Talk:Refractive index

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Poincaré symmetries


From the article:

"If in a given region the values of refractive indices n or ng were found to differ from unity (whether homogeneously, or isotropically, or not), then this region was distinct from vacuum in the above sense for lacking Poincaré symmetry."

First, being that "refractive index" is such a common phenomenon it should be addressed in layman's words. If mentioning the Poincaré symmetry would be interesting I think it would be better if there would be a separate section about that near the end of the article.

Second, I don't fully understand why the entire Poincaré group is considered. What do the "boosts" from this symmetry group have to do with an isotropic material? Moreover, does it make sense to talk about "to differ from unity (whether homogeneously, or isotropically, or not)"? what's the difference between a homogeneously different than unity refractive index and an isotropically different than unity one?


unheadered stuff


From the article:

In a dielectric material such as glass, none of the light is absorbed and therefore k = 0.

This statement is wrong. While it's true that if light is not absorbed then k = 0, it's not true that in a dielectric material no light is absorbed. In this context does light mean visible light or electromagnetic radiation?

I have rewritten this part. It is true that perfect dielectrics (i.e. perfect insulators) do not absorb electromagnetic radiation at low frequencies, however at visible light frequencies there is always some dielectric loss due to polarization delays. R6144 08:03, 23 August 2005 (UTC)

www.ultra-faster-than-light.com

The above was added by an anonymous user. Hmmm... I wonder who. See http://groups.google.com.au/groups?th=ed639d47fcb6ca32 for some jaded responses to the website. -- Tim Starling


From article:

When light enters a diamond, the high refractive index causes it to suffer multiple total internal reflections, which is the reason for the brilliance of these gemstones.

Removed. The total interhjbvbnugvjnyjtjknal reflection is not special to diamonds, nor is is a natural property of diamonds. The stone must be cuts specially to show it, and the same can be done with other stones (most noticablly with cubic zirconia, and rock crystal). I can't think of a useful way yugftxerzw3azerdct6udtyswe4tZtcto put this that illuminates (har-har!) anything to do with refractive index.

!! Recommendation: phase velocity shbhy8g7yif76f54as4tezthfraqhjur76tfg5drse4d5rd4rd65dtydyould be named v instead of v, which does not differ from greek letter Germendax 09:20, 3 Mar 2004 (UTC)

The problem is, it's standard in publishing and in Wikipedia to use italic letters for variables. The Tex-wiki markup does this when rendering as HTML, for instance. Anyway, the how distinguished v is from ν depends on your browser and which fonts you are using - they are quite clearly distinct on my setup (default IE6), for instance. -- DrBob

Why not use v_p for phase velocity and v_g for group velocity. This seems to be fairly common. Or, use c for phase velocity (reserving c_0 for the vacuum speed of light).

Quoted Indeces

I took the liberty of removing the incomplete table of refractive indices. It was the same as the one in list of indices of refraction, so it's still available. Incidentally, I don't think it's all that useful to quote indices for X-rays. Which wavelength do we pick? Tantalate 16:08, 16 May 2004 (UTC)

It is standard practice to quote the index at nD20, that is the sodium 'D' doublet is used at 20 C. You will see such values tabulated as nD20. --Askewmind | (Talk) 01:47, 15 Mar 2005 (UTC)

Intro

I'm no physicist, but this seems incorrect to me:

For a non-magnetic material, the square of the refractive index is the material's dielectric constant ε (sometimes expressed as the relative permittivity εr multiplied by the permittivity of free space, ε0). For a general material it is given by:
where μ is the permeability of free space.

First of all, isn't dielectric constant εr? Second, , with μ the permeability of free space, can't apply to a "general material"; it takes no account of μr. Should this be ? Josh Cherry 15:33, 17 Apr 2005 (UTC)

You are absolutely right. Askewmind | (Talk) 02:29, 13 May 2005 (UTC)
"General material" could be refering to material that is either nonmagnetic or nearly nonmagnetic. In these materials

What about Eta?

