical instruments, dispersion leads to [[chromatic aberration]]; a color-dependent blurring that sometimes is the resolution-limiting effect. This was especially true in [[refracting telescope]]s, before the invention of [[Achromatic lens|achromatic]] objective lenses.<br />
<br />
==Lossy, absorbing, or conducting media==<br />
{{see also|Mathematical descriptions of opacity}}<br />
In a conducting medium, permittivity and index of refraction are complex-valued. Consequently, so are the angle of refraction and the wave-vector. This implies that, while the surfaces of constant real phase are planes whose normals make an angle equal to the angle of refraction with the interface normal, the surfaces of constant amplitude, in contrast, are planes parallel to the interface itself. Since these two planes do not in general coincide with each other, the wave is said to be inhomogeneous.<ref>Born and Wolf, sec.13.2, "Refraction and reflection at a metal surface"</ref> The refracted wave is exponentially attenuated, with exponent proportional to the imaginary component of the index of refraction.<ref>Hecht, ''Optics'', sec. 4.8, Optical properties of metals.</ref><ref>S. J. Orfanidis, ''Electromagnetic Waves & Antennas'', sec. 7.9, Oblique Incidence on a Lossy Medium, [http://www.ece.rutgers.edu/~orfanidi/ewa/ch07.pdf]</ref><br />
<br />
==See also==<br />
*{{annotated link|Brachistochrone curve}} for a simple proof by Jacob Bernoulli<br />
*{{annotated link|Calculus of variations#Snell's law|Calculus of variations}}<br />
*{{annotated link|Computation of radiowave attenuation in the atmosphere}}<br />
*{{annotated link|Evanescent wave}}<br />
*{{annotated link|Hamiltonian optics}}<br />
*{{annotated link|List of refractive indices}}<br />
*{{annotated link|N-slit interferometric equation}}<br />
*{{annotated link|Reflection (physics)}}<br />
*{{annotated link|Snell's window}}<br />
*{{annotated link|Sellmeier equation|The refractive index vs wavelength of light}}<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[http://materiaislamica.com/index.php/History_of_Islamic_Physics_(Snell%27s_Law) Ibn Sahl and Snell's Law]<br />
* [http://www-rohan.sdsu.edu/~aty/explain/optics/discovery.html Discovery of the law of refraction]<br />
* [http://demonstrations.wolfram.com/SnellsLawOfRefractionWaveFronts/ Snell's Law of Refraction (Wave Fronts)] by Todd Rowland, [[Wolfram Demonstrations Project]]<br />
* [http://ilorentz.org/history/wallformulas/images/pages/page_4.html Snell's law on a wall in downtown Leiden] {{Webarchive|url=https://web.archive.org/web/20180427184259/http://ilorentz.org/history/wallformulas/images/pages/page_4.html |date=2018-04-27 }}<br />
*[http://www.boldmethod.com/learn-to-fly/navigation/shoreline-effect/ Shore line effect]<br />
<br />
{{authority control}}<br />
<br />
{{DEFAULTSORT:Snell's Law}}<br />
[[Category:Eponymous laws of physics]]<br />
[[Category:Geometrical optics]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Talk:Afghan%E2%80%93Sikh_Wars&diff=1223317207Talk:Afghan–Sikh Wars2024-05-11T09:09:41Z<p>Casteiswrong: /* Result 4 */ Reply</p>
<hr />
<div>{{Contentious topics/talk notice|topic=ipa}}<br />
{{WikiProject banner shell|class=C|1=<br />
{{WikiProject Afghanistan|importance=mid}}<br />
{{WikiProject Military history|South-Asian=yes|class=C|b1=no|b2=no|b3=yes|b4=yes|b5=yes}}<br />
{{WikiProject India|importance=low}}<br />
}}<br />
<br />
== Source bombardment ==<br />
<br />
*Jaques ,Tony.Dictionary of Battles and Sieges<br />
*Singh Ganda, ''Ahmad Shah Durrani: Father of Modern Afghanistan'', page=285<br />
*Anil Chandra Banerjee, ''The Khalsa Raj'', (Abhinav Publications, 1985), 78.<br />
*Ganda Singh, ''Maharaja Ranjit Singh: First Death Centenary Memorial''. Nirmal Publishers<br />
*Harnik Deol, Religion and Nationalism in India <br />
*Brief History of the Sikh Misls<br />
*J.S Grewal, The Sikhs of the Punjab <br />
*A Concise History of Afghanistan in 25 Volumes, Volume 14<br />
[[user:Ama975193]] has added each of these sources which seems to indicate the Sikhs won the war(s) against the Afghan/Durrani. A quote from each source would help to confirm this. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 05:52, 2 June 2018 (UTC)<br />
<br />
== Source misrepresentation ==<br />
<br />
[https://en.wikipedia.org/w/index.php?title=Afghan%E2%80%93Sikh_Wars&diff=next&oldid=929549372 This source] makes [https://books.google.com/books?id=PkVeBAAAQBAJ&pg=PA44&dq=Pashtun+Question+Unresolved+Key++Future++Pakistan+Afghanistan+On+a+sunny+afternoon+in+autumn&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiKh6rIiO7mAhVIU80KHeMfBzMQ6AEwAHoECAQQAg#v=onepage&q=Pashtun%20Question%20Unresolved%20Key%20%20Future%20%20Pakistan%20Afghanistan%20On%20a%20sunny%20afternoon%20in%20autumn&f=false no mention] of the Afghan Sikh wars. I have removed it. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 03:49, 6 January 2020 (UTC)<br />
:{{ping|Kansas Bear}} It does makes mention of many battles about this war.<br />
:Would you be using [https://books.google.com/books?id=XxwIDgAAQBAJ&pg=PA20&dq=afghan-sikh+wars#v=onepage&q=afghan-sikh%20wars&f=false this sourceinstead]? It provides overview of the wars fought between the two and the wars started from 1748 not 1751 contrary to this article.<br />
::Here is another [https://books.google.com/books?id=XWJxAAAAIAAJ source] written by a military expert and published by [[Jonathan Cape]], which makes it clear that "Sikhs had defeated the Afghans in a previous war, they reasoned that they could easily vanquish the British". <br />
::There is a clear case of Sikh victory against the Afghans. [[User:NavjotSR|NavjotSR]] ([[User talk:NavjotSR|talk]]) 05:23, 7 January 2020 (UTC)<br />
<br />
:*"''It does makes mention of many battles about this war.''"<br />
:::Not on the page number given. Proper citation works wonders. Page 45 of that book, starts off with: "The Taliban in Power".<br />
:*"''There is a clear case of Sikh victory against the Afghans.''"<br />
:::Fine. Bring a source, with a page number and quote. <br />
:::[https://books.google.com/books?id=XWJxAAAAIAAJ This source] brings up ''Remember you are an Englishman: a biography of Sir Harry Smith, 1787-1860'' Joseph H. Lehmann, Cape, Sep 15, 1977. Unviewable and unverifiable. <br />
:::[https://books.google.com/books?id=XxwIDgAAQBAJ&pg=PA20&dq=afghan-sikh+wars#v=onepage&q=afghan-sikh%20wars&f=false This source] gives an overview of the war, yet I am not seeing where it states the Sikhs won this war. Which page, specifically, is it stated? --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 05:53, 7 January 2020 (UTC)<br />
::::[https://books.google.com/books?id=XWJxAAAAIAAJ This source] concludes that: "Sikhs had defeated the Afghans in a previous war, they reasoned that they could easily vanquish the British", on page 228. [https://books.google.com/books?id=XxwIDgAAQBAJ&pg=PA20&dq=afghan-sikh+wars#v=onepage&q=afghan-sikh%20wars&f=false This source] is nonetheless detailing that Sikhs won all the battles. Why it should be controversial to state that Sikhs won the war? Sure we can't state that Sikhs won the war based on this single source but instead we can mention specific result about all 3 phases, and each of them would be 'Sikh victory'. [[User:NavjotSR|NavjotSR]] ([[User talk:NavjotSR|talk]]) 05:44, 18 January 2020 (UTC)<br />
::::::I would suggest you take [https://books.google.com/books?id=XWJxAAAAIAAJ This source] to [[Wikipedia:Reliable sources/Noticeboard]]. Accordingly, "[https://en.wikipedia.org/w/index.php?title=User_talk:Peacemaker67&diff=prev&oldid=937119339 We only use a result for the whole war that is in the reliable sources. It is OR to analyse the results of individual battles and decide on an overall result.]" --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 06:00, 23 January 2020 (UTC)<br />
<br />
Buddy the afghans lost. Why are you so salty? [[User:CapChecker123|CapChecker123]] ([[User talk:CapChecker123|talk]]) 20:07, 14 January 2021 (UTC)<br />
<br />
:Why are you trying to make this personal? Like [https://en.wikipedia.org/w/index.php?title=User_talk:Kansas_Bear&diff=prev&oldid=1001215093 here]? Either post a reliable secondary source with a page number to support your changes or you will be reported for [[WP:TE|disruptive editing]]. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 19:23, 18 January 2021 (UTC)<br />
<br />
Mate it’s not personal, you can report whatever you want, you’re literally deleting any additions to this page if it’s not your own. I will let the admins decide [[User:CapChecker123|CapChecker123]] ([[User talk:CapChecker123|talk]]) 01:29, 19 January 2021 (UTC)<br />
<br />
:Nope, I am restoring referenced information. As explained below you are engaging in [[WP:OR|original research]] and have chosen to edit war instead of discussion. Your choice. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 01:59, 19 January 2021 (UTC)<br />
<br />
It is original research, the sources I have used are approved by Oxford University and also is as recent as 2004. So just behave yourself and quit censoring this page [[User:CapChecker123|CapChecker123]] ([[User talk:CapChecker123|talk]]) 20:15, 19 January 2021 (UTC)<br />
<br />
*"''So just behave yourself and quit censoring this page''"<br />
:'''3rd time'''. Supply the page number, volume number and quote for your source. Since you appear to be unable to comply. Which means you are writing [[WP:OR|original research]]. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 00:04, 20 January 2021 (UTC)<br />
<br />
== 120.21.61.157 ==<br />
This IP is using references as misrepresentation of comments being added by him/her. Continue to vandalize page. [[User:WorldWikiAuthorOriginal|WorldWikiAuthorOriginal]] ([[User talk:WorldWikiAuthorOriginal|talk]]) 05:08, 23 February 2020 (UTC)<br />
<br />
== Sikh Territorial Gain, not Stalemate ==<br />
The Afghan Sikh wars resulted in Sikhs conquering several of cities/territories of Afghans. This is why the result though was originally Sikh Victory, was changed to Sikh Territorial Gains.<br />
<br />
:No source, just another opinion by an IP. Typical edit warring which is the only way they can "form consensus". Notice there is '''no discussion''' and there are no sources to back up their claim. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 17:35, 25 March 2020 (UTC)<br />
<br />
::Neither do you. It about what the article refers to if you can understand english. Typical reverts by you due to your own personal opinion and not coming to a mutual understand as previous editors have. On talk page here (pasted below) there was already sources shown to you which you neglected. Obviously, again because of your own personal opinion. So stop reverting changes even when sources are already there and the whole article already states that.<br />
This source concludes that: "Sikhs had defeated the Afghans in a previous war, they reasoned that they could easily vanquish the British", on page 228. This source is nonetheless detailing that Sikhs won all the battles. Why it should be controversial to state that Sikhs won the war? Sure we can't state that Sikhs won the war based on this single source but instead we can mention specific result about all 3 phases, and each of them would be 'Sikh victory'. NavjotSR (talk) 05:44, 18 January 2020 (UTC) <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/199.82.243.106|199.82.243.106]] ([[User talk:199.82.243.106#top|talk]]) </small> <!--Autosigned by SineBot--><br />
<br />
:Now we have a fictitious discussion and now you decide to take a questionable source, that makes an arbitrary comment on some undefined war, with a statement from a POV pusher to back your fairy tale? That source does not support what you continue to edit war into the infobox and the source is hardly reliable for this article. Typical POV pusher. <br />
*"''It about what the article refers to if you can understand english.''"<br />
:Typical POV pusher comment, a personal attack. *yawn* <br />
*"''This source is nonetheless detailing that Sikhs won all the battles.''"<br />
:More [[Wikipedia:OR|original research]].<br />
*"''Sure we can't state that Sikhs won the war based on this single source but instead we can mention specific result about all 3 phases, and each of them would be 'Sikh victory'.''"<br />
:This is [[Wikipedia:OR|original research]], another move by POV pushers.<br />
:So far, you have [[Wikipedia:OR]], [[Wikipedia:NPA|made a personal attack]] and made a [[Wikipedia:False consensus]]. Looks like you are the one pushing their own personal views and sentiments. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 18:15, 25 March 2020 (UTC)<br />
::Because you do not want to understand the opinion on others and jump to conclusion, now you have opted to go with [[Wikipedia:OR]], [[Wikipedia:NPA|made a personal attack]] and made a [[Wikipedia:False consensus]]. Again all due to your personal views, with no understanding of the article, and causing disruptive reverts. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/199.82.243.106|199.82.243.106]] ([[User talk:199.82.243.106#top|talk]]) 18:24, 25 March 2020 (UTC)</small> <!--Autosigned by SineBot--><br />
*"''Because you do not want to understand the opinion on others and jump to conclusion, now you have opted to go with [[Wikipedia:OR]], [[Wikipedia:NPA|made a personal attack]] and made a [[Wikipedia:False consensus]]. Again all due to your personal views, with no understanding of the article, and causing disruptive reverts.''"<br />
:::Wow. More unsubstantiated accusations. Why am I '''not''' surprised. <br />
*"''[https://en.wikipedia.org/w/index.php?title=User_talk:Kansas_Bear&diff=947287114&oldid=947244536 It was the last mutual and neutral decision as per article that the result was Sikh Territorial Gain instead of SIkh Victory or Afghan Victory or Stalemate.]''"<br />
:::This is your false consensus statement for all the viewers reading this. There was nothing mutual or neutral about it, and it was clearly '''not''' a decision. [https://en.wikipedia.org/w/index.php?title=User_talk:Kansas_Bear&diff=947244536&oldid=947244027 Which I explained to you and you ignored it since it refuted your fairy tale consensus].<br />
:::The unreliable source does not even support your POV pushing edit of the infobox. That is [[Wikipedia:OR|original research]]. Maybe you should learn the rules before edit warring your opinion into article(s).--[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 18:33, 25 March 2020 (UTC)<br />
::::I clearly know how to wikipedia works and have made edits to various article and never had any issues till now. You yourself have no resources and you are pointing finger at me? There was already a source shown to you but you just ignored it. Also when you go through the article, you can clearly understand what the result was because it wasn't one battle or two battle, it a result of all accumulative war. But due to your own POV, there can clearly be no mutual understanding. And you are just causing reverts without any consensus or source of you own. So end of discussion! No need to delete my comments like you tried to do on your own talk page. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/199.82.243.106|199.82.243.106]] ([[User talk:199.82.243.106#top|talk]]) 18:39, 25 March 2020 (UTC)</small> <!--Autosigned by SineBot--><br />
<br />
*"''I clearly know how to wikipedia works...''"<br />
:::::Clearly not. [[Wikipedia:False consensus]], [[Wikipedia:OR|original research]], and [[Wikipedia:NPA|personal attacks]], show otherwise.<br />
*"''There was already a source shown to you but you just ignored it.''"<br />
:::::Wrong. The source, which is not even about Sikhs or Afghans or their wars, makes an arbitrary statement about ''some'' war between the Sikhs and Afghans and does not support your edit. That is [[Wikipedia:OR|original research]].<br />
*"''But due to your own POV...''"<br />
*"'' Also when you go through the article, you can clearly understand what the result was because it wasn't one battle or two battle, it a result of all accumulative war.''"<br />
:::::I do not have a POV over this issue, clearly someone that claims ''false consensus'', ''uses original research'' and ''issues personal attacks against another editor'' has a POV to push. As it stands now, there is not a reliable source for the result of these wars and according to an admin, "''[https://en.wikipedia.org/w/index.php?title=User_talk:Peacemaker67&diff=prev&oldid=937119339 We only use a result for the whole war that is in the reliable sources. It is OR to analyse the results of individual battles and decide on an overall result.]''"<br />
*"''No need to delete my comments like you tried to do on your own talk page.''"<br />
:::::If you know "oh-so-much" about how Wikipedia works, then you know I can ban anyone from my talk page.<br />
*"'' So end of discussion!''"<br />
:::::Nope. I have proven your edit is [[Wikipedia:OR|original research]] and that the so-called source you wish to pin your opinion to, does not support your edit. So, no, this discussion is not over. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 19:14, 25 March 2020 (UTC)<br />
::::::You have proven nothing. And yes this discussion is over. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/199.82.243.105|199.82.243.105]] ([[User talk:199.82.243.105#top|talk]]) 19:36, 25 March 2020 (UTC)</small> <!--Autosigned by SineBot--><br />
<br />
== NPOV? ==<br />
<br />
Added by user:Abdhul-ghani1990;<br />
*"''The Afghans were utterly defeated by the Sikhs.[13] The Afghans Were no match to the Sikhs and were defeated.''"<br />
:Seriously? HAVE to mention they were defeated in both sentences? Even the battle of Jamrud article indicates the result of the battle is disputed. Nothing like pushing your own opinion.<br />
*"''Maharaja Ranjit Singh successfully absorbed and united the Sikh misls and took over other local kingdoms to create the Sikh Empire. This leveled the playing field, since the Sikhs finally were united, just like the Afghans.''"<br />
:What does this have to do with the Afghans? Nothing! More irrelevant information. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 18:45, 18 December 2020 (UTC)<br />
<br />
==Capchecker's response==<br />
The Sikhs did indeed win all 3 wars. What’s your agenda with deleting the factual outcome of the war? [[User:CapChecker123|CapChecker123]] ([[User talk:CapChecker123|talk]]) 20:06, 14 January 2021 (UTC)<br />
<br />
And why aren’t you writing the outcome of the third phase of the war. If the Sikhs did not win, does that mean the afghans won the wars? I don’t think so pal, so I’ll keep adding in the facts, and you can keep deleting, I’ll just add it back. It’s about time you stop censoring this page. [[User:CapChecker123|CapChecker123]] ([[User talk:CapChecker123|talk]]) 20:12, 14 January 2021 (UTC)<br />
