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... of light exactly 180 degrees (pi radians) out of phase.
I do not know what technological applications there were, however I believe that the theoretical usefulness was considerable, and that it led to a deeper understanding of matter. I believe that the demonstration of circular polarization was important in establishing a consensus at the time that light was a transverse wave. It was based on the realization that if light were a two-dimensional transverse wave it could explain phenomena such as Malus' law. (It appears that up until this time it was assumed that if light were a wave, it could just as well be a longitudinal wave. I believe the reasoning followed was similar to the string analogy in the transverse wave article.) I believe this rhomb must have been the first demonstration that light could be circularly polarized, as implied by this transverse wave hypothesis. Further, it led to new understanding of matter and the discovery of new phenomena, for instance, the timeline of electromagnetism and classical optics says that Fresnel "phenomenologically explains optical activity by introducing circular birefringence" in 1825. --AJim (talk) 05:00, 27 December 2010 (UTC)[reply]
Hi, thank you for your hard work on this! I would suggest however that the detailed treatment of phase shift at TIR be shifted to Total internal reflection#Phase shift upon total internal reflection since it is more general than this one single application. Also, many of the equations in that section don't get properly printed and need to be fixed. This page should just refer to the TIR page for the equations due to which a quarter wave retarder Fresnel rhomb is possible. The page is too messy right now and not conducive to a more casual reader who just wants to know about 1/4 wave retarders. Before the explanation of its operation there should be a short section just describing it in brief (what is already in the lede, but the lede should be shorter). Since you wrote so much, could you take on moving the math to the TIR page (after fixing the equations) and helping to make the article more readable? Thanks, Interferometrist (talk) 17:31, 13 April 2018 (UTC)[reply]
Alternative suggestion: Because one can't explain the phase shift on TIR without deriving the Fresnel equations in almost their full generality (as I just did), perhaps the article "Fresnel equations" should include that general derivation, which should then be cited in the article "Total internal reflection", which in turn should be cited in "Fresnel rhomb". (Yes, I could do all that; but the time commitment wasn't budgeted for... I would also appreciate more details on the printing problem.)
I got into this mess because I belatedly discovered that textbook writers tend not to commit themselves explicitly as to whether the phase shift on TIR is an advance or a delay. Usually the answer is only implicit in the sign of the phase shift and the use of the time-dependent factor e−iωt. Worse, at least two authors who do commit themselves get it wrong. One of them, coming from an electrical engineering background (like me!), uses the time-dependent factor ejωt, but then assumes without justification that when the quantity under a square root sign turns negative, you can blindly take the square root in the direction of +j. (No, you can't!) The other uses the "physics" convention (e−iωt) but somehow misses or misinterprets the sign of the argument. So I had to prove the phase advance more thoroughly than expected.
That may help to explain why I was so keen to "explain away" the Goos-Hänchen shift (see article history). I have seen diagrams of the G-H effect showing the "apparent reflective surface" displaced towards the rarer medium. If one wrongly believed the phase shift on TIR to be a delay, one might also wrongly interpret the G-H displacement of the "apparent reflective surface" as evidence supporting that belief.
For what it's worth, the expression given by Berman for the G-H shift, in terms of the derivative of the TIR phase shift w.r.t. angle of incidence, can be derived very easily for the special case of the interference pattern between two reflected plane waves with nearly equal angles of reflection. The derivation is reminiscent of, but simpler than, standard textbook explanations of group velocity. Thus I have satisfied myself that a phase advance on TIR gives the correct direction for the G-H shift, contrary to "superficial" appearances.
Alright @Gavin R Putland:, very interesting. Don't have much time now, but a few quick answers:
1) I haven't looked in detail at the math you supplied or compared it to the page on the Fresnel coefficients. I simply observed that you did it for the general case of TIR that is much more general than the specific case of 45 degree retardance, so it didn't really belong here. Also, the page needs to be more user-friendly to readers just looking for the basics and avoid heavy math especially early in the article.
2) Many of your equations don't even display, which is unacceptable (I'm actually surprised no one has therefore deleted them). Note that the Wikipedia engine does NOT use standard Latex in math mode, but only a subset/variation of it. When I'm inputting heavy equations I usually just find a more complicated equation that already works and edit it down to what I'm trying to write! So hit "preview" frequently to see what you're getting and you'll converge to what you intended.
I have checked every browser on every platform that I can get my hands on, and both the <math>...</math> (LaTeX) equations and the Template:Math equations display correctly in every browser except Konqueror (which instead displays underlying code for <math>...</math>). The use of <math>...</math> does not seem to be deprecated, and the documentation for Template:Math suggests that it's for "inline, non-complex formulas". I could laboriously convert everything to Template:Math and tolerate the non-optimal fonts. But then would some other critic change it back to <math>...</math>? — Gavin R Putland (talk) 07:28, 20 April 2018 (UTC).[reply]
3) Your confusion on this is understandable, I remember being similarly confused on this general issue. But there is "optical distance" referring to OPD -- phase delay, and then there is the distance to focus based on geometrical optics. These happen to be rather unrelated! So just take the very simple case of a flat pane of glass. What happens when it is placed within a converging beam of light? Well, the phase of the light is clearly delayed by (n-1)*k*D, the Nth wavefront is moved CLOSER to the source. But the focus? While the light is INSIDE the glass, its convergence is decreased. The focal point moves FARTHER along the beam due to the glass plate, OPPOSITE to the shift of a constant phase plane of the wavefronts! When I realized that, I quit worrying about any relation at all between the two!