The refractive index is often written with the Greek letter Eta (). The article Eta (letter) refers to this, and links to the Refractive index page. It seems to be common practice to use the letter for the refractive index, but I think that might have stemmed from typographical inconvenience. I think it would be valuable to mention the different representations, and give evidence for the most common and most "correct" usage. The page on Snell's law uses too, and there are probably others. Does anyone have any thoughts? -- Andrew 00:05, 28 September 2005 (UTC)

  • It's possible that η was the original usage, and n came later. (I don't actually know who came up with the whole idea of refractive index - if I find out I'll add it to the article.) However, n is by far the most common symbol for it in optics. It's used everywhere, and in practically every textbook. -- Bob Mellish 16:24, 28 September 2005 (UTC)
Newton's Opticks, a century after Snell, was still not using a name for the concept, much less a letter. Newton talked only about the "Proportion of the Sines of Incidence and Refraction", which is the same thing but rather a mouthful. Maxwell's famous 1865 paper (which uses practically every letter of the alphabet as a symbol, both upper and lower case and both Greek and Roman) used the term "index of refraction" but gave it the letter i. I don't know when the term "index of refraction" first appeared, nor the letter n (I've never seen η myself), nor when the notation was standardized, unfortunately. — Steven G. Johnson (talk) 01:21, 6 March 2010 (UTC)
It seems that Thomas Young was the first to use the name "index of refraction", in 1807. He defined it as a number having the same proportion to 1 that the sine of incidence has to the sine of refraction. This definition reduced the traditional ratio composed of two numbers to a single number. In the past before Young, Newton had called it the "proportion of the sines of incidence and refraction". He wrote its value as a ratio of two numbers, like "529 to 396" (water, "nearly 4 to 3"). In 1710, Hauksbee called it the "ratio of refraction". He wrote its value as a ratio with a fixed numerator, like "10000 to 7451.9" (human urin). In 1795, Hutton wrote the value as a ratio with a fixed denominator, like 1.3358 to 1 (water).
Young did not use a symbol for the index of refraction, in 1807. In the next years, others started using different symbols:
m (Brewster 1815),
n (Fraunhofer 1817; Exponent des Brechungsverhältnisses is index of refraction),
µ (Herschel 1828).
The symbol n gradually prevailed. Ceinturion (talk) 18:53, 6 March 2013 (UTC)

Superluminal speeds, and n<1

From the short amount I read in the external link, I gathered that n can never be less than 1 for a *specific* frequency, IE n is only less than one for combined frequencies. Is this right? If so it should be User: fresheneesz

n can be less than one when the incident EM wave has a frequency higher than the resonant frequency of the atoms in the medium.

Is n<1 even possible? Because the velocity of light is given by v=c/n and no velocity can ever be greater than c. —Preceding unsigned comment added by 91.23.9.163 (talk) 06:49, 24 October 2007 (UTC)

It looks like there is confusion between the real-valued definition of n, and the complex-valued n. It looks like we should say that the real part of complex n may be less than one. It is not meaningful to use the < operator with complex numbers. Consequently, the mention of Re(n)<1 should be moved into that more advanced section on complex numbers, not left where it is to keep confusing people (like it did me at first), per WP:ASTONISH. CosineKitty (talk) 20:45, 4 March 2010 (UTC)
n<1 is perfectly possible, because it only implies a phase velocity of light exceeding c, which is perfectly fine. However, it always coincides with strong material dispersion, and hence a complex index (at least a nonzero imaginary part for nearby frequencies). — Steven G. Johnson (talk) 03:06, 5 March 2010 (UTC)
Hi Sevenj. Do you agree with my proposed edits? (I can't tell.) I specifically think it is meaningless to say that a complex number is "less than" another number of any kind. For example, which is less, 4+3i, or 3+4i? CosineKitty (talk) 17:03, 5 March 2010 (UTC)
It's certainly meaningless to talk about ordering complex numbers, so one should either use Re(n)<1 or restrict statements like n<1 to sections where it has been made clear that one is thinking of n as a real quantity (as is sometimes done...sometimes the imaginary part is given a different letter κ and called the extinction coefficient, or in transparent media one often makes the Im(n)=0 approximation...but the latter cannot be done for Re(n)<1 materials). I honestly don't care which notation is used in the article, as long as it is made clear. The point I was making is that, wherever Re(n)<1 is discussed, it should be made clear that these situations cannot be discussed physically without (thanks to causality constraints and Kramers–Kronig relations) also including dispersion and absorption (Im(n)>0), and differentiating phase velocity from group/energy/information velocity. So, it makes the most sense to discuss Re(n)<1 in the article after dispersion and absorption have been introduced. — Steven G. Johnson (talk) 00:40, 6 March 2010 (UTC)