<br />
:Why are you changing what referenced information is stating?[https://en.wikipedia.org/w/index.php?title=Afghan%E2%80%93Sikh_Wars&diff=1000360382&oldid=1000312739]<br />
:'''First request''' Your so-called source(Singh) does not have page numbers and is not listed in this article.<br />
:Why did you change this sentence<br />
*"''Ahmad marched on to [[Amritsar]], massacring the population and destroying the city...''"<br />
: to this;<br />
*"''Abadly marched on to [[Amritsar]], massacring the civilian population and destroying the holy city.''"<br />
:What the hell does this even mean? If you can not write legible English then you should not be editing English Wikipedia!<br />
:You also added;<br />
*"''''' Third Phase''': Decisive Sikh Empire victory, all of the [[Punjab]], [[Kashmir]], [[Peshawar Valley]] and [[Khyber Pass]] annexed by the Sikh Empire''" <br />
:'''Using Singh as a source, what page is all of this information on??'''<br />
:You also changed this<br />
*"''Afghans driven from country; Lahore and surronding regions taken by Sikhs''"<br />
:Using Mehta, page 303. That is not what Mehta states. That is source misrepresentation.--[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 21:08, 14 January 2021 (UTC)<br />
<br />
:Also, your addition of,<br />
*"[[Durrani occupation of Delhi (1757)]]"<br />
:Your source Mehta page 229 makes no mention of Sikhs. That is [[WP:OR|original research]] --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 00:02, 15 January 2021 (UTC)<br />
<br />
Your silly buddy, you clearly do not know what massacring the civilian population means. Civilians are people who live in a city. He massacred the inhabitants of Amritsar and then desecrated the Holy site. Typo error is a typo error, I don’t know why you’re so triggered. It’s just a history article. Have you got something personal at stake here? [[User:CapChecker123|CapChecker123]] ([[User talk:CapChecker123|talk]]) 17:02, 20 January 2021 (UTC)<br />
<br />
== Result of the war ==<br />
<br />
Can certain users stop editing and removing the outcome of these wars. The Sikhs won all of these wars. That is plain and simple fact. There’s no two ways about it. All gains that the afghans made into modern India/Pakistan were all annexed by the Sikh Empire. Why are users so salty at this fact. If annexing parts of an empire is not considered a victory, I’m not sure what is. Keep your personal biases out of this, the Afghans lost most battle and every war against Sikh misls/Empire. Plain and simple fact. I will keep updating the result as certain users are clearly just censoring or downplaying the outcome of the wars.<br />
<br />
Durrani invaded at least 9 times. After Sikh misls came to power. He was sent back to Kabul each time. Sikh empire under Ranjit Sikh pushed the afghans back to Kyber Pass territory. <br />
<br />
If I’m using my head, it’s quite clear the afghans lost all the wars, mainly because they failed to wipe out the Sikhs after multiple massacres. They then lost Punjab, Peshawar, and Kyber pass to the Sikhs. Sources state this, and it is just what happened, go cry to somewhere else with your salty censoring of the outcome of this war. [[User:CapChecker123|CapChecker123]] ([[User talk:CapChecker123|talk]]) 16:57, 20 January 2021 (UTC)<br />
<br />
== [[Afghan–Sikh Wars]] and [[Indian campaign of Ahmad Shah Durrani]] ==<br />
<br />
Hi there! I'm starting a discussion to ask whether these two articles are over the same exact topic. I was recently asked by [[User:Kansas Bear|Kansas Bear]] on my user talk page [[Special:Permalink/1005466401#Duplicate_page?|here]] if these two articles were inadvertent duplicates. I'm obviously no expert in this topic, so I wanted to start a discussion and ask other editors about this and get input. The timeline of these series of invasions appear to overlap, and I believe that the articles are referring to the two same countries. Are these two articles about the same series of wars, and if so - should they be merged? I'm going to ping [[User:HistoryofIran|HistoryofIran]] and [[User:Falcaorib|Falcaorib]] - as these editors have recently made multiple changes to this article. I'm also going to ping [[User:Zeex.rice|Zeex.rice]], as this user made recent changes to the other article. Thanks for looking into this! Please let me know. :-) Cheers - [[User:Oshwah|<b><span style="color:#C00000">~Oshwah~</span></b>]]<sup><small><b>[[User_talk:Oshwah|<span style="color:blue">(talk)</span>]] [[Special:Contributions/Oshwah|<span style="color:green">(contribs)</span>]]</b></small></sup> 04:54, 12 February 2021 (UTC)<br />
<br />
:The Indian campaign of Ahmad Shah Durrani includes battles with the Mughals,Marathas,Rajputs,Jats,etc.Because of this,it makes sense to have the two pages be seperate. [[User:Tarunveer Singh Aujla|Tarunveer Singh Aujla]] ([[User talk:Tarunveer Singh Aujla|talk]]) 04:46, 26 November 2022 (UTC)<br />
<br />
{{reply|utcursch}}? Your thoughts? --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 17:43, 2 March 2021 (UTC)<br />
<br />
: Sorry, but I haven't read much on the topic. Maybe drop a note at [[WT:IND]]? [[User:Utcursch|utcursch]] &#124; [[User talk:Utcursch|talk]] 02:51, 3 March 2021 (UTC)<br />
<br />
== Rv, disruption ==<br />
<br />
@Historyofiran.<br />
<br />
Explain how this is a disruption? [[User:BorisTheBulgar|BorisTheBulgar]] ([[User talk:BorisTheBulgar|talk]]) 21:32, 13 February 2021 (UTC)<br />
:The fact that you removed loads of well-sourced information? --[[User:HistoryofIran|HistoryofIran]] ([[User talk:HistoryofIran|talk]]) 21:39, 13 February 2021 (UTC)<br />
<br />
The sourced information is not relevant towards the Battle of Attock. Why is the conquests of Kashmir mentioned under the battle of attock? [[User:BorisTheBulgar|BorisTheBulgar]] ([[User talk:BorisTheBulgar|talk]]) 21:43, 13 February 2021 (UTC)<br />
<br />
The sources information is not relevant to the battle, when reviewing this page. I see that you tend to remove a large amount of information without actually adding anything to this article. Do you have a reason of why you only remove information from this article instead of adding any? [[User:BorisTheBulgar|BorisTheBulgar]] ([[User talk:BorisTheBulgar|talk]]) 21:45, 13 February 2021 (UTC)<br />
<br />
Refrain from 3RR please. [[User:BorisTheBulgar|BorisTheBulgar]] ([[User talk:BorisTheBulgar|talk]]) 21:45, 13 February 2021 (UTC)<br />
::The article is about Afghan–Sikh Wars, which the Battle of Attock amongst other things was part of. I'm the one removing large amount of information? Isn't that a bit ironic coming from you? [https://en.wikipedia.org/w/index.php?title=Afghan%E2%80%93Sikh_Wars&diff=1006617022&oldid=1003400369]. Instead of trying to give me advise regarding the rules, I suggest you read [[WP:RS]] and [[WP:DISRUPT]], thanks. --[[User:HistoryofIran|HistoryofIran]] ([[User talk:HistoryofIran|talk]]) 21:55, 13 February 2021 (UTC)<br />
<br />
What do you mean coming from me? What are you trying to insinuate? [[User:HistoryofIran|HistoryofIran]]<br />
You still haven't answered the question of why you only delete information instead of adding any?<br />
:I mean, the diff says it all. And if you insist; No, I only delete disruptive information, and whether I add information or not is-no offense-really none of your business. I do have 35 GA articles, so I'm not sure where you're getting this from. This has gone off rails, I'm out. --[[User:HistoryofIran|HistoryofIran]] ([[User talk:HistoryofIran|talk]]) 22:05, 13 February 2021 (UTC)<br />
<br />
Didn't really ask about your other articles, and quite frankly, your constant deletion of information on this article has literally no relevance with your other articles. I will add referenced information from referenced journals and textbooks. I will like to you see try and delete that information before I report you. Good day [[User:HistoryofIran|HistoryofIran]]<br />
:I will try my best. --[[User:HistoryofIran|HistoryofIran]] ([[User talk:HistoryofIran|talk]]) 22:22, 13 February 2021 (UTC)<br />
::{{ping|BorisTheBulgar}} Coming back after some time and resuming your removal of sourced information is highly disruptive. I would highly advise you to stop, or I will take this to [[WP:ANI]]. Either reach [[WP:CONSENSUS]] or leave the information alone. --[[User:HistoryofIran|HistoryofIran]] ([[User talk:HistoryofIran|talk]]) 13:06, 23 February 2021 (UTC)<br />
<br />
== Change to referenced information ==<br />
<br />
Show me where Mehta states "Afghan Victory", on page 303?<br />
<br />
What page does Lee state "Sikh Victory"?<br />
<br />
What page(s) does Lee state "Sikh offensive into Punjab Halted and recapture of [[Multan]]"?<br />
<br />
Malleson does not appear to be an historian. So all that information needs a reliable source.--[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 19:18, 3 October 2021 (UTC)<br />
<br />
<br />
And you answered NONE of my questions. Still waiting. And Malleson is still not a reliable source. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 23:06, 3 October 2021 (UTC)<br />
<br />
Nope. Still nothing. You saying you have answered my questions is not answering them. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 23:09, 3 October 2021 (UTC)<br />
<br />
Apparently you can not see. Still waiting for an explanation to your edits. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 23:31, 3 October 2021 (UTC)<br />
<br />
::Still no quotes to verify any of these edits.--[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 23:48, 3 October 2021 (UTC)<br />
:Apologize, I did not see your talk here and will respond accordingly. I was focused on my own in "reason for phase edifications"<br />
:Here is the claim to Lee. [https://archive.org/details/Book_1094/page/n125/mode/2up] and [https://archive.org/details/Book_1094/page/n149/mode/2up]. <br />
:I am going to replace Mallesons sources with better ones as I said. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:50, 3 October 2021 (UTC)<br />
::Here is also a quote from [https://archive.org/details/Book_1094/page/n149/mode/2up], "In January 1775 Arsala Khan persuaded the king to allow his musketeers to assemble inside peshawar prior to being sent to join the siege of MULTAN. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:54, 3 October 2021 (UTC)<br />
:::Also mehta was not the source I meant to use, I accidently must have overlooked it when I was editing. @[[User:Kansas Bear|Kansas Bear]] [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:56, 3 October 2021 (UTC)<br />
::::@[[User:Kansas Bear|Kansas Bear]] Also another source for the recapture of Multan. [http://prr.hec.gov.pk/jspui/bitstream/123456789/5209/1/188.pdf] [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:58, 3 October 2021 (UTC)<br />
:::::for source [http://prr.hec.gov.pk/jspui/bitstream/123456789/5209/1/188.pdf], page 165 and 166. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:01, 4 October 2021 (UTC)<br />
::::::@[[User:Kansas Bear|Kansas Bear]] Does this clear up Lee's source? And especially my added one as I said was going to replace Mallesons. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:01, 4 October 2021 (UTC)<br />
:::::::@[[User:Kansas Bear|Kansas Bear]] Please respond so this situation can be resolved. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:15, 4 October 2021 (UTC)<br />
{{od}}<br />
My apologies my phone must not have shown your section either. Do you have where Mehta states Afghan victory? You really need to write out the gov.pk source(along with page number(s), in case we get an anti-pakistan editor. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 00:21, 4 October 2021 (UTC)<br />
<br />
I don’t specifically have access to mehta’s source, But I didn’t plan on using that specifically, so IDRK. <br />
<br />
Also yeah, I’ll write it out in a momento, I mentioned page numbers below. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:23, 4 October 2021 (UTC)<br />
<br />
I’ll try and check mehta’s source as well to see if I can find anything from that that would also say so, so give me a bit. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:26, 4 October 2021 (UTC) <br />
<br />
:No rush. Everything checks out, except the Mehta. You can always add a source and change it to Afghan victory. Make sure it is quite explicit about that, this article gets hit frequently by vandals. I will self-revert. --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 00:31, 4 October 2021 (UTC)<br />
::@[[User:Kansas Bear|Kansas Bear]] Thanks, will try to see if I can find something for it as well. I apologize for saying you were disruptive editing, didn't notice your section. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 01:31, 4 October 2021 (UTC)<br />
:::Not a problem. Simple misunderstanding. Go forth and edit! --[[User:Kansas Bear|Kansas Bear]] ([[User talk:Kansas Bear|talk]]) 01:36, 4 October 2021 (UTC)<br />
<br />
== Reason for phase editifications ==<br />
<br />
Well, as continued from my edit summary, the second phase had already ignored those facts including zaman shahs campaigns, hence I extended them out with proper material, these conflicts were also VERY loose over time, as the fighting only irrstandarded over different periods of time, hence they were changed to these different phases that I implemented and still am working on to change. (mostly directed for user @[[User:Kansas Bear|Kansas Bear]]<br />
<br />
The old revision ignores afghan victories and also the campaigns of timur shah and zaman shah. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 22:46, 3 October 2021 (UTC)<br />
<br />
:will also be adding more sources in the time being while I am editing [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 22:47, 3 October 2021 (UTC)<br />
::@[[User:Kansas Bear|Kansas Bear]] I already explained why these phases are being shifted out into new sections, read here as I go on about why. You claiming malleson isn't a reliable source is questionable, and in action you are slightly right hence I have replaced some of his sourcing as you clearly saw I was doing. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:06, 3 October 2021 (UTC)<br />
:::You wanted to go to the talk page but are not responding whatsoever, you do realize this is considered disruptive editing? if you do not reply soon I will leave a complaint. @[[User:Kansas Bear|Kansas Bear]] [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:25, 3 October 2021 (UTC)<br />
<br />
[[User:Kansas Bear]], since Noorullah isn't supposedly answering your questions will answer them for you. I can't say anything on Mehta's claim since I don't have access to the book. However, I can confirm the claims backed up by Lee's book. Look at [https://archive.org/details/Book_1094/page/n125/mode/2up] and [https://archive.org/details/Book_1094/page/n149/mode/2up]. [[User:Kailanmapper|Kailanmapper]] ([[User talk:Kailanmapper|talk]]) 23:35, 3 October 2021 (UTC)<br />
<br />
:(I am noorullah) Kansas bear isn't responding but is talking on his talk page. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:39, 3 October 2021 (UTC)<br />
<br />
Multiple problems with the new changes abd the sources. First of all the sources referenced with First phase has false information about author. The PDF is a thesis written by Aashiq Muhammad Khan Durrani and the title is The last phase of Muslim rule in Multan. Third issue is the page number which was provided as 103 which had absolutely no information about Afghan Sikh war of first phase. Then the page number was removed. Now other sources, its just a link to the archive book. I already mentioned that, page numbers should be provided for verification of each phase that the source is referencing. If these informations cannot be provided then the content needs to be reverted. There is no need to remove the existing sources such as Mehta. Once again Malleson is not reliable source. [[Special:Contributions/134.195.198.201|134.195.198.201]] ([[User talk:134.195.198.201|talk]]) 20:59, 4 October 2021 (UTC)<br />
<br />
:1. The author is Sughra at [http://prr.hec.gov.pk/jspui/handle/123456789//3787]. Not false info about the author. <br />
:"103 which had absolutely no information about the Afghan Sikh war of first phase." The source states that the Afghans captured lahore and multiple other states from the Mughals. (they were supported by the sikhs in this conflict), this is apart of the First conflict with the Sikhs, as mentioned with the capture of Lahore and these varying states. <br />
:Page numbers were provided to all and you were just ignorant of 103. <br />
:You saying malleson is not a reliable source again makes no sense, his sources have already been removed and you are just going in circles talking about the same thing over and over again. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 22:42, 4 October 2021 (UTC)<br />
::Page 116 (on tp) also then states the 1758 recapture of Multan as for the second phase as well in cordination. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 22:44, 4 October 2021 (UTC)<br />
::you need to clear this up that what is mentioned on the pdf is the actual author or Shugra. And is Shugra historian? Abd why is ignorant about page 103 when it has no mention of Afghan Sikh war? Its about Afghan Mughal war. Why make unnecessary attempt to cite this as first phase? Also you have Malleson as the 4th phase reference. And no pages for the archive book for the phases you referenced which shows the result of your claims. Also page 101 and 102 says that Lahore was conquered as well as Multan in April and May. So how is first phase win for Afghan? Get your sources straight instead of deliberately citing incorrect information. [[Special:Contributions/134.195.198.201|134.195.198.201]] ([[User talk:134.195.198.201|talk]]) 23:24, 4 October 2021 (UTC)<br />
:::Did you not read the time periods between the first phase of the war and the second phase of the war?<br />
:::Lahore and Multan were recaptured in the second phase and you are blatantly ignoring this claiming I am citing incorrect information, look more carefully before neglecting everything a person has said against you.<br />
:::I already explained that the sikhs supported the mughals in the conflict, and as a result were defeated following the capture. You can see this at [[Indian campaign of Ahmad Shah Durrani]].<br />
:::" And no pages for the archive book for the phases you referenced which shows the result of your claims", You do realize you actually have to read in, not from the start and expect it to be exactly at the start, right? [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:43, 4 October 2021 (UTC)<br />
