Talk:Snell's law

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Old thread[edit]

Consistency problem:

In the top explanatory figure n2>n1 is explicitly stated. 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. (talk) 11:53, 1 October 2009 (UTC)

It would be nice to spell Snel's name correctly (i.e., with a single "l"). 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.

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.

I have some information about this at

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.

  • 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). -- Bob Mellish 17:36, 30 September 2005 (UTC)

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?

Image wrong?[edit]

The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, and are wrongly labelled as a result. The image disagrees with the text. See ScienceWorld [1] for how the image should be corrected.

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.

  • 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°, and you'll see how they match. -- Bob Mellish 18:25, 26 September 2005 (UTC)

Snell's law spelling[edit]

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.

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. Iterator12n Talk 05:29, 11 July 2007 (UTC)
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! Iterator12n Talk 20:07, 14 July 2007 (UTC)

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.

Other formulae[edit]

I've seen this formula used quite a lot in some establishments as an expansion of the original law for wavelength...


James S 00:12, 11 December 2006 (UTC)

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... Dicklyon 20:04, 22 December 2006 (UTC)
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. Dicklyon 20:40, 22 December 2006 (UTC)

Merge from Angle of refraction?[edit]

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. Dicklyon 08:36, 23 December 2006 (UTC)

support The Photon 03:46, 24 December 2006 (UTC)
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. Dicklyon 05:30, 24 December 2006 (UTC)

Reverting JCraw's extensive uncommented changes[edit]

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. Dicklyon 17:00, 4 January 2007 (UTC)

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. Dicklyon 23:24, 4 January 2007 (UTC)

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? James S 23:23, 7 January 2007 (UTC)

Which book are you referring to? I have Huygens. The others I mostly just find on Dicklyon 01:14, 8 January 2007 (UTC)

As a slight offshoot to the topic here, perhaps the introduction should be more explanatory:

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.

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).

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. Dicklyon 01:14, 8 January 2007 (UTC)

Similarly, i was just taking a glance at the 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 pick up on the article.

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? Dicklyon 01:14, 8 January 2007 (UTC)

I'll leave it in your hands, as my edits would undoubtedly be reverted ;-) James S 23:36, 7 January 2007 (UTC)

Not if you don't hijack the "ref" mechansim again ;^} Dicklyon 01:14, 8 January 2007 (UTC)
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. Dicklyon 06:51, 8 January 2007 (UTC)

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.

It the alternate name is really that rare, it only adds clutter to mention it in the Wikipedia article. It adds no useful information.

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:

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. (talk) —Preceding undated comment was added at 18:39, 1 September 2008 (UTC)

The original form of the law[edit]

Here's 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. Dicklyon 01:42, 5 January 2007 (UTC)

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. --Gerard1453 (talk) 16:51, 24 October 2017 (UTC)

Applicability to sound waves[edit]

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. 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. -- Myth (Talk) 05:50, 16 April 2007 (UTC)

It says "light or other waves, passing through a boundary between two different isotropic media". Is that not sufficient to encompass sound? Dicklyon 06:05, 16 April 2007 (UTC)
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. -- Myth (Talk) 06:21, 16 April 2007 (UTC)
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. Dicklyon 14:58, 16 April 2007 (UTC)
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. Ephesians 2:10 (talk) 23:10, 8 September 2009 (UTC)

How to reach consensus[edit]

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. Dicklyon 05:26, 1 August 2007 (UTC)

Proposal to rotate the image[edit]

Snells law.svg
Snells law2.svg

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? Oleg Alexandrov (talk) 00:58, 25 December 2007 (UTC)

In optics, rays are most often traced from left to right. But I agree it looks good going top to bottom. Dicklyon (talk) 01:59, 25 December 2007 (UTC)
Done. Rotated, the image shows the details better while taking less real estate. Oleg Alexandrov (talk) 04:54, 1 January 2008 (UTC)

Explanation for section removal[edit]

I removed a section from the article, for the following reasons:

  1. The informational content of the section is minimal, it repeats what is already stated both in the article and the diagram
  2. Then name of the section is misleading, that section is not about calculating refractive indeces
  3. 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?

Comments? Oleg Alexandrov (talk) 04:34, 10 January 2008 (UTC)

Formula confusion[edit]

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? STYROFOAM☭1994TALK 22:58, 29 January 2008 (UTC)

The equation is satisfied with θ1 = 0 and θ2 = 0 for any indices of refraction. That is, if the ray comes in perpendicular to the surface, it stays that way. Dicklyon (talk) 00:09, 30 January 2008 (UTC)

Vector Form Inconsistency[edit]

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).

The article does not give a source for the formula. Does anyone have a source (and therefore a way to verify the correct formula)? —Preceding unsigned comment added by (talk) 03:03, 30 January 2008 (UTC)

I had difficulty with this formula in 3D vector mode:

Note: must be positive. Otherwise, use

I got results to agree with Breault ASAP raytrace results by modifying the first formula:

to the more general:

This worked for both cases.