First of all, shouldn't the first explanation of what v is after the first equation be changed? It says that "v is the velocity of light in the medium", however this is not strictly correct. As pointed out here, it is really the phase velocity. Secondly, in the section about n<1 a citation about the meaning of phase velocity can be found in J. D. Jackson, Classical Electrodynamics (Wiley 1962). More specifically, the footnote on page 211 is quite relevant. I think I have the first edition of the book so it might be on another page in later editions. The title of the section is "Superposition of Waves in One Dimension; Group Velocity". Perhaps someone more used to editing Wikipedia would like to double check this and and the reference. — Preceding unsigned comment added by 2001:660:2402:14:FA1E:DFFF:FEDA:FF88 (talk) 16:30, 23 February 2013 (UTC)

For the layperson

Perhaps Wikipedia needs a new guideline: The intro to any scientific topic should answer the question, 'who cares and why do they care?' Refractive index is carefully defined, but help the layperson put it in context. —Preceding unsigned comment added by 66.92.53.49 (talkcontribs)

Better now? Han-Kwang 14:28, 26 March 2007 (UTC)
Excellent, nicely done. 66.92.53.49 02:22, 28 March 2007 (UTC)

Does light slow down?

The light waves that go through the glass don't actually slow down. The effect is only apparent and applies to the speed of light 'in the material' as opposed to the speed of light 'in vacuum' where light ALWAYS travels at the speed of light c.

The reason you treat the light as if it did slow down is an effect of the wave nature of light. We treat light as a wave, with a wavefront propagating with velocity c in vacuum. The wavefront represents a plane in which all the light waves are in the same phase. Now, when this wavefront hits a material, some of the wavelets will hit atoms and excite electrons to a higher energy state. Effectively, the electrons are 'swallowing' the light photon. Every material does this in a different way. The excited electron soon after releases the stored energy in the form of another photon. The key idea here is what happens to the phase of the wave as it gets absorbed and re-emitted. Depending on the resonant or natural frequency of the atom and the frequency of the incoming wave, the emitted photon will have changed phase when compared to it's unaffected brethren. It falls either back of forward a bit. The wavelet will do this every time it hits an atom, and there are quite a bit of atoms in even a small piece of material. This has the effect of retarding (or advancing) the wavefront as the wavelets go through the substance. The effect is most pronounced when the incoming waves are near, but not at, the resonant frequency of the material. At these frequencies, the change in phase lag (or change in effective wave speed depending on how you look at it) is great for a given change in wavelength. Most materials will have the effect of slowing the speed of the wavefront, but plasmas will actually speed it up. Notice the light wave is still only propagating at c, the phase velocity of the wave, however, may travel less, or even greater than at the speed of light.

Definition Error

The phenomenon This has practical technical applications, such as effective mirrors for x-rays based on total internal reflection. is actually called total external reflection. This allows for grazing incident mirrors to be used in x-ray optical systems, the light never enters the optic. --64.212.80.158 02:08, 28 June 2007 (UTC)

Along with this error is a second problem, the notion of refractive index < 1 either: (a) does not belong in the introductory paragraphs, or (b) needs clarification (the unusual refractive index is a special property of the material, not the x-ray. In many materials x-rays *do* propagate with n>1; the index less than one is not peculiar to x-rays, rather it is the special material). Second, I challenge the quality of the reference [7], which contains non-encyclopaedic writing. I have adjusted the text, but left the reference. — Preceding unsigned comment added by Rwestafer (talkcontribs) 04:49, 26 January 2011 (UTC)