::::I will also requote this for you:<br />
::::"<br />
::::First Phase: November 1748 – April 1758<br />
::::Second Phase: April 1758 – 1773"<br />
::::The afghans lost the second phase, the second phase was where the sikhs recaptured Multan and Lahore, NOT THE FIRST PHASE. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:45, 4 October 2021 (UTC)<br />
:::::You are again, also ignoring the changes with the page numbers added on very clearly with sfns. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:55, 4 October 2021 (UTC)<br />
::::::(you are also reverting the page before I can fix the above ie mallesons source still at 4 which I was actually about to replace) [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 23:59, 4 October 2021 (UTC)<br />
::::::: you need to replace all your changes. Phase 1 starts 1751 and Mughal-Afghan war cannot be considered a Afghan-Sikh war nor has any such mention on page 103. Read 101 abd 102 where Afghans lost both Multan and Lahore in April and May 1758. You started replacing only after I told you about the errors. Sane issue with your sources. And do not expect readers to go through the whole archive book to verify your changes. Provide page numbers which references the results of each phase. [[Special:Contributions/134.195.198.201|134.195.198.201]] ([[User talk:134.195.198.201|talk]]) 00:04, 5 October 2021 (UTC)<br />
::::::::the results of each phase cannot be provided as a source because no book claims these as "phases". [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:08, 5 October 2021 (UTC)<br />
:::::::::you can only conclude phases from certain events such as in the first campaign, the fall of multan and lahore, which then preludes to the second phase as it starts in 1758. the first phase is what is considered in these terms from 1748 (which was when the afghans began campaigning for lahore but lost on first attempt), they had later returned and captured lahore, hence I would call that the end of phase 1. Phase 2 begins with the sikhs recapturing multan and reaking havoc on the durranis for the periods to follow until timur shah. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:10, 5 October 2021 (UTC)<br />
::::::::::Why would the campaign start in 1751? it makes no sense especially since the durranis were fighting in Lahore since 1748. Hence why 1748 is the chosen date, literally. You can even see this year in source [https://archive.org/details/Book_1094/page/n121/mode/2up] on page 121. It talks about campaigning against the sikhs as well. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:14, 5 October 2021 (UTC)<br />
:::::::::::As you can clearly see in the source, The sikhs were in lahore in 1748 as well. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:15, 5 October 2021 (UTC)<br />
::::::::::::And again, you are being completely ignorant, all page numbers were being provided with SFNS, which you still completely ignore and you are still rambling about there not being page numbers. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:18, 5 October 2021 (UTC)<br />
:::::::::::::Although, since 1751 is the petid date, I suppose it can count. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 00:20, 5 October 2021 (UTC)<br />
::::::::::::::phase cannot be concluded by one battle or capture of one city. Phase 1 result of your reference point to page 123. I do not see any mention of capture of Lahore by April 1758 on that page. Please check again. Also why 3rd phase, the offensive was halted in Punjab being mentioned? Afghans captured Multan should be enough. Why 4th phase is inconclusive? By 1799, page 160 states that Lahore was taken. And that is when Sikh Empire was established with Lahore as capital. [[Special:Contributions/134.195.198.201|134.195.198.201]] ([[User talk:134.195.198.201|talk]]) 00:58, 5 October 2021 (UTC)<br />
:::::::::::::::Sorry, 123 was the wrong source I meant to use drahans for that. Also a phase is concluded by the end of fighting, fighting had ended after the afghans captueed lahore until th esikhs returned in 1758, hence why I end the first phase there. <br />
:::::::::::::::Also for the 4th phase, the afghans captured lahore a total of 3 times and sacked it multiple times, however Zaman Shah had to withdraw from the city all 3 times due to internal issues, and the sikhs could never actually beat him in battle, hence why it is inconclusive. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 01:39, 5 October 2021 (UTC)<br />
::::::::::::::::actually i might merge phase 1 and 2 then [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 01:59, 5 October 2021 (UTC)<br />
:::::::::::::::::What do you think about the new changes and do you think it needs any changes? I fixed the dates to the appropriate times for now from what I know to when conflict started breaking out to determine phases better. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 02:16, 5 October 2021 (UTC)<br />
::::::::::::::::: Here are some changes. Zaman Shah didn't attack three times. Just 2 times. 1796 and 1799. 1796 he captured Lahore and returned but Sikh captured after he left. 1799 he recaptured again but on return to Peshawar, sources say that the Sikh army all along harried the Afghans and when crossing the river Jhelum, the sudden order of water swept away the men....when Shah Zaman and his remaining army reached Kandahar, they were exhausted. After that on page 162, it just states that 1800, Shah Zaman gathered any army to fight rebellious Ranjit Singh but doesn't mention about any capture of city of Lahore or anything. So how was this third invasion? This needs fixed. [[Special:Contributions/134.195.198.201|134.195.198.201]] ([[User talk:134.195.198.201|talk]]) 11:08, 5 October 2021 (UTC)<br />
::::::::::::::::::otherwise good effort. Made couple of fixes and rewordings as well and dates especially due to Sikh Interlude Period", from 1772-1780. [[Special:Contributions/134.195.198.201|134.195.198.201]] ([[User talk:134.195.198.201|talk]]) 12:06, 5 October 2021 (UTC)<br />
<br />
Zaman Shah marched on Lahore but didn’t capture Lahore in his third campaign because his brothers rose up before he could do anything, so I’ll fix that. But he still technically did a third invasion as it said he marched on Punjab, then was forced to retreat from his campaign after his brothers rose up. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 14:16, 5 October 2021 (UTC)<br />
:according to source, he technically marched third time but was cut short with return due to Instability back home. There were various skirmishes between 1800 and 1811. One of them was battle of kasur in 1807. So that is why I had 1800 as the date. [[Special:Contributions/134.195.198.201|134.195.198.201]] ([[User talk:134.195.198.201|talk]]) 15:14, 5 October 2021 (UTC)<br />
::rest all good effort made on your part. Appreciate it. [[Special:Contributions/134.195.198.201|134.195.198.201]] ([[User talk:134.195.198.201|talk]]) 15:43, 5 October 2021 (UTC)<br />
<br />
Alright we can keep it at 1807 then and thanks [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 16:39, 5 October 2021 (UTC)<br />
<br />
== footnote ==<br />
<br />
@[[User:MehmoodS|MehmoodS]] I added a note that states why the third war could be inconclusive, "Zaman Shah had captured and sacked Lahore 2 times, however he was forced to retreat back to Afghanistan due to internal issues and could not solidify his gains." [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 18:04, 31 October 2021 (UTC)<br />
:@[[User:Noorullah21|Noorullah21]] Good day to you. The note isn't necessary because the note doesn't comply with the source. When I read the source by Mr. Lee, it says that while returning, Sikhs pursued Shah Zaman and his forces, over pushing all the way to river Jhelum where Shah Zaman had no option but to cross the heavy terrain river where thousands of his soldiers died and the supplies and artilleries were sacked. Now when you read the sources by Mr. Lafont and Mr. Cunningham, it becomes more clear that it was strategy of the Sikhs to evacuate the city of Lahore before the arrival of Shah Zaman and then use Guerilla tactic to attack on their return. The source by Mr. Drahm also supports this even though it doesn't give more detail as other historians have about the strategy. So when you put all this information together, it can create conflicted opinions. So I would say that the note isn't necessary as it becomes a conflicted opinion and keeping the conflict of interest neutral, inconclusive is good enough without any note. Source is enough. [[User:MehmoodS|MehmoodS]] ([[User talk:MehmoodS|talk]]) 18:58, 31 October 2021 (UTC)<br />
::Source [http://prr.hec.gov.pk/jspui/bitstream/123456789/5209/1/188.pdf] on page 202 (inbook) and 216 (doc) states that the Afghans were successful in most of their campaigns (including the seizure of the rohtas fort), they had fielded very little losses, but had to retreat due to internal issues. [http://prr.hec.gov.pk/jspui/bitstream/123456789/5209/1/188.pdf] page 203 (inbook) and 217 (indoc) Shows Shah Zaman dispatching 20,000 men, in the following pages after it of course goes over his success in the region. (The sikhs ran away but did not return and did not plan to it seems until they had a better opportunity to strike, ie came the opportunity with Zaman having to leave due to Shah Mahmud. You can see this in page 204 and 205, and One of Zaman's generals had even consolidated some of his gains with the capture of Kot Kamalia. (page 205 inbook and 219 indoc) <br />
::The source you stated where "Sikhs pursued Shah Zaman and his forces, over pushing all the way to river Jhelum where Shah Zaman had no option but to cross the heavy terrain river where thousands of his soldiers died and the supplies and artilleries were sacked.", this was not true to an extent. The source says Shah Zaman was forced to retreat to deal with the Persians, but had to leave some of his supplies at the river were swept. RANJIT SINGH, who was UNDER Shah zaman at the time had recovered some of the guns, and as a result Shah Zaman rewarded him when he went to Peshawar, the sikhs did not pursue the afghans in this retreat. (page 206 inbook) and (220 indoc) <br />
::I hope you understand. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 22:03, 31 October 2021 (UTC)<br />
:::@[[User:MehmoodS|MehmoodS]] [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 22:04, 31 October 2021 (UTC)<br />
::::AbdeL's source also does not cover the issue of what happened. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 22:06, 31 October 2021 (UTC)<br />
:::::@[[User:Noorullah21|Noorullah21]]<br />
problem is that there are many historians who have mention the versions of this incident and relying on just one won't be justified. I am going to stick to discission to reliable sources only and not to any particular sites as claims are very conflicted through such sites. Lafont in his book [https://books.google.com/books?id=YrG_aJTgnw0C&pg=PA17#v=onepage&q&f=false] tells that 1797 Shah Zaman entered Lahore without any struggle and on his return appointed his general Ahmad Khan Shahanchi-Bashi who was then defeated and killed with Sikhs capturing the fort of Lahore. Also here is document by Cunningham [https://books.google.com/books?id=fVdEAAAAIAAJ&pg=PA119]. He tells that during the second occupation in 1798, Shah Zaman sent an advance army of 5000 who were attacked and dispersed on the Jhelum. And later he entered Lahore without any opposition. Later some RESULTLESS skirmishes took place but the designs of Mahmud led the ill fated king to withdraw to the west. And Mr. Lee's book, page 161, states that Sikhs pursued Afghans all along the river Jhelum where thousands swept away along with supplies and artilleries bogged down in the mud. These can create various notes based on these other sources which i was trying to explain can create conflict. That is why I was trying to explain that note doesn't help. [[User:MehmoodS|MehmoodS]] ([[User talk:MehmoodS|talk]]) 22:38, 31 October 2021 (UTC)<br />
<br />
@[[User:Noorullah21|Noorullah21]] I added Mr. Cunningham's reference as its more supportive towards inconclusive. Removed notes keeping your opinion in respect as it conflicted. Hope you are ok with this change and we can end this <br />
on good note. [[User:MehmoodS|MehmoodS]] ([[User talk:MehmoodS|talk]]) 22:52, 31 October 2021 (UTC)<br />
<br />
:oooooookkkkkkkkk @[[User:MehmoodS|MehmoodS]] [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 14:54, 1 November 2021 (UTC)<br />
<br />
== Semi-protected edit request on 6 May 2022 ==<br />
<br />
{{edit semi-protected|Afghan–Sikh Wars|answered=yes}}<br />
Edit the false information [[User:Jeep singh16|Jeep singh16]] ([[User talk:Jeep singh16|talk]]) 14:16, 6 May 2022 (UTC)<br />
:[[File:Red question icon with gradient background.svg|20px|link=|alt=]] '''Not done:''' it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a [[Wikipedia:Reliable sources|reliable source]] if appropriate.<!-- Template:ESp --> [[User:ScottishFinnishRadish|ScottishFinnishRadish]] ([[User talk:ScottishFinnishRadish|talk]]) 14:26, 6 May 2022 (UTC)<br />
<br />
== Copyright problem removed ==<br />
<br />
[[File:Copyright-problem.svg|32px]] Prior content in this article duplicated one or more previously published sources. The material was copied from: https://journals.pen2print.org/index.php/ijr/article/download/34/22. Copied or closely paraphrased material has been rewritten or removed and must not be restored, ''unless'' it is duly released under a compatible license. (For more information, please see [[WP:COPYRIGHT#Using copyrighted work from others|"using copyrighted works from others"]] if you are not the copyright holder of this material, or [[WP:Donating copyrighted materials|"donating copyrighted materials"]] if you are.)<br />
<br />
For [[WP:Copyrights|legal reasons]], we cannot accept [[WP:Copyrights|copyrighted]] text or images borrowed from other web sites or published material; such additions will be deleted. Contributors may use copyrighted publications as a source of ''information'', and, if allowed under [[fair use]], may copy sentences and phrases, provided they are included in quotation marks and [[WP:CS|referenced]] properly. The material may also be rewritten, provided it does not infringe on the copyright of the original ''or'' [[WP:Plagiarism|plagiarize]] from that source. Therefore, such paraphrased portions must provide their source. Please see our [[WP:NFC#Text|guideline on non-free text]] for how to properly implement limited quotations of copyrighted text. Wikipedia takes copyright violations '''very seriously''', and persistent violators '''will''' be [[WP:Blocking policy|blocked]] from editing. While we appreciate contributions, we must require all contributors to understand and comply with these policies. Thank you. <!-- Template:Cclean --> [[User:BalinKingOfMoria|BalinKingOfMoria]] ([[User talk:BalinKingOfMoria|talk]]) 02:22, 22 August 2022 (UTC)<br />
<br />
== Edit war? ==<br />
<br />
{{ping|Daredevils56|Noorullah21}} I'm concerned that an [[WP:EDITWAR]] might be shaping up:<br />
<br />
* Daredevils56 made [https://en.wikipedia.org/w/index.php?title=Afghan%E2%80%93Sikh_Wars&type=revision&diff=1105694597&oldid=1105657818&diffmode=source these edits]<br />
* Noorullah21 [https://en.wikipedia.org/w/index.php?title=Afghan%E2%80%93Sikh_Wars&diff=prev&oldid=1105522625&diffmode=source reverted them]<br />
* Daredevils56 [https://en.wikipedia.org/w/index.php?title=Afghan%E2%80%93Sikh_Wars&diff=prev&oldid=1105967904&diffmode=source readded them]<br />
<br />
According to [[WP:EPTALK]], it's probably a good idea at this point to start a discussion about this disagreement, and decide on next steps together (instead of continuing to revert back-and-forth).<br />
<br />
[[User:BalinKingOfMoria|BalinKingOfMoria]] ([[User talk:BalinKingOfMoria|talk]]) 18:53, 22 August 2022 (UTC)<br />
<br />
:@[[User:BalinKingOfMoria|BalinKingOfMoria]] I believe the issue ( @[[User:Daredevils56|Daredevils56]] ) me and him had have been resolved, the issue I had was that he was removing the phases. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 01:04, 23 August 2022 (UTC)<br />
<br />
== Peshawar sardars ==<br />
<br />
[[User:Noorullah21]] Peshawar sardars are led by Afghanis please read this https://archive.org/details/HistoryOfTheSikhsVol.VTheSikhLionOfLahoremaharajaRanjitSingh from page 181 [[User:Daredevils56|Daredevils56]] ([[User talk:Daredevils56|talk]]) 05:49, 24 August 2022 (UTC)<br />
<br />
And yes I agree that Sultan Mohammad Khan was on exile. but still he is an Afghani. [[User:Daredevils56|Daredevils56]] ([[User talk:Daredevils56|talk]]) 05:52, 24 August 2022 (UTC)<br />
<br />
== Regarding the old "Phases" ==<br />
<br />
I have decided to begin to phase out the old "phase" brought upon the Wikipedia page here. The reason I have done this is because it is old and inconsistent with sources provided which don't describe the war as an onset of phases. Alongside this, much of the early history is also very disregarded in its first phase and last phase(s) nonetheless, which is why I decided to remove them, if someone wishes to continue speak on the matter please share concerns here. [[User:Noorullah21|Noorullah21]] ([[User talk:Noorullah21|talk]]) 21:13, 30 January 2023 (UTC)<br />
<br />
== Semi-protected edit request on 3 March 2023 ==<br />
<br />
{{Edit semi-protected|Afghan–Sikh Wars|answered=yes}}<br />
Here in his article, it is mentioned that Ahmad shah didn't win a battle and went back to qandahar.. the ahmad shah abdali campaign was shows on based and biased history. [[Special:Contributions/39.40.5.99|39.40.5.99]] ([[User talk:39.40.5.99|talk]]) 06:58, 3 March 2023 (UTC)<br />
<br />
:[[File:Red question icon with gradient background.svg|20px|link=|alt=]] '''Not done:''' it's not clear what changes you want to be made. Please mention the specific changes in a [[WP:EDITXY|"change X to Y" format]] and provide a [[Wikipedia:Reliable sources|reliable source]] if appropriate.<!-- Template:ESp --> - @39.40.5.99 what ''specific'' changes do you wish to make to the article and what are your sources? [[User:ThethPunjabi|ThethPunjabi]] ([[User talk:ThethPunjabi|talk]]) 10:04, 3 March 2023 (UTC)<br />
<br />
== Result ==<br />
<br />
"Sikhs achieve hegemony over Punjab" looks odd since the Territorial changes pretty much already claim say that. "Sikhs seize control over Punjab, Khyber Pakhtunkhwa and Kashmir" with a bullet makes more sense. [[User:Lothyscraps|Lothyscraps]] ([[User talk:Lothyscraps|talk]]) 20:38, 28 March 2023 (UTC)<br />
<br />