4) When I'm not busy I will check myself the phase shift and try to get all my signs right, and verify the direction of the phase shift for each polarization. But again, it has no definite relation to shifts regarding focussing.
5) Before you started editing, the article had no sections. Now that it IS organized into sections, the material in the lede needs to be trimmed way down, just making the most important points (and not ones requiring extra explanation), and putting most actual content in the sections. I know it's often much harder to delete text than to write it in the first place! But to make the article more approachable, that needs to be done, and since it's your own editing that has led to this, it's best if you can do that yourself. Thanks! Interferometrist (talk) 19:34, 16 April 2018 (UTC)[reply]
Hi @Gavin R Putland:, I just checked the phase issue using my own system and hopefully didn't get any signs wrong or misinterpreted. Beyond the critical angle, the phase of both polarizations is ADVANCED after TIR. And the p polarization is MORE advanced than the s; this is all just as you had mentioned and plotted. But again, this has no relation to the direction of the Goos-Hanschen shift. I hope you can still work on your derivation of the phase shift so it can be placed in the TIR page and clean up the Fresnel rhomb page as I suggested. Thanks, Interferometrist (talk) 17:49, 17 April 2018 (UTC)[reply]
Hi @Gavin R Putland:. Well I'm sorry but I have looked at the page on at least 4 different computers and EACH of them display the message " Failed to parse (syntax error)" for many of the equations. I didn't report it for just one computer that may have been weird but looked at it usually using Firefox on 2 different Linux and one Windows systems. Could you look again possibly using a different computer? There is nothing wrong with <math/math> (I didn't even know there was a different way!). The offending equations include the 5 following "Hence the wave vectors are..." . Thanks, Interferometrist (talk) 18:59, 20 April 2018 (UTC)[reply]
Update: I just found that the problem doesn't occur when I'm logged out of Wikipedia and is probably related to the feature I have (from Wikipedia, forgot what it's called) which lets you see information when your mouse passes over links among other nice things. If it were just that, then I'd refer the problem to the maintainer of that software, but the fact is that I have never ever seen on any other Wikipedia page this happen (and I'm normally logged in). When I get that massage while I'm editing, I always fix it before publishing a change. So it is still a problem but I understand that maybe you can't fix it without seeing it yourself. Interferometrist (talk) 19:17, 20 April 2018 (UTC)[reply]
Update 2: I played around with one problem equation. Eventually I found that the problem goes away if I remove every \bf in the equation. Could you look into that? Interferometrist (talk) 19:26, 20 April 2018 (UTC)[reply]
@Gavin R Putland: Yes, that's much more readable now! When I have a chance I will go through the material you added and make some edits which (if or after we agree on them) should be in the version that winds up on the TIR page.
Please don't take offence at this, but your writing is what I'd want to see in a textbook, but much too wordy for Wikipedia. When people go to an encyclopedia it's usually to answer very specific questions and they learn MORE if there is LESS text to distract them (or which puts them off from starting to read it). The important thing is that it be concise, get right to the point, with links to other pages (or external sources) as reference material on everything mentioned which is not primarily the subject of the page. So as far as finding the retardance phase, this page should just have short section on how to achieve 45 degrees as a special case using the formulae on the TIR page, and likewise the TIR page should just be a special case using the results from the Fresnel coefficients page. Now that you have prepared all this text, you can add the appropriate content to each of those 3 pages with minimal overlap.
I looked at the page on Fresnel coefficients, and it just states them but does not have a derivation, so you would be helping out by incorporating your work onto that page, where it belongs. If you want to leave it here for the meantime, that's probably fine (but I will move it further down the page) while we work on it.