Removed the reference, as it seems to be a student page. Do you have a more reliable reference at hand to replace it? Materialscientist (talk) 05:06, 26 January 2011 (UTC)
According to total external reflection, "For X-rays, however, all materials have indices of refraction slightly below 1." I thought this was surprising at first, but now I think it's sort of plausible, at least for a sufficiently energetic x-ray and maybe for any x-ray at all. I found this reference, [1], it's a bit vague but maybe elsewhere in the book...? --Steve (talk) 07:01, 26 January 2011 (UTC)
I've added another book, but there are many. Most materials have n<1 for most X-ray energies, but there are materials and energy regions where this doesn't hold. Say, I have data for diamond at hand and there is a narrow range around 290 eV where n is slightly above 1. Carbon is a very light atom, and I guess more prominent absorption resonances occur in heavier materials. Materialscientist (talk) 07:29, 26 January 2011 (UTC)
Thanks for the references; agree that n<1 is prevalent for x-rays in absorptive media. Furthermore, references on x-ray diffraction should show that crystalline vs. amorphous materials (e.g. diamond vs. soot) have x-ray behavior strongly varying with energy and direction. These details should be relegated to other pages (linked) and not discussed in the introductory material. —Preceding unsigned comment added by 24.126.222.79 (talk) 23:51, 26 January 2011 (UTC)

unhelpful definition

article (now corrected per Intro above) says in the Into

This provides no insight. It's an index that used in calculations to ratio the speed of propagation of the wave in two medias. And it is itself the ratio of the speed of propogation between the media of interest and free space. It's better written as:

where

155.104.37.17 14:22, 11 August 2007 (UTC)

I would recommend against the use of and . Many authors are rather sloppy as to whether they are dimensionless quantities (equivalent to and , as in Gaussian/CGS units) or in the correct (SI) way that you use. I've had enough trouble using equations from physical papers that were inconsistent in this respect, so let's not add to the confusion. Han-Kwang 14:45, 11 August 2007 (UTC)
It's certainly true that many authors drop the "r" subscript for relative permittivity. However, it is also true that the Wikipedia article should relate the refractive index to ε and μ. Omitting this relationship would be remiss; we just have to be clear about whether relative vs. absolute permittivity is meant. —Steven G. Johnson 20:14, 11 August 2007 (UTC)
My reflex about the the proposed equation is to rewrite it as:
so I don't really see the advantage. Whenever I encounter an absolute permittivity, I separate it into eps_0 and eps_r. But then, I'm not a theoretical physicist, so maybe you think there is a deeper truth to keep it in terms of the absolute permittivity. Han-Kwang 20:21, 11 August 2007 (UTC)
Sorry, I misread the discussion above; leaving everything in terms of the relative permittivity and permeability seems fine to me. The difference between relative and absolute is just a choice of units, and therefore fairly uninteresting in my opinion, as long as the choice of units is clear. (I am a theoretical physicist, but theorists just set c=1 most of the time anyway.) —Steven G. Johnson 20:28, 11 August 2007 (UTC)


Negative Refractive Index - better explanation

It may just be my short attention span, but from the above section, I don't get what the EFFECTS of a negative refractive index would be. Anybody can make a try at explaining this a bit more? It certainly sounds like it couldn't mean that light suddenly gets quicker than light... Ingolfson (talk) 08:33, 21 April 2008 (UTC) Bold text

Yes, I was also confused by this section. I started with an article in Science News about "cloaking devices" that would bend light around an object, using metamaterials with a "negative index of refraction". Index of refraction N is normally defined as c/v, where c = speed of light in a vacuum, and v = speed of light in that medium.