== Azim Khan wikilink ==<br />
<br />
{{Edit semi-protected|ans=y}}<br />
Can we add a wikilink to [[Azim Khan]] in §'''Campaigns of Maharaja Ranjit Singh'''? While the ''Azim Khan'' article is wikilinked in the infobox, that has not been done in the body of the article. Wikilink on first use in the actual article text would be consistent with many of the other names found in the infobox. -- [[Special:Contributions/97.124.47.226|97.124.47.226]] ([[User talk:97.124.47.226|talk]]) 17:32, 6 July 2023 (UTC)<br />
:{{done}}<!-- Template:ESp --> [[User:Xan747|Xan747]] ([[User talk:Xan747|talk]]) 17:52, 6 July 2023 (UTC)<br />
<br />
== Result ==<br />
<br />
Can’t be a stalemate when one side clearly established control over the lands where the battles were being fought. All of Kashmir fell under sikh rule and majority of Punjab aswell. The afghans had no lands left in Punjab. War ended in 1837 after the battle of Jamrud. Even in 1838 Sikhs and afghans were on better terms. So no the Anglo-Afghan war did not cause the end of the afghan-sikh wars. [[User:Historian2325|Historian2325]] ([[User talk:Historian2325|talk]]) 07:07, 6 February 2024 (UTC)<br />
<br />
== Result ==<br />
<br />
This was a military statement with many regions nevertheless falling to the Sikhs. The Sikhs aimed to go deep into Afghanistan but failed partly because of the poor weather and because of their key commanders killed.<br />
<br />
Wazir Aqbar Khan requested the British to assist the Afghans after the battle of Jamrud to fight the Sikhs when the British chose to side with the Sikh Empire and 2 years later, the first Anglo-Afghan War began. [[User:Pathaan2024|Pathaan2024]] ([[User talk:Pathaan2024|talk]]) 15:45, 17 March 2024 (UTC)<br />
<br />
== Result ==<br />
<br />
Change result from “Sikh Victory” to “Military stalemate” which was agreed upon by wiki users prior to “Historian2325” began edit warring. His last edit was the final edit for the result prior to the extended protection for the page which thus, disallowed the result to be altered back to its original form. This needs to be changed back as the wiki user altered the result prior to another well known wiki user applied the protection without reviewing “Historian2325”s edit or to revert it back before the extended protection came into place. [[User:Pathaan2024|Pathaan2024]] ([[User talk:Pathaan2024|talk]]) 16:23, 17 March 2024 (UTC)<br />
<br />
:<s>Bad edit was done by Dunki2024 who has been indefinitely blocked. Result was “Rise of Sikh Empire” before Dunki2024 made the change. {{ping|Historian2325}} I hope this is good decision for you. {{ping|Noorullah21}}. </s>[[User:Dekhoaayadon|Dekhoaayadon]] ([[User talk:Dekhoaayadon|talk]]) 19:20, 17 March 2024 (UTC)<br />
::I also noticed something else; since neither side officially declared war, is it a wiser choice of words to change the page's title of "Afghan-Sikh wars" to Afghan-Sikh battles or skirmishes? There were no aims mentioned by either side and neither side declared war which is obligatory for war. [[User:Pathaan2024|Pathaan2024]] ([[User talk:Pathaan2024|talk]]) 05:26, 21 March 2024 (UTC)<br />
:<s>Were you Dunki2024 account?</s> [[User:Dekhoaayadon|Dekhoaayadon]] ([[User talk:Dekhoaayadon|talk]]) 19:20, 17 March 2024 (UTC) {{small|Sock of HaughtonBrit}}<br />
:Sikh victory is commonsense. Half of Pashtun land got taken over by the armies of righteousness. The gash created by the sword of Sikhs is still visible in the Durand line. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 09:09, 11 May 2024 (UTC)<br />
<br />
== Missing battle pages ==<br />
<br />
The pages of battle of Amritsar 1767, Amritsar 1797, gurjat 1797 and both Rohats 1764 and 1767 are all gone. Why were these pages deleted? [[User:Historian2325|Historian2325]] ([[User talk:Historian2325|talk]]) 14:13, 5 April 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=Muhammad_of_Ghor&diff=1223314865Muhammad of Ghor2024-05-11T08:39:20Z<p>Casteiswrong: almost got killed here</p>
<hr />
<div>{{leadcite comment}}<br />
{{Short description|Sultan of the Ghurid Sultanate (c. 1173–1206)}}<br />
{{Use dmy dates|date=January 2016}}<br />
{{Use Indian English|date=January 2016}}<br />
{{Infobox royalty<br />
| name = Muhammad of Ghor<br />
| title = {{ubl|Champion of Islam|Sultan-i-Ghazi|al-Sultan al-Azam|Sikander al-Thani (Second [[Alexander]])}}<br />
| image = Mu'izz al-Din Muhammad. AH 599-602 AD 1171-1206.jpg<br />
| caption = Gold coin of Muhammad from [[Ghazni]], for circulation in [[Central Asia]] and what is present-day Afghanista].<br />
| succession = [[Ghurid dynasty|Sultan of the Ghurid Empire]]<br />
| reign1 = 1173–1203 (with his brother [[Ghiyath al-Din Muhammad]])<br />
| coronation = <br />
| predecessor = [[Ghiyath al-Din Muhammad]]<br />
| successor = {{ubl|Ghor and Firuzkuh: [[Ghiyath al-Din Mahmud]]|Lahore and Delhi: [[Qutbu l-Din Aibak]]|Ghazni: [[Taj ad-Din Yildiz]]|Bamiyan: [[Jalal al-Din Ali]]|Bayana: [[Bahauddin Tughril]]|Bengal: [[Bakhtiyar Khalji]]|Multan: [[Nasir-ud-Din Qabacha]]|Herat: [[Husain ibn Kharmil]]|Sindh: [[Soomra dynasty|Bhungar II bin Chanesar]]}}<br />
| spouse = <br />
| royal house = [[Ghurid dynasty]]<br />
| father = [[Baha al-Din Sam I]]<br />
| mother = <br />
| religion = [[Sunni Islam]]<br />
| reign2 = 11 February 1203–15 March 1206 (as sole ruler)<br />
| birth_date = 1144<br />
| birth_place = [[Ghor]] (present-day Afghanistan)<br />
| death_date = {{date of death and age|1206|3|15|1144|df=y}}<br />
| death_place = [[Dhamiak|Damyak]] (present-day Pakistan)<br />
| place of burial = [[Ghazni]] (present-day Afghanistan)<br />
}}<br />
'''Mu'izz ad-Din Muhammad ibn Sam''' ({{lang-fa|معز الدین محمد بن سام}}; 1144&nbsp;– March 15, 1206), also known as '''Muhammad of Ghor''' or '''Muhammad Ghori''', was a ruler from the [[Ghurid dynasty]] based in the [[Ghor province|Ghor region]] of what is today central Afghanistan who ruled from 1173 to 1206. Muhammad and his elder brother [[Ghiyath al-Din Muhammad]] ruled in a [[dyarchy]] until the latter's death in 1203. Ghiyath al-Din, the senior partner, governed the western Ghurid regions from his capital at [[Firozkoh]] whereas Muhammad extended Ghurid rule eastwards, laying the foundation of [[Islamic rulers in India|Islamic rule]] in [[South Asia]], which lasted after him for nearly half a millennium under evolving Muslim dynasties.<br />
<br />
During his early career as governor of the southern tract of [[Ghurid Empire]], Muhammad subjugated the [[Oghuz Turks]] after a series of forays and annexed [[Ghazni]] where he was installed by [[Ghiyath al-Din Muhammad]] as an independent sovereign. Expanding the Ghurid dominion east of the [[Indus Delta]] from his base in Ghazni, Muhammad crossed the river [[Indus]] in 1175, approaching it through the [[Gomal Pass]] and captured [[Indian campaigns of Muhammad of Ghor#Conquest of Multan and Uch|Multan]] and [[Indian campaigns of Muhammad of Ghor#Uch|Uch]] from the [[Carmathians]] within a year. Afterwards, Muhammad took his army by the way of lower [[Sindh]], endeavoring to penetrate into present-day [[Gujarat]] through the [[Thar Desert]], only to end up getting wounded and routed [[Battle of Kasahrada|near Mount Abu at Kasahrada]] by a coalition of Rajput chiefs led by the [[Chaulukya dynasty|Chaulukya]] king [[Mularaja II|Mularaja]], which forced him to change his route for future inroads into the Indian Plains. Hence, Muhammad pressed upon the [[Ghaznavids]] and [[Siege of Lahore (1186)|uprooted them by 1186]], conquering the upper [[Indus Basin|Indus Plain]] along with most of the [[Punjab]]. After expelling the Ghaznavids from their last bastion, Muhammad, thus secured the [[Khyber Pass]], the traditional route of entry for invading armies into [[northern India]].<br />
<br />
Extending the Ghurid dominion further eastwards into the [[Gangetic Plain]], the Ghurid forces suffered a decisive reverse and Muhammad himself got wounded in engagement with the [[Rajput|Rajput Confederacy]] led by the [[Chahamanas of Shakambhari|Chahamana]] ruler [[Prithviraj Chauhan]] [[First Battle of Tarain|at Tarain]] in 1191. Muhammad returned to [[Khurasan]], and returned a year later with a vast army of mounted archers to secure a decisive victory in the [[Second Battle of Tarain|return engagement on the same battleground]] and executed Prithviraj shortly afterwards. He limited his presence in India afterwards, deputing the political and military operations in the region to a handful of elite slave commanders who swiftly [[Indian campaigns of Muhammad of Ghor|raided local Indian kingdoms]] and extended the Ghurid influence as far east as the [[Ganges delta]] in [[Bengal]] and regions to the north in [[Bihar]].<br />
<br />
After the death of Ghiyath al-Din Muhammad in 1203, Muhammad of Ghor ascended the throne of [[Firozkoh]] as well, becoming the supreme [[Sultan]] of the [[Ghurid Empire]]. Within a year or so, Muhammad suffered a devastating defeat [[Battle of Andkhud|at Andkhud]] against their Turkish rivals [[Khwarazmian Empire|Khwarazmians]] aided by timely reinforcements from the [[Qara Khitais]], which resulted in the Ghurid power ebbing out in most of the [[Khurasan]]. Muhammad quelled the widespread insurrection throughout his empire after the debacle and ordered the construction of a bridge over the [[Oxus River]] to launch a full-scale invasion of [[Transoxiana]] in order to avenge his defeat at Andkhud, although a rebellion by the [[Hindu]] [[Khokhars]] forced him to move towards the [[Salt Range]], where he brutually [[Battle of Jhelum (1206)|crushed the Khokhar revolt]] during his last campaign. <br />
<br />
On his way back, Muhammad of Ghor was assassinated on the bank of [[Indus]] at [[Dhamiak|Damyak]] on 15 March 1206, by the [[Ismaili Muslim|Ismāīlī]] emissaries while offering evening prayers. Muhammad's assassination led to the rapid decline of the [[Ghurid]]s and enabled [[Muhammad II of Khwarezm|Shah Muhammad II]] to annex remaining Ghurid territories west of the [[Indus River]] by 1215. However, his conquests east of the Indus in the [[Indian Subcontinent]], evolved into the formidable [[Delhi Sultanate]] under his slave commander [[Qutbuddin Aibak]].<br />
<br />
==Early life==<br />
===Birth===<br />
Muhammad of Ghor was born in the [[Ghur]] region of present-day west-central Afghanistan to the Ghurid ruler [[Baha al-Din Sam I]] who ruled his ancestral realm briefly before he died in 1149, when Muhammad of Ghor was a child.{{sfn|Khan|2008|page=38-39}} His name is variously transliterated as Muizuddin Sam, Shihabuddin Ghuri, Muhammad Ghori and Muhammad of Ghor.{{sfn|Lal|1992|page=27}} According to the [[Tabaqat-i-Nasiri]], his birth name was "Muhammad" which is vernacularly spelt as "Hamad" by the Ghurids. During his childhood, his mother used to call him "Zangi" due to his [[Dark skin|dark skin tone]]. After the coronation in Ghazni, he styled himself as "Malik Shihabuddin" and after his occupation of [[Khurasan]], he took the title of "Muizzuddin" or "Mu'izz al-Din".{{sfn|Nizami|1970|page=155-156}}<br />
<br />
The synchronous accounts did not write much about Muhammad's exact birth date, although based on the writings of [[Minhaj-i-Siraj|Juzjani]] - Muhammad was younger to Ghiyath al-Din by three years and few months, who was born in 1140. Therefore, Muhammad's birth year can be dated to 1144.{{sfn|Flood|2009|page=95}}<br />
<br />
===Accession to the throne===<br />
The early years of both Muhammad and his brother Ghiyath al-Din were spent in constant hardship. Their uncle [[Ala al-Din Husayn]] after his campaign in Ghazni, initially installed them as governors of Sanjah.{{sfn|Habib|1981|page=108}} However, their efficient administration of the province, made him doubtful of their uprise and seeing a possible challenge to his own authority, he ordered his nephews to be imprisoned in the castle of [[Gharjistan]].{{sfn|Habib|1981|page=108}} Although, they were released from the captivity by his son [[Sayf al-Din Muhammad]] after the death of his father in 1161.{{sfn|Thomas|2018|page=59}}{{sfn|Nizami|1998|page=181}} Sayf al-Din, later died in a battle against the nomadic [[Ghuzz Turks|Oghuzs of Balkh]].{{sfn|Wink|1991|page=138}}{{sfn|Habib|1981|page=109}}<br />
<br />
After their release from the captivity, "[[Ferishta|Tarik-i-Firishtah]]" states that the Ghurid siblings were reinstated in Sanjah, although the earlier account of "[[Tabaqat-i-Nasiri]]" stated that the hardship continued due to their financial conditions. Muhammad thus, took shelter in the court of his uncle [[Fakhr al-Din Masud|Fakhruddin Masud]] who held the principality of [[Bamiyan]] as vassal of their uncle Alauddin Husayn.{{sfn|Habib|1981|page=135}}<br />
<br />
Later, [[Fakhr al-Din Masud]] laid his own claim for the succession after Sayf al-Din death as the elder member of the Ghurid family. Muhammad helped his brother in suppressing the revolt of Fakhruddin who garnered a sizeable army in alliance with the chiefs of [[Balkh]] and [[Herat]] who both were executed in the battle, although Fakhruddin was reinstated in Bamiyan in 1163.{{sfn|Thomas|2018|page=47-48}}{{sfn|Bosworth|1968|page=163}} Afterwards, with the support of the remaining local Ghurid officers and "[[malik]]s", his brother succeeded Sayf al-Din to the throne in 1163 and initially placed Muhammad as a minor officer in his court, which result in him retiring (unhappy with his position) to the court of [[Sistan]] where he spend a whole season. However, later Ghiyath-al din sent an envoy to brought him back who subsequently placed him in charge of the southern part of the Ghurid domains which possibly included Istiyan and Kajuran.{{sfn|Habib|1981|page=135-136}}{{sfn|Nizami|1998|page=182}} <br />
<br />
During the early campaigns of Muhammad as a prince, he was instructed to subdue the [[Ghuzz Turks|Oghuz]] tribes whose power and influence began to wane, although they were still controlling extensive territories.{{sfn|Habibullah|1957|page=21}} He used [[Qandhar]] as a base and raided the principality of Oghuzs multiple times, before defeating them decisively along with Ghiyath al-Din and followed up their victory by conquering Ghazni in 1169 along with some other territories in what is present-day eastern Afghanistan.{{sfn|Habib|1981|page=109}}{{sfn|Wink|1991|page=138}}{{sfn|Habibullah|1957|page=21-22}} Soon, Muhammad's coronation took place in Ghazni in 1173 and his brother returned to [[Firuzkuh]] for the westwards expansion in [[Transoxania]].{{sfn|Nizami|1998|page=182}} Subsequently, Muhammad utilized the city of Ghazni as a launch pad to led a series of lucrative forays down to the [[Indus Delta]] and beyond. In 1174, Muhammad led an expedition against the [[Ghuzz]]s [[Sanjan (Khorasan)|of Sanquran]] in present-day Turkmenistan and subdued them.{{sfn|Wink|1991|page=143}} <br />
<br />
In 1175, Muhammad marched from Ghazni and helped his brother in the annexation of the cosmopolitan city of [[Herat]] and [[Pushang]] after defeating a former general of the [[Seljuk Empire|Seljuks]].{{sfn|Bosworth|1968|page=168-169}}{{sfn|Nizami|1998|page=182}} The Ghurid siblings advanced into the present-day Iran and brought [[Nasrid dynasty (Sistan)|Nasrid dynasty]] of [[Sistan]] under their sway whose ruler [[Nasrid dynasty (Sistan)#Nasrid maliks|Taj al-Din III Harb ibn Muhammad ibn Nasr]] acknowledged the Ghurid suzerainty and later sent his armies several times assisting the Ghurids in their warfares.{{sfn|Bosworth|1968|page=163}} Afterwards, Ghiyath al-Din captured [[Balkh]] and territories adjoining [[Herat]] in [[Khurasan]].{{sfn|Habibullah|1957|page=22}}<br />
<br />
===Title===<br />
After the death of Ghiyath Al-Din Muhammad – the senior partner in the dyarchy – Muhammad assumed the title of "Al-Sultan Al-Azam" which meant the "Greatest Sultan".{{sfn|Flood|2009|page=94}} On one of colonnade in the [[Qutb Minar]] along with some of his golden mints circulated in India – Muhammad is eulogized as the "Sikander Al-Thani". (Second Alexander){{sfn|Flood|2009|pages=106, 289}} <br />
<br />
Muhammad's courtier rhetorically aggrandize him as the champion of [[Islam]] styling him as the "Sultan-i-Ghazi" (sultan of the holy warriors) portraying his Indian expeditions as the engagement between the army of Islam (''Lashkar-i Islam'') and the army of infidels (''Lashkar-i Kuffar'').{{sfn|Flood|2009|page=106-107}}<br />
<br />
== Invasion of India ==<br />
{{Main article|Indian campaigns of Muhammad of Ghor}}<br />
<br />
===Early invasions===<br />
{{South Asia in 1175|right|{{center|Main South Asian polities in 1175, on the eve of the [[Ghurid Empire]] invasion of the subcontinent (orange line: Ghurid territorial conquests under Muhammad of Ghor from 1175 to 1205).<ref>{{cite book |last1=Schwartzberg |first1=Joseph E. |title=A Historical atlas of South Asia |date=1978 |publisher=University of Chicago Press |location=Chicago |pages=37, 147|isbn=0226742210 |url=https://dsal.uchicago.edu/reference/schwartzberg/pager.html?object=074}}</ref>}}|{{location map~ |South Asia |lat=24.5|N |long=75|E |label=|position=|label_size=|mark=Ghurid invasions in India (map overlay).png|marksize=225}}{{location map~ |South Asia |lat=30.5|N |long=67.5|E |label=|position=|label_size=|mark=Chess drt45.svg|marksize=35}}}}<br />
<br />
The Ghurid brothers ruling in a [[dyarchy]] with the senior partner Ghiyath al-Din Muhammad engaged in a protracted duel with the [[Khwarazmian Empire|Khwarazmians]] from his capital [[Firuzkuh]] situated in west-central [[Afghanistan]], while Muhammad expanded the Ghurid domains eastwards into the Indian plains from his capital at Ghazni.{{sfn|Flood|2009|page=89}} The expeditions into the Indian plains and the plunder extracted from the sacking of lucrative [[Hindu]] temples in the [[Gangetic Plain]], gave Muhammad access to a vast amount of treasure in Ghazni which according to chronicler [[Minhaj al-Siraj|Juzjani]] based on the authority of Muhammad's comptroller included 60,000 kg (1500 [[Maund|mann]]) of jewels.{{sfn|Jackson|2000|page=210}}<br />
<br />
Muhammad's [[Indian campaigns of Muhammad of Ghor|expeditions in the Indian subcontinent]] started against the [[Qarmatians]] ([[Sevener|sevener branch of Isma'ilis]]) who regained a foothold in [[Multan]], soon after the death of [[Mahmud of Ghazni]] who installed a [[Sunni]] governor there.{{sfn|Khan|2008|page=116}} Muhammad defeated the Qarmatian ruler Khafif in 1175 and annexed Multan.{{sfn|Wink|1991|page=245}} The defeat turned to be a death blow for the Qarmatian power in Multan, who never regained their influence in the region again.{{sfn|Hooja|2006|page=261}}<br />
<br />