Palmeroo (talk) 17:34, 28 February 2008 (UTC)

Are there any reasons why this hasn't been corrected?

Anyway, I've updated it, so please check if it is correct now. Anders Ytterström (talk) 20:26, 2 May 2008 (UTC)

Is the formula still wrong? it disagrees with this webpage:'s-law 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. (talk) 00:19, 30 November 2008 (UTC)

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. Dicklyon (talk) 00:58, 30 November 2008 (UTC)

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). (

I changed the formula for a better understanding for symmetry. it used to read and i changed it toso 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. Ibuwan (talk) 01:37, 8 May 2012 (UTC)


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). (talk) 15:02, 26 November 2008 (UTC)

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. Dicklyon (talk) 16:44, 4 December 2008 (UTC)

Al Haythem, A.I.Sabra and the Sine Law of Refraction[edit]

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 Theories of Light From Descartes to Newton 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):

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...

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.Thony C. (talk) 13:12, 4 December 2008 (UTC)

Snell's Law Obsolete?[edit]

This was from the Faster-Than-Light article:

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".

Shouldn't something to that effect be added to this article, then? SineSwiper (talk) 01:52, 18 December 2008 (UTC)

Negative-index metamaterials still obey Snell's law, just with a negative index of refraction. — Steven G. Johnson (talk) 04:41, 5 August 2009 (UTC)

Finding the speed of light[edit]

I think the formula for finding the actual speed of light () 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. Fireedud (talk) 18:14, 3 January 2009 (UTC)

I just found it on Refractive index, but I think it should also be added here. Fireedud (talk) 18:21, 3 January 2009 (UTC)

"Today's Featured Picture" for 9/23/2009 incorrect !![edit]

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, Wwheaton (talk) 15:53, 23 September 2009 (UTC)

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. Dicklyon (talk) 16:02, 23 September 2009 (UTC)
I'm going to have to disagree with you as well. According to Snell's Law, . Note that n1 (air) = 1 and n2 (water) = 1.33 (and thus n2/n1 = 0.75), and that , 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 . Due to some lovely trigonometry, 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 , as defined above, in WolframAlpha. You'll see that changes close to zero (the central axis), but that it quickly approaches an asymptote on both the positive an negative ends. (Near-)constant (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. -- tariqabjotu 20:38, 23 September 2009 (UTC)
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. Wwheaton (talk) 14:25, 25 September 2009 (UTC)
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 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. Dicklyon (talk) 03:46, 26 September 2009 (UTC)

Is it really a law?[edit]

About 20 years ago, I remember being told in college that Snell's Law is not a law because

  1. It can be derived (which has since made me wonder about the nature of laws)
  2. It is an approximation

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. AngusCA (talk) 23:35, 13 June 2010 (UTC)

Without a source, there's not much you can do. Lots of things are called laws; I wonder where those criteria come from. Dicklyon (talk) 05:25, 15 June 2010 (UTC)

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?Thony C. (talk) 13:23, 15 June 2010 (UTC)

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. AngusCA (talk) 02:39, 16 June 2010 (UTC)

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 P & Q define the ray!It is exactly the Q point whitch defines the ray. (talk)10:28, 8 January 2015 (UTC)

Wolf's paper[edit]

Did anybody get a chance to check Wolf's paper to see what it says about history of mathematics? Tkuvho (talk) 11:08, 3 June 2011 (UTC)

Second Picture is Incorrect[edit]

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. — Preceding unsigned comment added by Chapin J (talkcontribs) 21:07, 26 September 2013 (UTC)

Vector form[edit]

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 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. Dicklyon (talk) 18:33, 26 January 2014 (UTC)

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. Dicklyon (talk) 19:35, 26 January 2014 (UTC)

Elaborate on Ibn Sahl's authorship of the law[edit]

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):

Image 1: For any given angle of the incoming ray with the surface normal, one is able to construct a refracted ray (at an angle with the surface normal) by keeping the ratio of the two hypothenuses constant. The constant is characteristic of the interface, its value being the reciprocal of the nowadays known relative refractive index .
Image 2: An excerpt from Ibn Sahl's manuscript

I am not convinced by the material I have found on the internet so far. Here are a few reasons:

  1. 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.
  2. 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.
  3. 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:
Refracted ray reconstruction
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.
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.
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.
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.

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.

Refracted ray reconstruction with a modified aspect ratio
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.
Step 2: The center of the red circle now falls in point C. This is promising. The surface normal is the line CP.
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.
Step 4: However, the ray is now refracted even less, the relative refractive index being around 1.18.

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.

Marko Petek 00:05, 15 July 2015 (UTC) — Preceding unsigned comment added by Marko Petek (talkcontribs)

Here's the actual supporting passage:

"The hyperbola as a conic section: The law of refraction.