So a negative index of refraction seems to imply a negative speed of light. That is, if you send a beam of light into the medium, it arrives before you send it. ???? 76.168.193.190 (talk) 06:05, 13 December 2009 (UTC)

I don't have time to write an explanation now, but this is totally wrong; negative-index media are still causal. (You're confusing phase and group velocity.) Also, negative indices have nothing to do with cloaking proposals, except insofar as they both use composite metamaterial structures (the material properties required for cloaking are not negative indices, and hence the actual metamaterial structures proposed in the two cases are totally different). — Steven G. Johnson (talk) 00:46, 6 March 2010 (UTC)

Measurement

Would like to see something in this article about how this property is measured in practice. —Preceding unsigned comment added by 203.0.35.33 (talk) 04:25, 13 July 2009 (UTC)

I have written a section Refractive index#Refractive index measurement about how refractive index of liquids and solids are measured for visible light and about phase-contrast imaging. If someone knows how it is measured for gases and plasmas or other types of radiation, please feel free to add that. Ulflund (talk) 19:02, 3 September 2011 (UTC)

Relation to dielectric constant

The quantities involved under Refractive index#Relation to dielectric constant need to be defined. —Preceding unsigned comment added by 128.138.43.113 (talk) 06:30, 19 July 2009 (UTC)

Done. Ulflund (talk) 20:23, 3 September 2011 (UTC)

Annoying image

The annoying image needs to be moved down or out of the article. It's ugly, poorly thought out, and doesn't help with understanding of refractive index because it's so unpleasant to look at. Some people would like to read the article rather than being assaulted by the time tunnel. --69.226.111.130 (talk) 06:58, 24 October 2009 (UTC)

Mineral Oil and Glass

I think a picture with a stirring rod in mineral oil would be a good image to have on this page. It shows how if two substances with the close indexes of refraction are together it looks as if one of them has disappeared. Maybe even have one beaker with water and one with the mineral oil and you can see the difference between the two. --76.115.218.65 (talk) 03:10, 16 November 2009 (UTC)

If you have one such image and have permission to use it (public domain, own work), free free to add it to the article. Headbomb {ταλκκοντριβς – WP Physics} 05:29, 16 November 2009 (UTC)

Reference medium

So far I have not come across anything that says the refractive index involves a "reference medium". It is usually stated as a quantity (numerical value) and this is the measure of how much light is bent as it travels from one medium to another, generally speaking. Then each substance has a stated refractive index, such as water has an RI of 1.33, air has an RI of 1.00029. I guess I am saying that I do not agree how the introduction is written. I don't think there is any need to refer to a "reference medium", because doing so doesn't seem to follow conventions of main stream (physics, or science) descriptions. ----Steve Quinn (formerly Ti-30X) (talk) 03:30, 3 May 2010 (UTC)

Part of the problem is that no source has been provided for the simple concepts, such as the definition and the fact that the bending of light can be derived from a slowing of the speed of the wave as it enters a different medium at an angle. You could look at File:Huygens Refracted Waves.png, used in Snell's law, which illustrates the effect. The article would be improved for someone who just wants to know the basics if more explanation were added.
Having said that, I understand your objection to needing a "reference medium", but consider this: refractive indices from your view have a meaning when light travels from one medium to another, and it is the ratio of those RIs that you use to calculate refraction. Now, bearing in mind the given refractive indices you quote, what 'substance' has a refractive index of 1? You probably already know that the answer is a vacuum. You then can see that when light travels from vacuum to another medium the ratio you use in your calculations is (RI of medium)/(RI of vacuum) = (RI of medium)/1 = RI of medium. So only when you are considering light traversing the interface between a vacuum and another medium, does the ratio between the sines of the angles of incidence and refraction actually equal the RI of that other medium. I hope you would agree that is a reasonable definition of a "reference medium", and that the reference medium is a vacuum. Hope that helps. --RexxS (talk) 04:21, 3 May 2010 (UTC)
Thanks for your response RexxS. I added some stuff to the introduction before I saw your response. I left a note in my last edit summary - if other editors wish to intergrate sound waves and / or water waves into the introduction feel free. I was unable to find quick information (sources) on refraction in sound waves or water waves. Also, I reccomend adding a seperate paragraph for that. (Just a reccomendation). ----Steve Quinn (formerly Ti-30X) (talk) 07:25, 3 May 2010 (UTC)

Section removed from article

I've removed the following section from the article as it is unsourced - possibly OR, confused, not about minerals and seems more about reflectance than refraction.—Preceding unsigned comment added by Vsmith (talkcontribs)