After the conquest of Multan, Muhammad captured [[Uch]] which was situated south of the confluence of the rivers [[Chenab]] and [[Jhelum]]. His campaign in Uch is not mentioned in detail in the near contemporary accounts except [[The Complete History|Kāmil fit-Tārīkh]], although the detail in the text about his expedition in [[Uch]] is possibly blurred by a [[Indian campaigns of Muhammad of Ghor#Uch|legend associated with the Bhati Rajputs]]. Nonetheless, [[Firishta]], a later chronicler mentioned the year of Uch conquest as 1176. It was placed under Malik Nasiurdin Aitam until his death in the [[Battle of Andkhud]] in 1204. Afterwards, it was placed under Nasiruddin Qabacha.{{sfn|Nizami|1970|p=156}}<br />
<br />
During the course of his early invasions, Muhammad avoided [[Punjab]] and instead focused on lands bordering the middle and lower course of the [[Indus]]. Therefore, to outflank the Ghaznavids in Punjab and to open up an alternative route to the [[Northern India]], Muhammad turned south towards present-day [[Gujarat]] in [[Anhilwara]].{{sfn|Wink|1991|page=142}} Before entering in [[Anhilwara]], he laid siege to the fort of [[Nadol]] (around [[Marwar]]) and captured it after a short siege from [[Kelhanadeva]] along with sacking the [[Shiva]] temple in [[Kiradu temples|Kiradu]]. After marching through the dry [[Thar Desert]] south of [[Marwar]], the Ghurid army got exhausted, when they reached [[Mount Abu]] where they were routed [[Battle of Kasahrada|in the mountainous pass of Gadararaghatta]], by the [[Solanki (clan)|Solanki]] ruler [[Mularaja II]] who was also aided by other Rajput chiefs mainly the [[Chahamanas of Naddula|Naddula Chahamana]] ruler [[Kelhanadeva]] (who was earlier deposed by from [[Nadol]] by Muhammad), the [[Chahamanas of Jalor|Jalor Chahamana]] ruler [[Kirtipala]], and the [[Paramaras of Chandravati|Arbuda Paramara]] ruler Dharavarsha.{{sfn|Hooja|2006|p=262}} The Ghurid army suffered heavy casualties during the battle, and also in the retreat back across the desert to Ghazni.{{sfn|Wink|1991|p=143}} The defeat forced Muhammad to opt for the northern routes who thenceforth, concentrated on creating a suitable base in Punjab and northwest for further incursions into [[northern India]].{{sfn|Chandra|2007|page=68}}<br />
<br />
===Conquest of Punjab===<br />
{{Main|Siege of Lahore (1186)}}<br />
In 1179, Muhammad conquered [[Peshawar]] which was possibly ruled by the Ghaznavids.{{sfn|Lal|1992|page=109}} Thereafter, he advanced further and besieged [[Lahore]] in 1181, although [[Khusrau Malik]] managed to keep him around the borders of Lahore for few more years by sending tributes along with one of the Ghaznavid prince (Malik Shah) under his custody in Ghazni as a hostage. In 1182, Muhammad followed a southerly arc to the port city of [[Debal]] on the [[Arabian]] Sea coast of [[Sindh]], subjugating the [[Soomra dynasty|Soomras]].{{sfn|Nizami|1970|page=157-158}} In the subsequent years, he expanded and consolidated his conquests around present-day Pakistan and annexed [[Sialkot]] along with sacking [[Lahore]] and the countryside.{{sfn|Nizami|1970|page=158}}{{sfn|Chandra|2006|page=24}} After Khusrau Malik made an unsuccessful attempt to [[Siege of Lahore (1186)#Second raid|dislodge the]] Ghurid garrison in Sialkot, Muhammad made the final assault on [[Lahore]] and forced him to surrender after a short siege.{{sfn|Khan|2008|page=90}} He imprisoned Khusrau Malik in the fort of [[Gharchistan]], breaching his own agreement of safe conduct for his presence. Khusrau Malik was sent to [[Ghiyath al-Din Muhammad]] in [[Firuzkuh]] where he and all his kinfolks were executed before 1192.{{sfn|Nizami|1970|page=158}}{{sfn|Habib|1981|page=112}} Thus, ended the lineage of Ghaznavids and their historic struggle with the [[Ghurids]].{{sfn|Bosworth|1968|page=165}}<br />
<br />
After uprooting the Ghaznavids, Muhammad now established his sway over the strategic [[Indus Basin]] including most of the Punjab.{{sfn|Wink|1991|page=144}}{{sfn|Khan|2008|page=141-142}} He, appointed Mulla Sirajuddin who was earlier a high-ranking [[Qadi|Qāḍi]] in his father court, as the head of judicature department in the newly conquered Ghaznavid territories along with the charge of Multan. His son [[Minhaj-i Siraj Juzjani|Minhaj al-Siraj Juzjani]] (born 1193) later composed the [[Tabaqat-i-Nasiri]] in 1260 which is regarded as a monumental work from the medieval period on the [[Ghurid dynasty]] and the [[Delhi Sultanate]].{{sfn|Khan|2008|page=102}}{{sfn|Nizami|1970|page=158}}<br />
<br />
=== First Battle of Tarain ===<br />
{{Main|First Battle of Tarain}}<br />
In 1190, after consildating in [[Sindh]] and western Punjab, the Ghurid generals began to raid the eastern Punjab region and captured a castle - [[Bathinda]] in present-day [[Punjab, India|Punjab state]] on the northwestern frontier of [[Prithviraj Chauhan]]'s kingdom. After appointing a Qazi Zia-ud-Din of [[Tulak District|Tulak]] as governor of the fortress with 1200 horsemen, Muhammad received the news that Prithviraj's army, led by his vassal prince Govind Rai were on their way to besiege the fortress. The two armies eventually met near the town of [[Tarain]], 14 miles from [[Thanesar]] in present-day [[Haryana]]. The battle was marked by the initial attack of mounted Mamluk archers to which Prithviraj responded by counter-attacking from three sides and thus dominating the battle. Muhammad mortally wounded Govind Rai in personal combat{{efn|Historian Kishori Saran Lal states Govind Rai was struck in the mouth, but does not mention any mortal wounds.{{sfn|Lal|1992|p=111}}}} and in the process was himself wounded, whereupon his army retreated{{sfn|Roy|2004|p=41}} and Prithvīrāj's army was deemed victorious.<br />
<br />
According to Juzjani, Muhammad was carried away from the battleground in wounded state by a Khalji horsemen.{{sfn|Ray|2019|page=42}} A largely different account from Za'inul Masir claimed that Muhammad after being wounded in combat with Govindraja fell unconscious and his forces withdrew in disarray after assuming him to be dead, later a remnant of his soldiers arrived in the night and searched for his body at the battlesite. Muhammad in extremely critical situation recognised his soldiers, who rejoiced after finding him alive and took him from the battlefield in a litter to Ghazni.{{sfn|Habib|1981|page=113}} However, the version from Za'inul Masir is not corroborated by any other contemporary and later writers, which made its authenticity dubious and the version of Juzjani more credible.{{sfn|Nizami|1970|page=158}}<br />
<br />
The Ghurid garrison of Tabarhind under Ziauddin, held out for thirteen months before being capitulated. The Rajputs could not make quick progressions during the siege due to absence of [[siege engines]] on their part, which strengthened the position of Muhammad during these months to raise a formidable army.<ref>{{harvnb|Roy|2004|page=40–42}}: "Cavalry was not suited for laying siege to forts and Rajputs lacked both the siege machines and infantry to storm and destroy fortress walls. Tulaki was able to keep Prithviraj at bay for thirteen months. Within this time, Muhammad had raised 120,000 cavalry"</ref><br />
<br />
=== Second Battle of Tarain ===<br />
{{Main|Second Battle of Tarain}}<br />
[[File:The last stan of Rajputs against Muhammadans.jpg|thumb|290px|''The last stand of Rajputs'', depicting the [[Second Battle of Tarain]] in 1192]]<br />
<br />
After the defeat in Tarain, Muhammad meted out severe punishments to the [[Ghurid]], [[Khalji]] and [[Afghan (ethnonym)|Afghan]] "emirs" who fled during the battle. The wallets filled with grains were tied around their necks and under this condition they were paraded through Ghazni, those who refused were beheaded.{{sfn|Lal|1992|page=110}} The late medieval historian [[Ferishta]] further states on the testimony of folklore in Ghazni, that Muhammad vowed not to visit his royal harem and heal his wounds sustained in the battle till he avenged the humiliation of his defeat.{{sfn|Lal|1992|page=110-111}} [[Husain ibn Kharmil|Husain Kharmil]], a prominent Iranian general of the [[Ghurid]]s, was called from Ghazni with a large contingent along with other seasoned warlords like Mukalba, Kharbak and Illah.{{sfn|Nizami|1970|page=162}} Muhammad made necessary arrangements to counter the elephant phalanx of the Rajput forces by having them attack mock elephants made of mud and wood.{{sfn|Wink|1991|page=145-146}} The near contemporary chroniclers Juzjani and [[Abdul Malik Isami|Isami]] stated that Muhammad brought 120,000-130,000 fully armoured men to the battle in 1192.{{sfn|Wink|1991|page=145}} Ferishta placed the strength of Rajput army in the decisive battle at 3,000 elephants, 300,000 cavalry and infantry (most likely a gross exaggeration).{{sfn|Chandra|2006|p=25}}<br />
<br />
[[Prithviraj Chauhan]] had called his banners but hoped to buy time as his banners (other Rajputs under him or his allies) had not arrived.{{sfn|Wink|1991|page=109, 141}} Instead of engaging in direct confrontation as they did in the initial Battle of Tarain, the Ghurids adopted a strategy of deceit and diplomacy to overcome the [[Rajput]]s, as documented in Taj-ul Ma'asir by [[Hasan Nizami]]. Upon Ghori's arrival on the battlefield, Prithviraj, the Rajput leader, purportedly sent a formal message suggesting a peaceful resolution, stating, "It would be wise for you to return to your homeland, and we have no intention of pursuing you." In response, Ghori replied, indicating that he had come to face challenges on the directive of his ruling sibling and proposing the dispatch of an envoy to negotiate peace.<ref>{{Cite book|last=Singh|first=R. B.|url=https://books.google.com/books?id=NeX0xX0_2rkC|title=History of the Chāhamānas|publisher=N. Kishore|year=1964|location=Varanasi|pages=199–202,461|language=en}}</ref><br />
<br />
According to accounts from Hasan Nizami, Muhammad Ufi, and Firishta, it becomes evident that Ghori employed deception, and Prithviraj, considering it a genuine truce, accepted the proposal. Before the next day, the Ghurids attacked the Rajput army. The assault occurred before sunrise, catching the Chahamana army off guard as they had spent the night in a state of unawareness.{{sfn|Singh|1964|page=199-202}} Although they were able to quickly form formations, they suffered losses due to surprise attacks before sunrise. Juzjani attributed the success of the Ghurid army to the 10,000 elite mounted archers whom Muhammad stationed at a small distance from the elephant phalanx of the Rajput forces and which ultimately scattered the "infidel host".{{sfn|Wink|1991|page=109, 141}} Prithviraj was captured during the battle on the bank of river Saraswati (present-day [[Sirsa]]) and summarily executed.{{sfn|Wink|1991|page=145}} After the victory, Muhammad took over much of the Chahamana kingdom and sacked their capital [[Ajmer]] during which several Hindu temples were desecrated by the Ghurids in Ajmer.<ref>{{harvnb|Eaton|2000|page=108}}: "From Ajmer in Rajasthan, the former capital of the defeated Cahamana Rajputs – also, significantly, the wellspring of Chishti piety the post-1192 pattern of temple desecration moved swiftly down the Gangetic Plain"</ref><br />
<br />
Muhammad captured and placed strong garrisons at the strategic military stations of [[Sirsa]], [[Hansi]], [[Samana, Punjab|Samana]] and [[Kohram]].{{sfn|Sharma|1959|page=87}} Muhammad later installed Prithviraja's minor son [[Govindaraja IV]] as his [[puppet ruler]] on condition of heavy tribute.{{sfn|Sharma|1959|page=100}} However, later after a revolt by his uncle [[Hariraja]], Govindraja was forced to move towards [[Chahamanas of Ranastambhapura|Ranthambore, where he established a new dynasty of the Chahamanas]]. Hariraja, briefly dislodged the [[Ghurid]] garrison from [[Ajmer]], but was later defeated by [[Qutb ud-Din Aibak]]. Subsequently, Hairaja immolated himself on a funeral pyre and the Ghurids reoccupied Ajmer and placed it under a Muslim governor.{{sfn|Chandra|2006|page=26-27}} Soon after, [[Delhi]] was also captured by Muhammad and Qutb al-Din Aibak in 1193,{{sfn|Kumar|2002|page=9}} although in continuation with the policy adopted earlier in [[Ajmer]], a puppet Rajput scion was installed in Delhi on tribute. (possibly the son of Govindraja who died in [[Second Battle of Tarain|Tarain]]) However, he was soon deposed on the account of treason.{{sfn|Chandra|2006|page=27}}{{sfn|Thomas|2018|page=63}}<br />
<br />
While, Muhammad continued to carry raids in the [[North India|north Indian plain]], although later he got preoccupied with the Ghurid expansion in [[Transoxiana]] against the [[Khwarezmian Empire]] as his brother Ghiyath al-Din began to have health problems. Notwithstanding, Muhammad as per the writings of [[Fakhr-i Mudabbir]] and [[Minhaj-i Siraj Juzjani]], appointed Aibak as his administraitor of the Ghurid domains in [[North India]] after the [[Second Battle of Tarain]].{{sfn|Kumar|2002|page=20}}{{sfn|Habib|1981|page=117}}{{sfn|Khan|2008|page=17,105}} His lieutenants - Qutb ud-Din Aibak, [[Bahauddin Tughril]], [[Bakhtiyar Khalji]] and [[Taj al-Din Yildiz|Yildiz]] before his assassination, swiftly raided the local kingdoms and expanded his empire in the [[Indian Subcontinent]] up to [[Bengal|north-western parts of Bengal]] in east, Ajmer and [[Ranthambore Fort|Ranthambore]] ([[Rajasthan]]) in north and till the borders of [[Ujjain]] in south.{{sfn|Chandra|2006|page=36}}<br />
<br />
=== Further campaigns ===<br />
[[File:Bengal. Muhammad Bakhtiyar Khalji. 1204-1206.Struck in the name of Mu'izz al-Din Muhammad bin Sam, Dated Samvat 1262 (1204 AD).jpg|thumb|300px|[[Bengal]] coinage of [[Bakhtiyar Khalji]] (1204-1206). Struck in the name of Mu'izz al-Din Muhammad, dated [[Samvat]] 1262 (1204).<br>''Obverse'': Horseman with [[Nagari script|Nagari]] legend around: ''[[samvat]] 1262 [[Bhadra (Hindu calendar)|bhadrapada]]'' "August, year 1262". ''Reverse'': Nagari legend: ''srima ha/ mira mahama /da saamah'' "Lord Emir [[Mu'izz al-Din Muhammad|Mohammed [ibn] Sam]]".]]<br />
After Aibak consolidated the Ghurid rule in and around the [[Delhi|Delhi doab]], Muhammad himself returned to India to further expand down the [[Ganges Valley]]. Accordingly, in 1194, he crossed the [[Yamuna|Jamuna river]] with an army of 50,000 horsemen where he confronted the forces of the [[Rajput]] [[Gahadavala dynasty|Gahadavala]] king [[Jayachandra]] in the [[Battle of Chandawar]]. The Ghurid army was victorious, Jayachandra was killed in the battle, and much of his army was slaughtered. Following the battle, the Ghurids took the fort at Asni, where they plundered the royal treasure of the Gahadavalas, and went on to take the pilgrimage city of [[Varanasi]], which was looted and a large number of its temples destroyed.{{sfn|Chandra|2007|page=71}} The Gahadavala capital [[Kanauj]] was annexed in 1198.{{sfn|Chandra|2006|page=27}}{{sfn|Saran|2001|page=119}}<ref name="Asher11">{{cite book |last1=Asher |first1=Frederick M. |title=Sarnath: A Critical History of the Place Where Buddhism Began |date=25 February 2020 |publisher=Getty Publications |isbn=978-1-60606-616-4 |page=11 |url=https://books.google.com/books?id=JMHEDwAAQBAJ&pg=PA11 |language=en|quote=And then, in 1193, Qutb-ud-din Aibek, the military commander of Muhammad of Ghor's army, marched towards Varanasi, where he is said to have destroyed idols in a thousand temples. Sarnath very likely was among the casualties of this invasion, one all too often seen as a Muslim invasion whose primary purpose was iconoclasm. It was of course, like any premodern military invasion, intended to acquire land and wealth}}</ref> During this campaign, the Buddhist city of [[Sarnath]] was also sacked.<ref name="Asher11"/><ref name="Asher74">{{cite book |last1=Asher |first1=Frederick M. |title=Sarnath: A Critical History of the Place Where Buddhism Began |date=25 February 2020 |publisher=Getty Publications |isbn=978-1-60606-616-4 |page=74 |url=https://books.google.com/books?id=JMHEDwAAQBAJ&pg=PA74 |language=en}}</ref><br />
<br />
===Conquest of Bayana===<br />
{{Main|Siege of Gwalior (1196)}}<br />
Muhammad returned to the Indian frontier again around 1196 to consolidate his hold around the present-day [[Rajasthan]]. The territory of Bayana at the time was under the control of a sect of [[Jadaun Rajputs]]. Muhammad along with Aibak advanced and besieged Thankar whose ruler Kumarpal was defeated. Muhammad placed the fort under his senior slave [[Bahauddin Tughril]], who later established Sultankot and used it as his stronghold.<ref>{{harvnb|Ray|2019|page=44}}:"Shihabuddin again came to India in 1195-1196. This time he attacked Biyana, Kumarpal king of Bayana was a Rajput of the Yaddo Bhatti sect. Once the attack of Shihabuddin started, the king went to Thankar and camped there. After some time, he was forced to submit. Bahauddin Turghil was given the charge of Thankar"</ref><ref>{{harvnb|Hooja|2006|page=276}}:"Nizami's Taj-ul-Maasir informs us that in the year 592 of the Hijri calendar (i.e. AD 1196), Muhammad bin-Sam Ghori, and his lieutenant Qutb-ud-din Aibak marched towards Thangar [Tahangarh]. Thereafter, noted Nizami, that centre of idolatry became the abode of [God's] glory, following the taking of the hitherto impregnable fortress and the defeat of the local ruler, Kunwarpal (Kumarapal), whose life was spared. The administration of the fort and area around it was then conferred on Baha-ud-din Tughril by the Sultan. In a like manner, the Tabaqat-i-Nasiri records that Sultan Ghazi Muizzuddin conquered the fortress of Thankar [Tahangarh] in the country of Bayana, and after dealing with the Rai [i.e. Raja], gave the governance of it into the hands of Baha-ud-din Tughril. The latter improved the condition of the land so much that merchants and men of credit came to it from many parts of Hindustan and Khorasan. To encourage them to settle, they were given houses and goods in the area. Baha-ud-din Tughril later established Sultankot (near Bayana), and made that his military-base and reside"</ref> After the conquest of Thankar, Bahaurddin Turghil reduced the fort of [[Gwalior]] whose [[Parihar]] chief Sallakhanapala surrendered after a long siege and accepted the Ghurid suzerainty.<ref>{{harvnb|Nizami|1970|page=171}}: "In 592/1195-96 Muizzuddin again carme to India. He attacked Bayana, which was under Kumarapala, a Jadon Bhatti Rajput. The ruler avoided a confrontation at Bayana, his capital, but<br />
went to Thankar and entrenched himself there. He vas, howvever, compelled to surrender. Thankar and Vijayamandirgarh were occupied and put under Bahauddin Tughril. Mu'izzuddin - next marched towards Gwalior. Sallakhanapala of the Parihara dynasty, however, acknowledged the suzerainty of Muizzuddin"</ref> After the assassination of Muhammad, Tourghil styled himself as the [[Sultan]] in [[Bayana]].{{sfn|Khan|2008|page=33}}<br />
<br />