As I said, this page still needs to be more concise especially toward the beginning, especially the lede. I will help with that when I get a chance. Please don't be offended when material is removed: 1) It may be repetitive; 2) It may belong on another page that gets linked to; or 3) It may be distracting, a detail or digression, which makes the article less readable. In the latter case, it is possible to use footnotes (not common in Wikipedia, but allowed), or to create a section toward the end of the article that won't distract readers seeking the basics. You can express any disagreements on this talk page, or by re-editing in a form that addresses the problems identified (and comments in edit summaries). Interferometrist (talk) 19:58, 23 April 2018 (UTC)[reply]
Cautionary note: The article "Fresnel equations" (to which I recently made some contributions) is plagued by editors who change equations because their favorite textbook uses a different sign convention from the one used consistently in the article. If a "Derivation" section is added to that article — as I was indeed planning to do — it will need to give enough detail to discourage such changes. I take the point that an encyclopedia is not a textbook. But neither does a traditional encyclopedia allow every passing Joe or Jane to edit it — which is the problem here. [Gavin R Putland]
I understand your discomfort and have had similar experiences. It is the price for Wikipedia being open and democratic which also makes it great. So SOMETIMES you cannot just express your understanding of a subject for the next 10000 readers to appreciate before you spend some time on the talk page educating (or negotiating with) a couple editors. But also, no one editor can dictate sign conventions (or where to put the 1/2π in the fourier transform etc.) and it has to be decided collectively by the editors involved on a page, and YOU have to remember that the sign of E or H on reflection (or the sign of or character used for i/j) are entirely arbitrary (unlike the sign of E or H or the electron charge etc.). So if it isn't the one you want, just change your equations accordingly (probably wouldn't take you 5 minutes) and move on. The equations you then write can still reference an authority that wrote them with a different sign or even a different leading constant (add a footnote if you think it would really be a source of confusion). I have added many equations that look different (opposite sign, i rather than j) than what I had scratched down on paper. It's much simpler than going into battle to decide which one is "right!" Interferometrist (talk) 16:36, 24 April 2018 (UTC)[reply]
Hi, I think that's a real bad idea. It should be at the bottom of the topic it is associated with. There is a real bad practice among some editors to create essentially duplicate articles (with a title sometimes changing the emphasis or just changing the wording) and the most amazing thing about these two pages is that they have absolutely no reference to each other (even though both link to the same OTHER pages!). The reason is that then two (sets of) editors can "own" their own page and not have to deal with the other editors. It's bullshit that has nothing to do with the purpose of Wikipedia. If I had come across the page you described, my first reaction would be to propose that it be merged into the page on the TOPIC of the derivation.
I hope one of us is soon able to clean up the Fresnel Rhomb page, move the math to the Fresnel coefficients page, and refer to it from the TIR page (and from the Rhomb page to that page). Interferometrist (talk) 18:13, 13 May 2018 (UTC)[reply]
I should add that there is also a way (I've never done it) that you can embed some messy math in an article with a button that says "SHOW" without the extensive math cluttering the page for people (most!) who do not want to "show" it. I think it's easier though just to have the derivation at the bottom with an internal link to it from where the results are presented. Please recognize that most readers (especially on a derivative topic) are NOT going to want to see that sort of math, often can't understand it or aren't concerned with it because they were just using the encyclopedia for reference (not education) after all, and just wanted the formula itself or other general information. Having derivations or other dense content in the middle of an article will often turn casual readers away before getting to subsequent content. Interferometrist (talk) 18:27, 13 May 2018 (UTC)[reply]
This article was last rated soon after a major deletion broke some important internal links. I concede, however, that much material previously included in this article needed to be distributed between the articles on the Fresnel equations and Total internal reflection. That has how been done.
Accordingly I submit that the present article, of which I admit being main author, now meets (at least) the criteria for a B-Class article, as follows.
1. The article is suitably referenced, with inline citations.
The article (at the time of this submission) has 35 inline citations, some appearing in more than one place, and some citing more than one source.
All but one of the inline citations link to the numbered "References". The more frequently-cited sources are collected in the later "Bibliography" and cited Harvard-style in the "References" (or, on one unusual occasion, in the text). "Bibliography" entries are in a "date second" format. No attempt has been made to impose this pattern on historic papers, whose provenance tends to be more complicated.
It has reliable sources...
It has 22 sources, comprising 4 standard textbooks, 5 other academic books (in which category I include Whewell 1857, and Whittaker 1910), one modern refereed paper, 9 historic papers or articles (Fresnel, Brewster, Young), one historic report (Lloyd, 1834), one set of collected works (Fresnel), and one manufacturer's website (commercial, but informative).
2. The article reasonably covers the topic, and does not contain obvious omissions...
The article does not seem to omit any major issue covered in the cited optical or electromagnetic texts, and goes beyond them in historical content.
...or inaccuracies.
The working equations are supported not only by citations but also by derivations in related articles. Effects of differing notations and sign conventions are noted. Many (not all) of the citations in the "History" section include both secondary and primary sources.
3. The article has a defined structure.
The main headings are (1) Operation, (2) Related devices, (3) Theory, (4) History. The last section is extensive and divided into subsections, because the device was invented in stages spanning a large part of the inventor's career, and because the last stage was apparently the first use of the argument of a complex number in physics.
The lead section gives the essentials of the operation and related devices, and the barest outline of the history.
4. The article is reasonably well-written.
That is the issue that other assessors can only settle by reading the article.
5. The article contains supporting materials where appropriate.
There are three illustrations: a diagram showing the operation, a graph of the phase shifts, and a portrait of the inventor. There are no apparent copyright issues. The diagram and the graph are my own work (and the diagram is a correction of File:Fresnel rhomb.svg, which is public-domain).
6. The article presents its content in an appropriately understandable way.
Although it obviously helps to be familiar with elliptical and circular polarization, the meanings of these terms could if necessary be gleaned from Fig. 1. The s and p components are explained before use. The operation of the device is described in functional terms before the theory of phase shifts is outlined. Parenthetical issues are relegated to the "Notes" section.
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Resolved by subsequent revisions. — Gavin R Putland (talk) 14:16, 3 May 2019 (UTC).