It also need a major rewrite to become encyclopedic. Materialscientist (talk) 03:55, 28 July 2010 (UTC)
I agree it needs to be worked on. I'll have to get back to it later (eschewing conversational tone of this section). ----Steve Quinn (talk) 05:56, 28 July 2010 (UTC)
===Refractive Index of Minerals===
The index of refraction reveals more than how much light will bend when crossing a boundary between substances. It also tells how much light will reflect off the boundary, like a weak mirror. And it tells what angle will be the Brewster angle, the slant angle at which one polarization is totally absorbed.
Black glass, like obsidian is really just glass. The light wave goes in and propagates through the solid just as it does for clear glass, but the light dies slowly as it goes forwards, and little or no light makes it out the far side. However, this does not describe the phenomenon of reflection.
A laser beam pointed at the polished front face will go in and die out. But about 5% will bounce back into a photocell.
The amount which bounces back is proportional to the square of the index change at the face:
R = [(n1-n2)/(n1+n2)]2... (in air, n1=1.000)
For plain glass, n2=1.55 ... -> Reflection = 0.046 = 4.6%
For water-clear sapphire, n2=1.77 -> R=0.077 = 7.7%
For dark gray glass, n2=(1.55+j*0.001); -> R=4.6%, and also the forward-transmitted light dies by a factor of 2.7 every millimeter.
If that glass was a ball 100mm across, no light would get to the other side, and it would look very black, in other words - opaque. Usually it is difficult to measure all the light in the laser beam, so it is hard to measure reflectance to better than about 1% error. However, index-matching fluids can be more precise.
With the amount of uncited material that I have seen on Wikipedia, getting impatient about citing a section of an article within a couple of days makes no sense to me. I get tired, or I get busy and some things have to be put off until a later time. ----Steve Quinn (talk) 08:05, 28 July 2010 (UTC)
In any case - Vsmith did the right thing removing this material. I apologize for the tenor of the material. I intended to come back on work on it and apply references. However, it could be this material was too rough, even for a rough draft. Anyway thanks to both of you (include Materialscientist) for your contributions regarding this matter. ----Steve Quinn (talk) 21:52, 28 July 2010 (UTC)

refractive index of a medium, variation with wavelength

A common confusion about the variation of refractive index with wavelength is that the wavelength referred to is always that of the incident wave. So formulae and graphical presentations should be cited explicitly as "incident wavelength". As the article clearly explains the incident wave frequency is preserved in the refractive medium, but the wavelength is not. — Preceding unsigned comment added by Brianb astrophys (talkcontribs) 03:11, 9 January 2011 (UTC)

n or η

In the article about the Greek letter eta (η) it says in section Eta#Lower_case that it is used as the symbol for refractive index. It goes on to say that the symbol n is more common but in this article eta is not even mentioned. Surely that should be remedied? 83.104.249.240 (talk) 01:25, 23 January 2011 (UTC)

Removed there. Never saw it used for refractive index. Materialscientist (talk) 01:33, 23 January 2011 (UTC)

Simple description or simplified description?

Existing: "A simple mathematical description of the refractive index is ..."
Suggested: "A simplified mathematical description of the refractive index is ..."
If "simple" is intended, the word should be removed per MOS:NOTED NOrbeck (talk) 05:20, 27 January 2011 (UTC)

I agree that statements of simplicity should be avoided although math doesn't get much simpler than this. To say that it is a simplified description wouldn't be good since it is a definition and not more simplified than the text in the introduction. My suggestion would instead be "The refractive index of a medium can be written mathematically as:" Ulflund (talk) 16:37, 26 August 2011 (UTC)

Dispersion and absorption as one section

Dispersion and absorption are two different phenomena (although related) and I think mixing what should be two sections only makes it difficult to find what one is looking for. Does anyone have a good reason for keeping this as one section Ulflund (talk) 16:12, 26 August 2011 (UTC)

Refractive Index is not only for e-m propagation.. that should be noted

Acoustics also uses the concept of refractive index, but nothing is mentioned in this article about other propagation. — Preceding unsigned comment added by 108.28.97.68 (talk) 14:48, 27 September 2011 (UTC)