In 1197, [[Qutb ud-Din Aibak]] invaded [[Gujarat]] and [[Battle of Kasahrada (1197)|defeated]] [[Bhima II]] in [[Sirohi]] after a sudden attack and afterwards sacked his capital [[Anhilwara]]. Thus, Aibak avenged the rout of Muhammad at the same place in [[Battle of Kasahrada|1178]].{{sfn|Saran|2001|page=121}}<br />
<br />
==Struggle in Central Asia==<br />
Muhammad continued to aid his brother for the expansion in west against the [[Khwarezmian Empire|Khwarezmian]]s in the interlude of his eastwards expansion. Meanwhile, in the affairs of [[Khurasan]], [[Sultan Shah of Khwarezm|Sultan Shah]] was defeated by his brother [[Ala al-Din Tekish]] in alliance with the [[Qara Khitai]] troops and the later succeeded the throne of Khwarezm in December 1172. Sultan Shah fled to the Ghurid brothers and asked for their assistance in order to expel his brother Tekish. While they received him well, they refused to give him military aid against Tekish, with whom the Ghurids were on good terms till then.{{sfn|Habib|1992|page=41-42}} Sultan Shah, carved out his independent principality in [[Khurasan]] and began plundering the regions of [[Ghor]] along with his governor Bahauddin Turghil. Thus, Ghiyath al-Din asked for aid from Muhammad, who was occupied with his [[Indian campaigns of Muhammad of Ghor|Indian expeditions]] at the time, marched with his army from Ghazni. The Ghurid feudatories: Shamsuddin Muhammad of [[Bamiyan]] and Tajuddin of [[Herat]] joined them with their respective contingents against the [[Khwarezmian Empire|Khwarezmians]].{{sfn|Habib|1981|page=117-118}}<br />
<br />
The Ghurid forces decisively defeated [[Sultan Shah of Khwarezm|Sultan Shah]] on the banks of [[Marghab River|river Murgabh]] after months of campaigning and executed their governor of [[Herat]] Bahauddin Turghil while Sultan Shah fled to [[Merv]].{{sfn|Habib|1981|page=118}} The Ghurids followed their victory by recapturing [[Herat]].{{sfn|Habibullah|1957|page=23}} Sultan Shah died after a year in 1191 possibly due to the drug overdose.{{sfn|Habib|1981|page=118}} According to historian [[Abu Mohammed Habibullah|A.B.M. Habibullah]], the Ghurids could not annex any territory in [[Khurasan]] outside [[Herat]] which remained under the sway of [[Ala al-Din Tekish|Tekesh]]{{sfn|Habibullah|1957|page=23}} and who by 1193 captured much of the [[Persia]] along with the [[Caspian Sea|Trans-Caspian belt]].{{sfn|Habib|1981|page=119}} Conversely, [[C. E. Bosworth]] stated that Ghurids annexed some part of Khurasan after their victory in [[Merv]].{{sfn|Bosworth|1968|page=163}}<br />
<br />
===Later===<br />
{{Main|Battle of Andkhud}}<br />
Tekish died in 1200, which led to a brief period of struggle for the succession between [[Muhammad II of Khwarezm|Alauddin Shah of Khwarezm]] and his nephew Hindu Khan. The Ghurid siblings seized the opportunity and amidst the turmoil in the Khwarezmian house for succession, Muhammad and Ghiyath al-Din invaded and captured the oasis cities of [[Nishapur]], [[Merv]] and [[Tus, Iran|Tus]] and reached as far as [[Gorgan]]. The Ghurids, thus, for a short span established their sway over most of the Khurasan for first time in their history.{{sfn|Habibullah|1957|page=24}}{{sfn|Nizami|1998|page=185}} However, their success turned to be a short-term affair as Alauddin succeeded the throne in August 1200{{sfn|Habib|1992|page=43}} and soon after recaptured his lost territories by 1201.{{sfn|Habibullah|1957|page=25}} Despite the success against the Ghurids, Alauddin sent an envoy for diplomacy to Muhammad, probably in order to focus solely on overcoming from the suzerainty of [[Qara Khitai]]s by sougthing peace with the Ghurids. However, the attempt turned to be futile and Muhammad marched again with his forces on [[Nishapur]] which forced Alauddin to shut himself inside the city walls. Muhammad recaptured [[Tus, Iran|Tus]] along with [[Herat]] and sacked the country-side.{{sfn|Habib|1992|page=43-44}}<br />
<br />
Ghiyath al-Din Muhammad around this time died at Herat on 13 March 1203,<ref>{{harvnb|Habib|1992|page=44}}:"At this juncture Sultan Ghiyasuddin Ghuri died at Herat on 27 Jamadi I.A. H 599 (13 March A.D 1203)"</ref> after months of illness which briefly diverted Muhammad's attention from the existing state of affairs. Thus, taking advantage of his absence from [[Herat]] where he appointed his nephew Alp Ghazi, [[Khwarezmian Empire|Khwarezmian forces]] captured [[Merv]] and beheaded the Ghurid governor Karang there.{{sfn|Habib|1992|page=45}} Muhammad of Ghor, possibly to take over the entire [[Khwarezmian Empire]], laid siege to their capital [[Gurganj]], instead of [[Herat]] which was besieged by the [[Khwarezmian Empire|Khwarezmians]] after Ghiyath al-Din's death. Alauddin retreated on the Ghurid advance and desperately requested aid from the [[Qara Khitai]]s, who sent a sizeable army to aid the Khwarezmians. Muhammad, because of the pressure from the Qara Khitai forces was forced to relieve the siege and retreat. However, he was chased on his way to [[Firuzkuh]] and was decisively defeated in the [[Battle of Andkhud]] in 1204 by the combined forces of [[Qara Khitai]] and [[Kara-Khanid Khanate]] under Taniku and [[Uthman ibn Ibrahim]].{{sfn|Ray|2019|p=53-54}} He was allowed to return to his capital, after paying a heavy ransom to the [[Qara Khitai]] general Taniku (Tayangu) which included several [[elephants]] and gold coins.{{sfn|Biran|2005|page=68}} According to [[Minhaj-i Siraj Juzjani|Juzjani]], the negotiations between Muhammad and Taniku were arranged by [[Uthman ibn Ibrahim]] of [[Samarkand]] who do not want the "Sultan of Islam" to be captured by the infidels.{{sfn|Habib|1981|page=132-133}} Following the defeat, the Ghurids lost the control over most of the Khurasan except Herat and [[Balkh]].{{sfn|Nizami|1998|page=184}} Thus, Muhammad of necessity agreed for a cold peace with the [[Khwarezmian Empire|Khwarezmians]].{{sfn|Habib|1992|page=46}}<br />
<br />
==Final days==<br />
After the disaster of Andkhud and the subsequent rumours of Muhammad's death in the battle led to widespread insurrections throughout the Ghurid Sultanate, most notably by Aibak Beg, [[Husain ibn Kharmil|Husain Kharmil]] and by the governor of Ghazni, Yildiz, as well.{{efn|This Yildiz is not [[Taj al-Din Yildiz]] who was in charge of Kirman then.}}{{sfn|Habib|1981|page=133,153}} Muhammad first marched to Multan instead of Ghazni, where his slave general Aibak Beg (who rescued him in [[Battle of Andkhud]]) assassinated the Ghurid governor Amir Dad Hasan in a personal meeting and issued a fake decree of him being appointed by Muhammad as the new governor of Multan. Muhammad defeated Aibak Beg decisively and captured him in the battle. Afterwards, he marched towards Ghazni, where Yildiz mutinied earlier and seized the city.{{sfn|Nizami|1970|page=178}} On the advance of a vast army of Muhammad of Ghor, foreseeing an inevitable defeat, Yildiz and his aristocrats surrendered to Muhammad, who pardoned them.{{sfn|Habib|1981|page=134}}<br />
<br />
Thus, Muhammad successfully restored his empire to stability, after suppressing the mutineers and turned his attention towards the affairs of [[Central Asia]] again to avenge the rout at Andhkhud and to reclaim his holdings in [[Khurasan]]. Accordingly, by July 1205, Muhammad's governor of [[Balkh]] besieged [[Tirmidh]] in the present-day [[Uzbekistan]] and captured the city following a short siege, destroying the [[Qara Khitai]] garrison stationed there and placed it under his son.{{sfn|Biran|2005|page=69}} Afterwards, <br />
Muhammad ordered his viceory in the [[Bamiyan Valley]], [[Baha al-Din Sam II]] to construct a boat bridge and a castle across the river [[Oxus]] to facilitate the march of his armies in [[Transoxiana]].{{sfn|Habib|1981|page=134}}{{sfn|Chandra|2006|page=29}} Muhammad also directed his Indian soldiers to join him in the expedition against the Qara Khitais.{{sfn|Biran|2005|page=70}} However, soon another political unrest broke out which turned Muhammad towards Punjab again where he was eventually assassinated.{{sfn|Nizami|1970|page=179}}<br />
<br />
===Campaign against Khokhars===<br />
{{Main|Battle of Jhelum (1206)}}<br />
The [[Khokhar]] tribe whose influence extended from the lower [[Indus]] until Siwalik hills, arose in the wake of Muhammad's rout in the [[Battle of Andkhud]] and rebelled by disrupting the Ghurid communication chain between [[Lahore]] and Ghazni along with plundering [[Lahore]].{{sfn|Nizami|1970|page=178}} According to Juzjani, the [[Khokhars]] were hostile to Muslims and use to "torment every "[[Muslims|Musalman]] they captured".{{sfn|Habib|1981|page=134}}<br />
<br />
Hence, Muhammad marched from Ghazni in December 1205 for his last campaign in order to subjugate the [[Khokhars]]. The [[Khokhars]] led by Bakan and Sarkha offered a battle somewhere between the [[Chenab]] and [[Jhelum]] rivers and fought valiantly until the afternoon but Muhammad carried the day after [[Iltutmish]] arrived with a reserve contingent, whom Muhammad earlier stationed on the banks of [[Jhelum]]. Muhammad followed his victory by a large scale slaughter of the [[Khokhars]]. His armies also burnt down the forests where many of them took refuge while fleeing.{{sfn|Saran|2001|page=124}}{{sfn|Habibullah|1957|page=63}}<br />
<br />
[[Iltutmish]] was rewarded for his gallantry against the Khokhars with a presentation of special [[robe of honour]] from Muhammad. According to Juzjani, Muhammad also [[manumitted]] Illtutmish, despite the fact that his master Aibak who purchased him originally was still a slave along with other senior slaves of Muhammad who were not manumitted until that point.{{sfn|Nizami|1970|page=212-213}}<br />
<br />
==Assassination==<br />
[[File:The murder of Muhammad Ghori, A.D. 1206.jpg|thumb|Artistic description of Muhammad's assassination while offering evening prayers.<ref>{{cite book |title=Hutchinson's story of the nations, containing the Egyptians, the Chinese, India, the Babylonian nation, the Hittites, the Assyrians, the Phoenicians and the Carthaginians, the Phrygians, the Lydians, and other nations of Asia Minor |publisher=London, Hutchinson |page=166 |url=https://archive.org/details/hutchinsonsstory00londuoft/page/166/mode/1up}}</ref>]]<br />
<br />
After crushing the Khokhars, on his way back to his capital in Ghazni, Muhammad's caravan rested at [[Dhamiak]] near [[Sohawa]] (which is near the city of Jhelum in the [[Punjab (Pakistan)|Punjab]] province of modern-day Pakistan) where he was assassinated on March 15, 1206, by the [[Isma'ilism|Ismāʿīlī]] emissaries.{{sfn|Chandra|2007|page=73}}<br />
<br />
{{blockquote|<br />
The martyrdom of the sovereign of sea and land, Muizz-ud-din,<br><br />
From the beginning of the world the like of whom no monarch arose,<br><br />
On the third of the month Sha`ban in the year six hundred and two,<br><br />
Happened on the road to Ghazni at the halting-place of Damyak.<br />
|[[Tabakāt-i-Nāsirī]], 1260 CE.<ref>{{cite book |last1=Smith |first1=Vincent Arthur |title=The Oxford student's history of India |date=1921 |publisher=Oxford ; New York : Clarendon Press |page=113 |url=https://archive.org/details/oxfordstudentshi00smit/page/113/mode/1up}}</ref>}}<br />
<br />
According to some sketchy accounts regarding the identity of Muhammad's assassins, claimed that the assassins were sent by [[Muhammad II of Khwarezm]]. However, the Khwarezmians already curbed the Ghurid ambition in [[Transoxiana]] after the Andkhud debacle and were not facing any potential danger from them. Hence, historian [[Mohammad Habib]] theorizes that this speculation that the Ismaili assassins were sent by the Khwarezmian Shah is unlikely to be correct. Muhammad's assassins were probably sent by the Imam of [[Alamut]] whose [[Alamut Castle|castle]] he sacked during the Khurasan expedition.{{sfn|Habib|1981|page=142}}<br />
<br />
Some later accounts possibly with the genesis in the writing of Ferishta claimed that his assassins were Hindu Khokhars. In "[[Ferishta|Tarikh-i-Firishta]]", he stated that "Twenty Khokhar infidels" who were cowed down by him earlier attacked his carvan and stabbed him with a "[[dagger]]". However, this account is not corroborated by the earlier authorities. [[Minhaj-i Siraj Juzjani|Minhaj al-Siraj Juzjani]], [[Hasan Nizami]] and [[Al-Dhahabi|Shams ad-Dīn adh-Dhahabi]] all contemporary or near contemporary accounts confirmed that Muhammad was assassinated by a "[[Heresy|Heretic devote]]" ("fida-i-mulahida"). The story of his assassination by the Khokhars is probably an invention of later times based on indirect evidences.{{sfn|Habib|1981|page=153}} Muhammad's coffin was carried from [[Dhamiak]] to Ghazni by his [[Vizier]] Moidul Mulk along with other elites, where he was buried (Ghazni) in the mausoleum of his daughter.{{sfn|Habib|1981|page=134}}{{sfn|Saran|2001|page=125}}<br />
<br />
Despite the debacle of Andhkhud and the successive plummet of their western frontier, Muhammad's empire at the time of his assassination still spread out as far as Herat in the west, [[Zamindawar|Zamindawar Valley]] in the south and the [[Yasin Valley]] in the north-east.{{sfn|Jackson|2000|page=209-210}}<br />
<br />
== Succession ==<br />
Muhammad's only offspring was his daughter who died during his own lifetime.{{sfn|Habib|1981|page=145}} His sudden assassination in Damyak led to a period of struggle among his slaves and other senior Ghurid elites for the succession. The Ghurid aristocrats of Ghazni and [[Firuzkuh|Fīrūzkūh]] supported the succession of [[Baha al-Din Sam II]] from the Bamiyan branch, although his Turkic slaves supported [[Ghiyath al-Din Mahmud]] who was his nephew and son of his brother Ghiyath al-Din.{{sfn|Nizami|1970|page=200}} Nonetheless, Baha al-Din died on his march to Ghazni on 24 February 1206 due to illness.<br />
{{sfn|Thomas|2018|page=64}}{{sfn|Nizami|1998|page=184}}<br />
<br />
Thus, Muhammad was succeeded by [[Ghiyath al-Din Mahmud]] in 1206, although most of his conquests in the [[Ganges|Ganga Valley]] were in the grasp of his lieutenants – [[Qutb ud-Din Aibak]], [[Taj al-Din Yildiz]], [[Bahauddin Tughril]], [[Nasir ad-Din Qabacha]] and [[Muhammad Bakhtiyar Khilji]] who barely consulted Ghiyath al-Din Mahmud in their affairs. Notwithstanding, they still paid him a minimal tribute.{{sfn|Habib|1981|page=145-146}} During his reign, Mahmud also officially grant "[[manumission]]" on Aibak and Yildiz.{{sfn|Nizami|1970|page=201}}{{sfn|Wink|1991|page=188}} Thus, freed from the slavery and with investment of a "chatr" from Mahmud, Yildiz established himself as the king of Ghazni in 1206{{sfn|Wink|1991|page=188}} and Aibak in Lahore (who declared independence in 1208) established the [[Delhi Sultanate]]. Historian Iqtidar Alam Khan though, doubted that Aibak styled himself as the "Sultan" as it is not attested by the numismatic evidences.{{sfn|Khan|2008|page=17}} Soon, Mahmud was enforced to accept suzerainty of [[Muhammad II of Khwarazm|Alauddin Shah of Khawarazm]] as attested by the numismatic evidences in which he minted his name along with placing Alauddin's name in the "''khuṭbah''" until his assassination in 1212.<ref>{{Cite book|chapter=The Seljuk and the Khwarazm Shah|author=[[C. E. Bosworth]]|editor1=M. S. Asimov|editor2=C. E. Bossworth|url=https://books.google.com/books?id=lHDBzgEACAAJ |title=History of civilizations of central Asia: Volume IV The age of achievement: A.D. 750 to the end of the fifteenth century : (part one) The historical, social and economic setting |date=1998 |publisher=UNESCO|isbn=978-92-3-103467-1|page=171|language=en}}</ref><br />
<br />
Afterwards, the [[Khwarazmian Empire|Khwarazmians]] established their puppet government in the Ghurid lands, although Yildiz drove them back in 1213{{sfn|Thomas|2018|page=65}} before Alauddin eradicated the Ghurids and annexed Fīrūzkūh from [[Zia al-Din Ali]] in 1215<ref>{{cite book|chapter=Periphery as Centre: The Ghurids between the Persianate and Indic Worlds|author=Alka Patel|editor1-first = David |editor1-last = Morgan |editor2-first = Sarah |editor2-last = Stewart |title = The Coming of the Mongols |url = https://books.google.com/books?id=gbqKDwAAQBAJ |year =2017 |publisher = Bloomsbury Publishing |page=22|isbn = 978-1788312851 }}</ref> who either died as his captive (burned in [[Iran]]) or retired to [[Delhi]] in exile.{{sfn|Thomas|2018|page=64}} Alauddin also defeated and executed the last Ghurid ruler [[Jalal al-Din Ali]] from the Bamiyan line in the same year. Thus, the [[Ghurid|Šansabānī house]] was extirpated by 1215.{{sfn|Habib|1992|page=47}}{{sfn|Nizami|1998|page=184}} Yildiz was toppled from Ghazni around the same time as well who later fled to [[Delhi]] and laid his own claim for succession of the Ghurid conquests of Muhammad of Ghor. However, he was defeated and executed in 1216 by [[Iltutmish]] in [[Tarain]].{{sfn|Khan|2008|page=77}}<br />
<br />
===Relations with slaves===<br />
According to Juzjani's [[Tabaqat-i-Nasiri]] (c.1260), Muhammad enthusiastically used to purchase several [[Slavery|slaves]] during his lifetime who later according to Juzjani became renowned for their calibre in "east". Muhammad purchased a young [[Nasir ad-Din Qabacha|Qabacha]] who was sold into slavery and was later bestowed with the domains of [[Kerman]] and [[Sanjan (Khorasan)|Sanjar]] for his [[Iqṭāʿ]] by the Ghurid Sultan. He raised his slaves with affection and treated them as his sons and successors, after his despondency with his own [[Ghurid]] household in his later days.{{sfn|Nizami|1970|page=198-199}} According to another contemporary account of [[Fakhr-i Mudabbir]] who wrote under the patronage of [[Qutb ud-Din Aibak]] also emphasized upon the importance of each of the Turkish slaves ("bandagan") to Muhammad. He further panegyrise Aibak for enduring the trust of his master.{{sfn|Kumar|2006|page=83-84}} Muhammad's slaves played a key role in the expansion and consolidation of the [[Indian campaigns of Muhammad of Ghor#Further campaigns|Ghurid conquests in the Ganga-Jamuna doab]] when he was engaged in the affairs of [[Khurasan]] and amidst this also raised their own authority in the [[North India]] while still regarding Muhammad as their supreme master until his assassination.{{sfn|Kumar|2006|page=86}}<br />
<br />
Muhammad, later also organized matrimonial alliances among the families of his slaves in accordance with the practise of [[endogamy]]. The notable among these alliances, were the marriages of the daughters of [[Taj al-Din Yildiz]] to [[Qutb ud-Din Aibak]] and [[Nasir ad-Din Qabacha]]. Further, two daughters of Aibak were married to Qabacha.{{sfn|Kumar|2006|page=90-91}} This policy was continued by Aibak as well, who married his daughter to his slave [[Illtutmish]].{{sfn|Kumar|2006|page=92}}<br />
<br />
In popular traditions, when a courtier lamented that the Sultan (Muhammad) had no male heirs, he retorted:<br />