Ibn Sahl first considers refraction on a plane surface. Defining as the plane surface of a piece of crystal of homogenous transparency, he emphasizes a relation that is the reciprocal of the refractive index of this crystal in relation to air.19

'Let be a light ray in the crystal, which is refracted [see figure] in the air along . The perpendicular to the plane surface at intersects line at and the refracted ray at .'

The ratio , which Ibn Sahl uses throughout his study, is the reciprocal of :

'Let and be the angles formed by and , respectively, with the normal; we have


Let be a point on segment such that , and let point be the middle of . We have . Therefore characterize the crystal for any refraction.'

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.

19[Tehran manuscript of ibn Sahl's treatise, pages] 5-9."

— Rashed (1990), p. 478
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. Conformancenut347 (talk) 19:01, 29 July 2016 (UTC)

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 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.

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.

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.

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 (various kinds of glass, water, other), no mention of the light source and its colour and how he created a bundle of (almost) monochromatic light.

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.”

On p. 465ff of the Isis-issue, ref [1], Rashed gives some background to his discovery (remarks between brackets [] are mine):

“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.”

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 paleographic, philologic and physical analyses (including carbon dating), as is done by specialized institutes like the Bodleian libaries; see for example the analysis of the Bakhshali manuscript that “contains the oldest recorded origins of the symbol 'zero'”.

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.

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.

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?

Curiously, nowhere the classical imaging peoperties and lens formulae are considered.

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 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 spectacles in the 13-th century or the telescope in the 17-th century.

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).

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.


  • Rashed/Ibn-Sahl only consider air-glass boundaries, so not Snell's Law in its full generality.
  • Rashed/Ibn-Sahl nowhere prove the refractive index to be constant, the sin/sin-ratio is simply relabeled to something sounding familiar
  • 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.)
  • Roshdi Rashed is tinkering with the original text. Where are the original manuscripts? Did other scholars take the trouble to analyse the manuscripts?


[1] Roshdi Rashed, , A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses, Isis Vol. 81, No. 3 (Sep., 1990), pp. 464-491

[2] Lab: Refraction of Light- Air into Glass Answers, (2016)

-- Gerard1453 (talk) 17:32, 13 October 2017 (UTC)

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. --Gerard1453 (talk) 14:51, 14 October 2017 (UTC)
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. Dicklyon (talk) 15:52, 14 October 2017 (UTC)
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. Dicklyon (talk) 16:38, 14 October 2017 (UTC)
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. Dicklyon (talk) 05:06, 14 October 2017 (UTC)
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. Dicklyon (talk) 05:13, 14 October 2017 (UTC)
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. Dicklyon (talk) 05:19, 14 October 2017 (UTC)
@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. --Gerard1453 (talk) 14:51, 14 October 2017 (UTC)
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. Dicklyon (talk) 15:52, 14 October 2017 (UTC)
Will send mail to Roshi Rashed with my comments on his article -- and ask for photocopies of the original manuscripts --Gerard1453 (talk) 15:15, 14 October 2017 (UTC)
Good idea. I look forward to hearing what you get from him. Dicklyon (talk) 15:52, 14 October 2017 (UTC)
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: here. Dicklyon (talk) 16:28, 14 October 2017 (UTC)
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. Dicklyon (talk) 17:28, 14 October 2017 (UTC)
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. Dicklyon (talk) 18:02, 14 October 2017 (UTC)
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. Dicklyon (talk) 18:18, 14 October 2017 (UTC)
@Dicklyon. Thanks once more for your comments. I will see if I can find Rashed's book in the library of nearby 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.
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.”.
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.
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.
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.
[3] Robert B. Waltz, The Encyclopedia of New Testament Textual Criticism, (Last Preliminary Edition, June 16, 2013)
[4] Roger Collins, Caliphs and Kings: Spain, 796-1031 (A History of Spain), (2012)
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.” --Gerard1453 (talk) 17:20, 24 October 2017 (UTC)

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.Thony C. (talk) 05:16, 25 October 2017 (UTC)

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 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.--Gerard1453 (talk) 16:50, 25 October 2017 (UTC)
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.Thony C. (talk) 05:49, 26 October 2017 (UTC)
Hi Thony congrats. Did you read the 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? 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. --Gerard1453 (talk) 08:41, 26 October 2017 (UTC)

The French wiki has the following in the section fr:Lois_de_Snell-Descartes#Historique:

“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.”

Which means:

“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.)

The editor of the French lemma uses source [5] (below) by physicist 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.

To conclude a word by Richard Feynman, in his famous The Feynman Lectures on Physics, Volume I, chapter 26, section26-2:

“(...) 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.”

[5] Dr. Gorden Videen, Whose Law of Refraction?, Optics & Photonics News (May 2008)

“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.” --Gerard1453 (talk) 18:32, 5 November 2017 (UTC)

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. Wikaviani (talk) 02:24, 10 January 2018 (UTC)

Popular media[edit]

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. (talk) 06:31, 1 October 2016 (UTC)