I added the last paragraph of lead section ("The concept of refractive index can be used with wave phenomena other than light, e.g. sound. In this case the speed of sound is used instead of that of light and a reference medium other than vacuum must be chosen.[5]") a few weeks ago, but since I don't know much about accoustics I didn't write a section in the article about it. In the reference I added ({{#invoke:citation/CS1|citation

|CitationClass=book }}) refractive index was defined, but not used much. In optics on the other hand it is used in almost every equation. If anyone knows how refractive index is used in acoustics I think it deserves a section in this article. Ulflund (talk) 19:27, 27 September 2011 (UTC)

Microscopic explanation - Relationship described, but no formula

I find this section very interesting and helpful for my current research. The four bullet points describe a relationship between the complex argument of the medium's refractive index and the relative phase shift imposed by the medium. It seems to go something like;

arg(n) ‒  π/2 = Δρ

(n is complex refractive index; Δρ is imposed phase shift)

When the sources for this section are found, please check this formula. If correct, it should be included since it concisely summarises most of the section.

ShadowOfMars (talk) 19:37, 26 July 2012 (UTC)

I agree that it is an interesting section. It bothers me a bit that I cannot find this explanation in my optics text books. I found the start of the explanation in {{#invoke:citation/CS1|citation

|CitationClass=book }} and included that reference. There is also a similar explanation but much more mathematical in {{#invoke:citation/CS1|citation |CitationClass=book }}.

The equation should probably be more like . Ulflund (talk) 20:33, 26 July 2012 (UTC)
Your formulation, with origin on , looks more correct. indicates vacuum-like propagation. This raises the question of what the micoscopic description of should be...
All cases where are explained as , with no explanation given for the qualitative distinction between and .
ShadowOfMars (talk) 15:19, 31 July 2012 (UTC)
I wrote that section off the cuff with no references on-hand (I was in an airport). Someone was complaining about the omission of this discussion, so I wanted to put something. I was planning to look more carefully and add references later but never got around to it. :-P
I was channeling Feynman Lectures Volume 1 Chapter 31. [2]. Maybe I should say "trying to channel", obviously I wasn't doing it justice. It has been many many years since I read it actually.
Anyway, the phase of electron motion is the phase of P, which is the phase of electric susceptibility , where is complex permittivity. In a lossless medium, P is in phase with the E of the incoming field. That makes sense: The electron current is J=dP/dt, which is 90° out of phase with E, which means that joule heating (average of E·J) is zero as required in a lossless medium. The E-field of the outgoing wave created by P is in phase with J, not P. (This is in Feynman after (31.16): "The field E at [a point] P is just a negative constant times the velocity of the charges retarded in time...")
So the phase difference between the driving wave and the wave created by the electrons -- i.e. the phase under discussion in that section -- is , where is the phase of complex electric susceptibility, and I didn't bother to figure out whether it's plus or minus.
The relation between electric susceptibility and index of refraction is (see Mathematical descriptions of opacity): . Therefore there is no direct relation between the wave phase discussed in the section and the phase of n. The phase of n is related to the phase of , while the wave phase discussed in the section is related to the phase of . --Steve (talk) 21:25, 31 July 2012 (UTC)
— Preceding unsigned comment added by 139.222.113.232 (talk) 14:21, 1 August 2012 (UTC)

Phase speed?

Shouldn't all 'phase speed' be changed to 'phase velocity'? 71.139.169.27 (talk) 07:01, 12 October 2013 (UTC)

They probably should. It makes sense to use the word speed since velocity usually denotes a vector and this is about the scalar, but my impression is that the commonly used term still is phase velocity, and that is what the wikipedia article on the subject is called. If no one objects I will change this eventually. Ulflund (talk) 11:56, 3 January 2014 (UTC)
The distinction between speed (magnitude) and velocity (vector) dates from 1901. The idea of a group velocity distinct from a wave's phase velocity was first proposed by Hamilton in 1839, and the first full treatment was by Rayleigh in his "Theory of Sound" in 1877.(1) I guess the original name survived the turbulence of history. Ceinturion (talk) 12:33, 3 January 2014 (UTC)
I have changed phase speed to phase velocity everywhere in the article. Ulflund (talk) 16:37, 11 January 2014 (UTC)