{{Quote|"Other monarchs may have one son or two sons; I have thousands of sons, my Turkish slaves who will be the heirs of my dominions, and who, after me, will take care to preserve my name in the Khuṭbah (Friday sermon) throughout these territories"|author=Muhammad of Ghor on his succession<ref>{{cite book |last1=Jackson |first1=Peter |title=The Delhi Sultanate: A Political and Military History |date=2003 |publisher=Cambridge University Press |isbn=978-0-521-54329-3 |page=31 |url=https://books.google.com/books?id=lt2tqOpVRKgC&pg=PA31}}</ref>}}<br />
<br />
== Legacy ==<br />
[[File:Ghurid_Empire_according_to_Schwartzberg_Atlas,_p.147.png|thumb|The largest extent of the Ghurid empire in 1200 during the reign of Muhammad Ghori and Ghiyath al-Din Muhammad]]<br />
<br />
During the [[dyarchy]] of Muhammad and his elder brother [[Ghiyath al-Din Muhammad]], the Ghurids emerged as one of the major powers in the eastern [[Islamic]] world.{{sfn|Jackson|2000|page=207}} The Ghurids reached the greatest extent of their territorial expansion, where they briefly ruled over a territory which spanned over 3000&nbsp;km from east to west. During these years, their empire stretched from [[Gorgan]] in eastern present-day Iran to [[Lakhnauti]] in present-day [[Bangladesh]] and from the foothills of the Himalaya south to [[Sindh]] (Pakistan).<ref>{{Cite book|author=David Thomas|chapter=Ghurid Sultanate|editor=John Mackenzie |url=https://books.google.com/books?id=W5SIjgEACAAJ|title=The Encyclopedia of Empire, 4 Volume Set |date=2016|publisher=Wiley|isbn=978-1-118-44064-3|quote=At its peak, the Ghurid empire, or perhaps more accurately the region across which its armies campaigned, briefly stretched for over 3000 km from east to west – from Nishapur in eastern Iran to Benares and Bengal and from the foothills of the Himalaya south to Sind}}</ref><ref>{{cite book |editor-last=Sarkar |editor-first=Jadunath |editor-link=Jadunath Sarkar |year=1973 |orig-year=First published 1948 |title=The History of Bengal |volume=II |location=Patna |publisher=Academica Asiatica |page=8 |oclc=924890 |quote=Bakhtyār fairly completed his conquest of the Varendra tract with the ... city of Gaur before the year 599 A.H.}}</ref>{{sfn|Habibullah|1957|page=24}}{{sfn|Nizami|1998|page=185}}<br />
<br />
[[Battle of Andkhud|The Catastrophe of Andkhud]] and the collapse of the [[Ghurids|Šansabānī dynasty]] within a decade of his assassination along with the [[rise of Genghis Khan]] who carved out the [[List of largest empires|largest contiguous empire in history]] made his short-lived successes in the Khurasan and [[Persia]] as less consequential in contrast to the [[List of Muslim states and dynasties|more substantial Islamic monarchs of Central Asia]].{{sfn|Habib|1981|page=144}} While, Muhammad was not much successful against his [[Khwarazmian Empire|Turkish adversaries]] in the [[Transoxiana]],{{sfn|Khan|2008|page=116-117}} notwithstanding, his success in the [[Indian Subcontinent]] had far flug consequences. The 13th century chronicle ''[[Jawami ul-Hikayat]]'', by [[Muhammad Aufi]], mentioned that the Sultan (Muhammad of Ghor) "[[khuṭbah]] was read in all the mosques from Herat to [[Assam]]".{{sfn|Habib|1981|page=132}} His decisive victory in the [[Second Battle of Tarain]] against the [[Rajput|Rajput forces]] of [[Prithviraja III]] laid to the establishment of the [[Delhi Sultanate]] by [[Qutb ud-Din Aibak]] which was further consolidated by his slave commander [[Illtutmish]].<ref>{{cite book |author1=Hermann Kulke |author1-link=Hermann Kulke |author2=Dietmar Rothermund |author2-link=Dietmar Rothermund|url=https://books.google.com/books?id=TPVq3ykHyH4C|title=A History of India|date=2004|publisher=Psychology Press |isbn=978-0-415-32919-4 |page=167|quote=The first battle of Tarain was won by the Rajput confederacy led by Prithviraj Chauhan of Ajmer. But when Muhammad of Ghur returned the following year with 10,000 archers on horseback he vanquished Prithviraj and his army}}</ref><ref>{{cite book|author1=Sugata Bose|author1-link=Sugata Bose|author2=Ayesha Jalal|author2-link=Ayesha Jalal|url=https://books.google.com/books?id=6ihNtzxy5GEC&q=Rajput|title=Modern South Asia: History, Culture, Political Economy|date=2004 |publisher=Psychology Press|isbn=978-0-415-30786-4|page=21|quote=It was a similar combination of political and economic imperatives which led Muhmmad Ghuri, a Turk, to invade India a century and half later in 1192. His defeat of Prithviraj Chauhan, a Rajput chieftain, in the strategic battle of Tarain in northern India paved the way for the establishment of first Muslim sultante|language=en}}</ref><ref>{{harvnb|Chandra|2007|p=73}}:"Muizzuddin Muhammad bin Sam has often been compared to Mahmud of Ghazni. As a warrior, Mahmud Ghazni was mnore successful than Muizzuddin, having never suffered a defeat in India or in Central Asia. He also ruled over a larger empire outside India. But it has to be kept in mind that Muizzuddin had to contend with larger and better organised states in India than Mahmud. Though less successful in Central Asia, his political achievements in India were greater"</ref> In the ensuring times, the [[Delhi Sultanate|Sultanate of Delhi]] turned to be the only major Islamic state that survived amongst the [[Destruction under the Mongol Empire|carnage in the Central Asia caused by the Mongols]] during the thirteenth century.{{sfn|Ray|2019|page=48}}{{sfn|Chandra|2007|page=84}}<br />
<br />
The Ghurids similar to the Ghaznavids were unpopular among their subjects of the [[Khurasan]]. According to Juzjani, Muhammad imposed heavy taxes, plundered and seized the property in [[Tus, Iran|Tus]] for the expanses of his army, which was committed for the protection of a Imam's shrine. These events eventually turned the people belligerent towards the Ghurids who retaliated when Muhammad besieged Gurganz and militarily supported the besieged Khwarezmian Shah who as a result collected a hughe army of 70,000 which eventually forced Muhammad to relieve the siege and retreat before being cornered by the [[Qara Khitai]] forces.{{sfn|Chandra|2006|page=22}}{{sfn|Bosworth|1968|page=164}}{{sfn|Habib|1992|page=45}}<br />
<br />
The Ghor region, however, during his reign did prospered and became a leading centre of learning and culture. He also gave grants to various theologians like Maulana Fakharudin Razi who preached the Islamic teachings in the backward regions of the Ghurid empire. Muhammad also briefly contributed in the archietectural aspect of his region, chiefly constructing distinctive kind of Islamic glazed tiles in his capital Ghazni.{{sfn|Ray|2019|page=48}}<ref>{{harvnb|Nizami|1970|page=182}}:"Muizzuddin's contribution to the cultural development of Ghur was not negligible. In fact it was he and his brother, Ghiyasuddin, who brought about a transformation in the culture-pattern of Ghur. He provided facilities to scholars, like Maulana Fakhruddin Razi, to spread religious education in those backward areas and helped in the emergence of Ghur as a centre of culture and learning. He made some note-worthy contribution ín the sphere of architectural traditions also. U. Scretto ascribes a unique type of glazed tile found at Ghazni to the period of Mu'izzuddin"</ref><br />
<br />
===Memorials===<br />
[[File:Shrine of Mu'izz al-Din Muhammad.JPG|thumb|Modern shrine to Muhammad, built by Pakistani scientist [[Abdul Qadeer Khan]] in 1994-1995, in [[Dhamiak]], [[Sohawa Tehsil]], Pakistan, where Muhammad was assassinated.<ref>{{cite news |last1=Yasin |first1=Aamir |title=The tomb of the man who conquered Delhi |url=https://www.dawn.com/news/1362383 |newspaper=Dawn (newspaper) |access-date=28 July 2021|language=en |date=8 October 2017}}</ref> Muhammad was actually buried in Ghazni, according to contemporary sources.]]<br />
* A shrine for Muhammad Ghori was built in Dhamiak by Pakistani scientist [[Abdul Qadeer Khan]] in 1994-1995 and was later handed over to the Punjab archaeology department.<ref name=":1362383">{{cite news |last1=Yasin |first1=Aamir |date=8 October 2017 |title=The tomb of the man who conquered Delhi |url=https://www.dawn.com/news/1362383 |newspaper=Dawn|location=Pakistan |access-date=28 July 2021}}</ref> Following his assassination in [[Dhamiak]], the corpse of Muhammad Ghori was actually placed in the mausoleum of his daughter in Ghazni.{{sfn|Habib|1981|page=134}}{{sfn|Saran|2001|page=125}}<br />
* Pakistani military named three of its [[medium-range ballistic missile]] [[Ghauri (missile)|Ghauri-I]], [[Ghauri-II]] and [[Ghauri-III]], in the memory of Mu'izz.<ref>{{cite web|url=http://www.atimes.com/atimes/South_Asia/GI03Df02.html |archive-url=https://web.archive.org/web/20061030030043/http://www.atimes.com/atimes/South_Asia/GI03Df02.html |url-status=dead |author=Sudha Ramachandran|archive-date=2006-10-30 |title=Asia's missiles strike at the heart |work=Asia Times |date=3 September 2005|access-date=28 July 2021}}</ref><br />
<br />
==Coins==<br />
<gallery class="center" widths="80px" heights="80px" perrow="3" mode="packed"><br />
File:Mu'izz al-Din Muhammad. AH 599-602 AD 1171-1206.jpg|Traditional gold coins of Muhammad from Ghazni for the circulation in [[Central Asia]] and Afghanistan<br />
File:Mu'izz al-Din Muhammad bin Sam. AH 599-602 AD 1171-1206. Pagoda coin with. Lakshmi seated facing.jpg|Muhammad's mint based on the [[Chahamanas of Shakambhari|Chahamana]]/[[Gahadavala dynasty|Gahadavala]] model<br />
File:Ghor1.jpg|Bull-and-horseman coins of Muhammad derived from the coinage of the [[Hindu Shahis]]<br />
</gallery><br />
<br />
The circulation of coins from Muhammad's court in Ghazni around 1199, confirming to the numismatic standards of the [[Islamic]] world, carried only [[Arabic]] calligraphy with the [[Six Kalimas|qalma]] and name of his sibling [[Ghiyath al-Din Muhammad]] along with his title on the obverse side of coin, whereas the reverse side of coin featured Muhammad's name and his title along with the title of [[Caliphate]].{{sfn|Flood|2009|page=103}} The paradigm of coins issued by Muhammad and Ghiyath al-Din shifted drastically from 1199 onwards to a further more orthodox ideologue with the Quranic verses on both sides. The radical shift to orthodoxy in the coinage is probably to propound their recent change of school from [[Karramiyya]] to the mainstream [[Hanafi]] and [[Shafi'i]] schools of Islam by Ghiyath al-Din and Muhammad respectively in order to embed themselves within cosmopolitan networks of the wider Islamic world and shed off their backward origin.{{sfn|Flood|2009|page=104}} <br />
<br />
The coins issued by Muhammad in northern India followed the Indian standards of weight and metallic purity.{{sfn|Eaton|2000|page=49-50}} The Ghurid coins in India except [[Bengal]], continued on the same paradigm of pre-conquest with the existing Hindu iconography juxtaposed with the name of Muhammad written in [[Sanskrit]], the language of northern Indian literate elites and not in the Arabic. {{sfn|Flood|2009|page=115-116}} Coins minted by Muhammad and his lieutenants in north India continued featuring the iconographic programme of [[Hindu]] deity [[Lakshmi]] (based on the existing pattern of Chahamanas) on one side and Muhammad's name in the [[Nāgarī script]] on other side written in [[Sanskrit]].{{sfn|Kumar|2002|page=30}} Similarly in [[Delhi]], the Ghurid circulation continued on the pre-conquest paradigm which had the iconography of [[Nandi (Hinduism)|Nandi Bull]] and a "Chahaman horsemen" juxtaposed with Muhammad's name written as "Shri Hammirah".{{sfn|Kumar|2002|page=29-30}}<br />
<br />
Finbarr Barry Flood commented on the notion of continuity of the pre-conquest arrangements in the numismatics as a pragmatic measure of Ghurids to met the economic realities in northern India.{{sfn|Flood|2009|page=116}} Sunil Kumar further elaborated on the basis of hoard evidences that the coins issued by Muhammad were accepted on the same scale by the local Indian financiers and bankers as the previous coins which were issued by the [[Rajputs]], despite a period of transition (regime change) in the political milieu of [[northern India]].<ref>{{harvnb|Kumar|2002|page=30}}: "As the hoard evidences from north India confirms, Mu'izzi wede valued as much as the earlier Rajput currencies and were fully assimilated within an economic word unimpressed with transition in the political realm"</ref><br />
<br />
==Popular culture==<br />
In the 2022 film ''[[Samrat Prithviraj]]'', [[Manav Vij]] portrayed Muhammad of Ghor.<ref>{{Cite web|title=Sources suggest that the movie is in the pre-production stage and the makers are making sure to match the deadline of November|url=https://english.newsnationtv.com/entertainment/bollywood/akshay-kumars-biopic-on-prithviraj-chauhan-to-see-sanjay-dutt-as-muhammad-ghori-233386.html|access-date=3 December 2020|website=News Nation|archive-date=27 February 2021|archive-url=https://web.archive.org/web/20210227115449/https://english.newsnationtv.com/entertainment/bollywood/akshay-kumars-biopic-on-prithviraj-chauhan-to-see-sanjay-dutt-as-muhammad-ghori-233386.html|url-status=live}}</ref><br />
<br />
==Notes==<br />
{{notelist}}<br />
<br />
== References ==<br />
{{Reflist}}<br />
<br />
==Bibliography==<br />
{{refbegin}}<br />
* {{cite book |last=Ahmed Farooqui|first=Salma|title=A Comprehensive History of Medieval India: From Twelfth to the Mid-Eighteenth Century |url=https://books.google.com/books?id=sxhAtCflwOMC |year=2011 |publisher=Pearson Education India |isbn=978-81-317-3202-1 }}<br />
*{{cite book | title =The Cambridge History of Iran, Volume 5: The Saljuq and Mongol periods | year =1968 | publisher =Cambridge University Press | location =Cambridge | editor-last =Frye | editor-first =R. N. | last =Bosworth | first =C. E. | author-link = C. E. Bosworth | chapter =The Political and Dynastic History of the Iranian World (A.D. 1000–1217) | pages = 1–202 | isbn =0-521-06936-X |url=https://books.google.com/books?id=16yHq5v3QZAC&pg=PA1}}<br />
* {{cite encyclopedia | first = C. Edmund | last = Bosworth | title = GHURIDS |url=http://www.iranicaonline.org/articles/ghurids | year = 2001 | encyclopedia = Encyclopaedia Iranica, Online Edition | access-date = 5 January 2014}}<br />
* {{Cite book|last=Biran|first=Michael|url=https://books.google.com/books?id=B934LaVBaz8C |title=The Empire of the Qara Khitai in Eurasian History: Between China and the Islamic World |date=2005|publisher=Cambridge University Press|isbn=978-0-521-84226-6 |language=en}}<br />
* {{Cite book|last=Chandra|first=Satish|author-link=Satish Chandra (historian)|url=https://books.google.com/books?id=L5eFzeyjBTQC |title=Medieval India: From Sultanat to the Mughals-Delhi Sultanat (1206–1526) – Part One |date=2006|publisher=Har-Anand Publications |isbn=978-81-241-1064-5|language=en}}<br />
* {{cite book |last=Chandra |first=Satish |author-link=Satish Chandra (historian)|title=History of Medieval India:800-1700|url=https://books.google.com/books?id=qHnHHwAACAAJ |year=2007|publisher=Orient Longman|isbn=978-81-250-3226-7}}<br />
* {{Cite book|last=Eaton|first=Richard|author-link=Richard M. Eaton|url=https://books.google.com/books?id=UEXZAAAAMAAJ |title=Essays on Islam and Indian History |date=2000 |publisher=Oxford University Press |isbn=978-0-19-565114-0 |language=en}}<br />
* {{Cite book |last=Flood |first=Finbarr Barry |url=https://books.google.com/books?id=OLNE_li8C10C |title=Objects of Translation: Material Culture and Medieval "Hindu-Muslim" Encounter |date=2009|publisher=Princeton University Press |isbn=978-0-691-12594-7 |language=en}}<br />
* {{Cite book |last=Habibullah|first=A. B. M.|author-link=Abu Mohammed Habibullah|title= The Foundation of Muslim rule in India |url= https://archive.org/details/in.ernet.dli.2015.199570/page/n71/mode/2up |year= 1957}}<br />
* {{Cite book |last=Habib|first=Mohammad|author-link=Mohammad Habib|chapter=The Asiatic Environment|editor1=Mohammad Habib |editor2=Khaliq Ahmad Nizami |title=A Comprehensive History of India: The Delhi Sultanat (A.D. 1206-1526) |volume=5 |edition=Second |year=1992|orig-year=1970|publisher=The Indian History Congress / People's Publishing House |url=https://books.google.com/books?id=_9cmAQAAMAAJ |oclc=31870180}}<br />
* {{Cite book|last=Habib|first=Mohammad|author-link=Mohammad Habib|url=https://books.google.com/books?id=iQ1uAAAAMAAJ |title=Politics and Society During the Early Medieval Period: Collected Works of Professor Mohammad Habib |date=1981 |publisher=People's Publishing House |language=en}}<br />
* {{Cite book|last=Hooja |first=Rima |url=https://books.google.com/books?id=qqd1RAAACAAJ|title=A History of Rajasthan |date=2006|publisher=Rupa & Company|isbn=978-81-291-1501-0}}<br />
* {{Cite book |last=Jackson |first=Peter|author-link=Peter Jackson (historian)|url=https://brill.com/display/book/edcoll/9789004491991/B9789004491991_s014.xml |title=The Fall of the Ghurid Dynasty|date=2000|publisher=Brill |isbn=978-90-04-49199-1|language=en}}<br />
* {{Cite book|chapter=Service, Status, and Military Slavery in the Delhi Sultanate:Thirteenth and Fourteenth Centuries|last=Kumar|first=Sunil|editor1=Indrani Chatterjee|editor2=[[Richard M. Eaton|Richard Eaton]]|url=https://books.google.com/books?id=Nsh8NHDQHlcC |title=Slavery and South Asian History|date=2006|publisher=Indiana University Press |isbn=978-0-253-11671-0 |language=en}}<br />
* {{Cite book|last=Kumar|first=Sunil |url=https://books.google.com/books?id=MF9uAAAAMAAJ |title=The Present in Delhi's Pasts |date=2002 |publisher=Three Essays Press |isbn=978-81-88394-00-5 |language=en}}<br />
* {{cite book|last=Khan|first=Iqtidar Alam|url=https://books.google.com/books?id=URluAAAAMAAJ |title=Historical Dictionary of Medieval India |date=2008|publisher=Scarecrow Press |isbn=978-0-8108-5503-8 |language=en}}<br />
* {{Cite book |last=Lal|first=Kishori Sharan|author-link=K. S. Lal|url=https://books.google.com/books?id=hxZuAAAAMAAJ |title=The Legacy of Muslim Rule in India |date=1992 |publisher=Aditya Prakashan |isbn=978-81-85689-03-6 |language=en}}<br />
* {{Cite book|chapter=The Ghurids|last=Nizami|first=K. A.|author-link=K. A. Nizami|editor1=M. S. Asimov|editor2=C. E. Bossworth|url=https://books.google.com/books?id=lHDBzgEACAAJ |title=History of civilizations of central Asia: Volume IV THe age off achievement: A.D. 750 to the end of the fifteenth century : (part one) The historical, social and economic setting |date=1998 |publisher=UNESCO|isbn=978-92-3-103467-1 |language=en}}<br />
* {{Cite book |last=Nizami|first= K. A.|author-link=K. A. Nizami |chapter= Foundation of the Delhi Sultanat|editor1=Mohammad Habib |editor2=Khaliq Ahmad Nizami |title=A Comprehensive History of India: The Delhi Sultanat (A.D. 1206–1526) |volume=5 |edition=Second |year=1970|publisher=The Indian History Congress / People's Publishing House |url=https://books.google.com/books?id=_9cmAQAAMAAJ |oclc=31870180}}<br />
