Talk:Snell's law

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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

http://mintaka.sdsu.edu/GF/explain/optics/discovery.html

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?

1 Image wrong?
2 Snel's Snell's law spelling
3 Other formulae
4 Merge from Angle of refraction?
5 Reverting JCraw's extensive uncommented changes
6 The original form of the law
7 Applicability to sound waves
8 How to reach consensus
9 Proposal to rotate the image
10 Explanation for section removal
11 Formula confusion
12 Vector Form Inconsistency

[edit] Image wrong?

The image shows that the normal is the boundary between the media, rather than being horizontal to the boundary. Also, $θ 1$ and $θ 2$ 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)

[edit] Snel's Snell's law spelling

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)

[edit] Other formulae

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

$\frac {\lambda_0}{\lambda_1} = \frac{v_o}{v_m} = \frac{c / n_1}{c / n_2} = \frac{n_2}{n_1}$

to... $λ 1 s i n θ 1 = λ 2 s i n θ 2$

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)

[edit] Merge from Angle of refraction?

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)

[edit] Reverting JCraw's extensive uncommented changes

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 books.google.com. 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)

[edit] The original form of the law

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)

[edit] Applicability to sound waves

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)

[edit] How to reach consensus

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)

[edit] Proposal to rotate the image

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)

[edit] Explanation for section removal

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

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

[edit] Formula confusion

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

The equation

n 1 sinθ 1 = n 2 sinθ 2

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)

[edit] Vector Form Inconsistency

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 71.235.123.252 (talk) 03:03, 30 January 2008 (UTC)

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

Note: $\mathbf{n}\cdot(-\mathbf{l})$ must be positive. Otherwise, use

$\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} - \left(\cos\theta_2 + \frac{n_1}{n_2}\cos\theta_1\right)\mathbf{n}.$

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

$\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \cos\theta_2\right)\mathbf{n}$

to the more general:

$\mathbf{v}_{\mathrm{refract}}=\left(\frac{n_1}{n_2}\right)\mathbf{l} + \left(\frac{n_1}{n_2}\cos\theta_1 - \left(sign \left(\cos\theta_1\right)\right) \cos\theta_2\right)\mathbf{n}$

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)