* {{Cite book|last=Ray|first=Aniruddha|author-link=Aniruddha Ray|url=https://books.google.com/books?id=jNSNDwAAQBAJ |title=The Sultanate of Delhi (1206–1526): Polity, Economy, Society and Culture |date=2019|publisher=Routledge |isbn=978-1-000-00729-9}}<br />
* {{Cite book |last=Roy |first=Kaushik |url=https://books.google.com/books?id=jpXijlqeRpIC |title=India's Historic Battles: From Alexander the Great to Kargil |date=2004 |publisher=Orient Blackswan |isbn=978-81-7824-109-8 |language=en}}<br />
* {{Cite book|chapter=The Turkish Conquest of Northern India|last=Saran|first=Paramatma|editor=S. Ramakrishnan|url=http://archive.org/details/struggleforempir05bhar |title=History and Culture of the Indian People, Volume 05, The Struggle For Empire |date=2001|orig-year=1957|publisher=Bharatiya Vidya Bhavan}}<br />
* {{cite book |last=Sharma |first=Dasharatha |author-link=Dasharatha Sharma |title=Early Chauhān Dynasties |publisher=S. Chand / Motilal Banarsidass |year=1959 |isbn=9780842606189 |url=https://books.google.com/books?id=n4gcAAAAMAAJ }}<br />
* {{Cite book|last=Thomas|first=David|url=https://books.google.com/books?id=6h2_DwAAQBAJ |title=The Ebb and Flow of the Ghūrid Empire|date=2018|publisher=Sydney University Press |isbn=978-1-74332-542-1|language=en}}<br />
* {{Cite book|last=Wink|first=Andre|author-link=Andre Wink|url=https://books.google.com/books?id=75FlxDhZWpwC |title=Al-Hind the Making of the Indo-Islamic World: The Slave Kings and the Islamic Conquest: 11th–13th Centuries |date=1991 |publisher=BRILL| isbn=9004102361 |language=en}}<br />
{{refend}}<br />
<br />
==External links==<br />
{{Ghurid dynasty}}<br />
<br />
{{Authority control}}<br />
<br />
{{DEFAULTSORT:Muizz al-Din}}<br />
[[Category:1144 births]]<br />
[[Category:1206 deaths]]<br />
[[Category:Muslim period in the Indian subcontinent]]<br />
[[Category:12th-century Iranian people]]<br />
[[Category:13th-century Iranian people]]<br />
[[Category:Ghurid dynasty]]<br />
[[Category:Muslim monarchs]]<br />
[[Category:Murdered Persian monarchs]]<br />
[[Category:Assassinated Iranian people]]<br />
[[Category:13th-century murdered monarchs]]<br />
[[Category:History of Ghor Province]]<br />
[[Category:History of Khorasan]]<br />
[[Category:Slave traders]]<br />
[[Category:Slave owners]]</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=User:Casteiswrong&diff=1223310178User:Casteiswrong2024-05-11T07:36:51Z<p>Casteiswrong: ←Created page with 'My IP account which I don't use anymore: 2405:6E00:B71:3000:81A1:CE20:EE4E:20C2 ~~~~'</p>
<hr />
<div>My IP account which I don't use anymore: [[User talk:2405:6E00:B71:3000:81A1:CE20:EE4E:20C2|2405:6E00:B71:3000:81A1:CE20:EE4E:20C2]] [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 07:36, 11 May 2024 (UTC)</div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=User_talk:Hu741f4&diff=1223309962User talk:Hu741f42024-05-11T07:33:48Z<p>Casteiswrong: Reply</p>
<hr />
<div><br />
You have good friends up ur sleeve my brother, probs Hussein. Don't forget we have consensus in the parliament lol <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2405:6E00:B71:3000:81A1:CE20:EE4E:20C2|2405:6E00:B71:3000:81A1:CE20:EE4E:20C2]] ([[User talk:2405:6E00:B71:3000:81A1:CE20:EE4E:20C2#top|talk]]) 23:42, 1 November 2022 (UTC)</small> <!--Autosigned by SineBot--><br />
: What do you mean?<br />
[[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 14:09, 2 November 2022 (UTC)<br />
<br />
:Nice meeting you again old friend after a long time. I meant there is consensus amongst the general public about the etymology of the word "Sherwani" and since, the parliament is the peak representative body of the public, I used it instead. Thought you were smart enough to figure this out lol. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 07:33, 11 May 2024 (UTC)<br />
<br />
== Welcome! ==<br />
Hi Hu741f4! I noticed [[Special:Contributions/Hu741f4|your contributions]] and wanted to welcome you to the Wikipedia community. I hope you like it here and decide to stay.<br />
<br />
As you get started, you may find this short tutorial helpful:<br />
<br />
{{Clickable button 2|Help:Introduction|Learn more about editing|class=mw-ui-progressive|style=margin-left: 1.6em;}}<br />
<br />
Alternatively, the [[Wikipedia:Contributing to Wikipedia|contributing to Wikipedia]] page covers the same topics.<br />
<br />
If you have any questions, we have a friendly space where experienced editors can help you here:<br />
<br />
{{Clickable button 2|Wikipedia:Teahouse|Get help at the Teahouse|style=margin-left: 1.6em;}}<br />
<br />
If you are not sure where to help out, you can find a task here:<br />
<br />
{{Clickable button 2|Wikipedia:Task Center|Volunteer at the Task Center|style=margin-left: 1.6em;}}<br />
<br />
Happy editing! <!-- Template:Welcome--> [[User:I dream of horses|I dream of horses]] [[Special:Contribs/I dream of horses|(Contribs)]] [[User talk:I dream of horses|(Talk)]] 19:21, 30 July 2022 (UTC)<br />
<br />
Thank you! [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 19:23, 30 July 2022 (UTC)<br />
<br />
== October 2022 ==<br />
<br />
Per Wikipedia policity [[WP:BRD]] you should open a talk page thread on that page and garner a consensus as dictated. A new consensus takes time, usually several weeks. It is not a matter of simply posting your rationale and restoring that image. Best regards, [[User:Fowler&amp;fowler|<span style="color:#B8860B">Fowler&amp;fowler</span>]][[User talk:Fowler&amp;fowler|<span style="color:#708090">«Talk»</span>]] 22:13, 6 October 2022 (UTC)<br />
<br />
== Important ==<br />
<br />
{{ivmbox | image = Commons-emblem-notice.svg |imagesize=50px | bg = #E5F8FF | text = This is a standard message to notify contributors about an administrative ruling in effect. ''It does '''not''' imply that there are any issues with your contributions to date.''<br />
<br />
You have shown interest in '''[[India]], [[Pakistan]], and [[Afghanistan]].''' Due to past disruption in this topic area, a more stringent set of rules called [[Wikipedia:Arbitration Committee/Discretionary sanctions|discretionary sanctions]] is in effect. Any administrator may impose [[Wikipedia:Arbitration Committee/Discretionary sanctions#Sanctions|sanctions]] on editors who do not strictly follow [[Wikipedia:List of policies|Wikipedia's policies]], or the [[Wikipedia:Arbitration Committee/Discretionary sanctions#Page restrictions|page-specific restrictions]], when making edits related to the topic.<br />
<br />
To opt out of receiving messages like this one, place {{tlx|Ds/aware}} on your user talk page and specify in the template the topic areas that you would like to opt out of alerts about. For additional information, please see the [[Wikipedia:Arbitration Committee/Discretionary sanctions#Guidance for editors|guidance on discretionary sanctions]] and the [[Wikipedia:Arbitration Committee|Arbitration Committee's]] decision [[Wikipedia:Requests for arbitration/India-Pakistan|here]]. If you have any questions, or any doubts regarding what edits are appropriate, you are welcome to discuss them with me or any other editor.<br />
}}<!-- Derived from Template:Ds/alert --> [[User:Akshaypatill|Akshaypatill]] ([[User talk:Akshaypatill|talk]]) 08:09, 18 October 2022 (UTC)<br />
<br />
== Muhammad of Ghor ==<br />
<br />
I have reverted your last edit. The discussion is on the talk page. Please check the discussion. [[Talk:Muhammad_of_Ghor]] [[User:Akshaypatill|Akshaypatill]] ([[User talk:Akshaypatill|talk]]) 08:13, 18 October 2022 (UTC)<br />
<br />
Ok [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 08:29, 18 October 2022 (UTC)<br />
<br />
== WikiProject Medicine ==<br />
<br />
A [[WP:WikiProject]] is a group of editors who like to work together on articles. You're welcome to join us at [[Wikipedia:WikiProject Medicine]]. It's a good place to ask questions or to help each other out. If you'd like to, you're also welcome to join the informal, low-key contest about adding citations to articles: https://outreachdashboard.wmflabs.org/courses/Wikipedia/WikiProject_Medicine_reference_campaign_2023?enroll=qyoufwds (All you have to do is sign up at that link, and then edit normally. Everything else is automated.) [[User:WhatamIdoing|WhatamIdoing]] ([[User talk:WhatamIdoing|talk]]) 19:36, 15 February 2023 (UTC)<br />
<br />
== February 2023 ==<br />
<br />
{{{icon|[[File:Information orange.svg|25px|alt=Information icon]]}}} Please do not add your own point of view to Wikipedia articles, as you did to [[Mercury(II) chloride]]. Doing so violates Wikipedia's [[Wikipedia:Neutral point of view|neutral point of view policy]].<br />
<br />
I had already pointed out to you the second part of [https://en.wikipedia.org/w/index.php?title=Mercury(II)_chloride&diff=prev&oldid=1139912590 this] in our earlier interaction [https://en.wikipedia.org/w/index.php?title=Sulfuric_acid&diff=prev&oldid=1139181196 here]: there is only one Latin work attributed to [[Abu Bakr al-Razi|al-Razi]] scholars regard as partially authentic, which is the {{lang|la|Liber secretorum Bubacaris}}. If you had read that or Moureau 2020 p. 117 you would not have done [https://en.wikipedia.org/w/index.php?title=Mercury(II)_chloride&diff=prev&oldid=1139845572 this].<br />
<br />
Your continued editing with the clear [[WP:TE|tendency]] of attributing discoveries to Arabic-Islamic authors without reading up on the sources or by mispresenting them or by partially ignoring them (cf. [https://en.wikipedia.org/w/index.php?title=Sulfuric_acid&diff=prev&oldid=1139181196 what Needham actually says] vs what you made of that [https://en.wikipedia.org/w/index.php?title=Sulfuric_acid&diff=prev&oldid=1139117512 here], also completely ignoring [https://books.google.com/books?id=xrNDwP0pS8sC&pg=PA195 Needham's clear] {{grey|It is generally accepted that mineral acids were quite unknown both to the ancients in the West and to the Arabic alchemists}}) is getting to be disruptive.<br />
<br />
Please find another topic area which you have less strong personal views about and more appetite to read in full multiple recent sources. That would help us all at this point. <span style="text-shadow:#000 0em 0em 1em">☿&nbsp;[[User:Apaugasma|<span style="color:#6a0dad">Apaugasma</span>]] ([[User talk:Apaugasma|<span style="color:#000">talk</span>]]&nbsp;[[Special:Contributions/Apaugasma|☉]])</span> 14:54, 17 February 2023 (UTC)<br />
<br />
::: Please read Wikipedia policy regarding Original research [[WP:OR]]. The source cited doesn't mention that it is Falsely attributed to al-Razi. Other editors also disagree with you. https://en.m.wikipedia.org/wiki/Special:MobileDiff/1139913867 [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 15:08, 17 February 2023 (UTC)<br />
::::I gave a long quote from the source [[Talk:Mercury(II)_chloride#Attribution_of_De_aluminibus_et_salibus_to_al-Razi|on talk]] showing that scholars view it as [[pseudepigrapha|pseudepigraphical]]. The other editor can be excused for having been ignorant of this when they reverted, but you should have already known about what I quoted ''before'' you reverted, because I had already pointed it out to you. You clearly have no interest in reading sources in full and in representing what they are saying in a neutral way. This is, by itself, disruptive –even if you don't mean it that way. Please reconsider. <span style="text-shadow:#000 0em 0em 1em">☿&nbsp;[[User:Apaugasma|<span style="color:#6a0dad">Apaugasma</span>]] ([[User talk:Apaugasma|<span style="color:#000">talk</span>]]&nbsp;[[Special:Contributions/Apaugasma|☉]])</span> 15:16, 17 February 2023 (UTC)<br />
:::::Both are falsely attributed but you are specifically using falsely only for al-Razi and not for Hermes implying that it was indeed a work of Hermes[[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 15:25, 17 February 2023 (UTC)<br />
::::::Attributions to legendary figures like [[Hermes Trismegistus]] (see also: ''[[Hermetica]]'') are self-evidently false, which is why scholars do not dwell upon this.<br />
::::::The attribution of the ''De aluminibus et salibus'' to [[Abu Bakr al-Razi|al-Razi]], on the other hand, could be of crucial historical importance if authentic, and that is why scholars do write about this at some length (see, e.g., Ferrarrio 2009 pp. 42–43, and the older sources he cites which also discuss this question). In an actual article about the book, we would have an entire section devoted to the traditional attribution to al-Razi, while the attribution to Hermes would only be mentioned in the passing.<br />
::::::Because scholars pay more attention to the attribution to al-Razi and because recent experts explicitly argue that it is untenable, this deserves to be mentioned whenever we mention both the ''De aluminibus et salibus'' and al-Razi.<br />
::::::But my point here on your user talk is that ''you'' could have known all this if you just had read the sources with a neutral and inquisitive mind. By forcing me to explain all of this to you, you are wasting an enormous amount of my time, as well as of other Wikipedia editors like the patroller who reverted my edit on [[Mercury(II) chloride]] and then had to restore it after discussion on talk [https://en.wikipedia.org/w/index.php?title=Mercury(II)_chloride&diff=prev&oldid=1139913867][https://en.wikipedia.org/w/index.php?title=Mercury(II)_chloride&diff=next&oldid=1139913867].<br />
::::::This cannot continue like this, and I would like you to reflect upon that. Thanks, <span style="text-shadow:#000 0em 0em 1em">☿&nbsp;[[User:Apaugasma|<span style="color:#6a0dad">Apaugasma</span>]] ([[User talk:Apaugasma|<span style="color:#000">talk</span>]]&nbsp;[[Special:Contributions/Apaugasma|☉]])</span> 15:57, 17 February 2023 (UTC)<br />
<br />
== October 2023 ==<br />
<br />
[[File:Stop hand nuvola.svg|30px|left|alt=Stop icon]] Your recent editing history at [[:List_of_Muslim_Nobel_laureates]] shows that you are currently engaged in an [[Wikipedia:Edit warring|edit war]]; that means that you are repeatedly changing content back to how you think it should be, when you have seen that other editors disagree. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the [[Wikipedia:Talk page guidelines|talk page]] to work toward making a version that represents [[Wikipedia:Consensus|consensus]] among editors. The best practice at this stage is to discuss, not edit-war; read about [[WP:EPTALK|how this is done]]. If discussions reach an impasse, you can then post a request for help at a relevant [[Wikipedia:Noticeboards|noticeboard]] or seek [[Wikipedia:Dispute resolution|dispute resolution]]. In some cases, you may wish to request temporary [[Wikipedia:Protection policy|page protection]]. <br />
<br />
'''Being involved in an edit war can result in you being [[Wikipedia:Blocking policy|blocked from editing]]'''&mdash;especially if you violate the [[Wikipedia:Edit warring#The three-revert rule|three-revert rule]], which states that an editor must not perform more than three [[Help:Reverting|reverts]] on a single page within a 24-hour period. Undoing another editor's work—whether in whole or in part, whether involving the same or different material each time—counts as a revert. Also keep in mind that while violating the three-revert rule often leads to a block, you can still be blocked for edit warring&mdash;'''even if you do not violate the three-revert rule'''&mdash;should your behavior indicate that you intend to continue reverting repeatedly.<!-- Template:uw-3rr --> – [[User:Dudhhr|dudhhr]]<small><sup>&nbsp;[[User talk:Dudhhr|talk]]</sup><sub>[[Special:Contribs/Dudhhr|contribs]]</sub><sup>she</sup><sub>her</sub></small> 18:42, 5 October 2023 (UTC)<br />
<br />
:I am cooperating The ip user has violated the the warning by reverting the edit recently after you warned the user. https://en.m.wikipedia.org/wiki/Special:MobileDiff/1178763465<br />
:Please revert his edit and ask him discuss it on talk page first [[User:Hu741f4|Hu741f4]] ([[User talk:Hu741f4#top|talk]]) 18:48, 5 October 2023 (UTC)<br />
<br />
== ArbCom 2023 Elections voter message ==<br />
<br />
<div class="ivmbox " style="margin-bottom: 1em; border: 1px solid #AAA; background-color: ivory; padding: 0.5em; display: flex; align-items: center; "><br />
<div class="ivmbox-image" style="padding-left:1px; padding-right:0.5em; flex: 1 0 40px; max-width: 100px">[[File:Scale of justice 2.svg|40px]]</div><br />
<div class="ivmbox-text"><br />
Hello! Voting in the '''[[WP:ACE2023|2023 Arbitration Committee elections]]''' is now open until 23:59 (UTC) on {{#time:l, j F Y|{{Arbitration Committee candidate/data|2023|end}}-1 day}}. All '''[[Wikipedia:Arbitration Committee Elections December 2023#Election timeline|eligible users]]''' are allowed to vote. Users with alternate accounts may only vote once.<br />
<br />
The [[WP:ARBCOM|Arbitration Committee]] is the panel of editors responsible for conducting the [[Wikipedia:Arbitration|Wikipedia arbitration process]]. It has the authority to impose binding solutions to disputes between editors, primarily for serious conduct disputes the community has been unable to resolve. This includes the authority to impose [[WP:BAN|site bans]], [[WP:TBAN|topic bans]], editing restrictions, and other measures needed to maintain our editing environment. The [[Wikipedia:Arbitration/Policy|arbitration policy]] describes the Committee's roles and responsibilities in greater detail.<br />
<br />
If you wish to participate in the 2023 election, please review [[Wikipedia:Arbitration Committee Elections December 2023/Candidates|the candidates]] and submit your choices on the '''[[Special:SecurePoll/vote/{{Arbitration Committee candidate/data|2023|poll}}|voting page]]'''. If you no longer wish to receive these messages, you may add {{tlx|NoACEMM}} to your user talk page. <small>[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|talk]]) 00:55, 28 November 2023 (UTC)</small><br />
<br />
</div><br />
</div><br />
<!-- Message sent by User:Illusion Flame@enwiki using the list at https://en.wikipedia.org/w/index.php?title=Wikipedia:Arbitration_Committee_Elections_December_2023/Coordination/MM/08&oldid=1187132475 --></div>Casteiswronghttps://en.wikipedia.org/w/index.php?title=User_talk:2405:6E00:B71:3000:81A1:CE20:EE4E:20C2&diff=1223309307User talk:2405:6E00:B71:3000:81A1:CE20:EE4E:20C22024-05-11T07:25:11Z<p>Casteiswrong: /* Old account */ new section</p>
<hr />
<div>Explain your message please https://en.wikipedia.org/w/index.php?title=User_talk:Hu741f4&diff=1119509603&oldid=1116778855<br />
<br />
== Old account ==<br />
<br />
This is my IP account and is no longer active. [[User:Casteiswrong|Casteiswrong]] ([[User talk:Casteiswrong|talk]]) 07:25, 11 May 2024 (UTC)</div>Casteiswrong