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There seems to be an incoherence on this page: while in the linked articles the transmission and reflection coeficient are defined as ratios of Amplitudes (in this case of the E-Field), the equations in this article seem to describe a ratio of intensities.
I see two possibilities to correct this:
with the intensities of the incident light and if the reflected light.
with the corresponding amplitudes of the electric field
I would prefer the second possibility since it corresponds to the majority of the literature I have at hand - but I don't have time to check and replace the graphs right now - I'll be back when I have more time and take care of this if nobody else has until then...—The preceding unsigned comment was added by Nanomage ( talk • contribs) .
I also think that the equations for the reflection and transmission coefficients of the electric field should be given, further more their relation to the intensities should be emphasized and not only linked to. Some people care about phase, for example when going from low index to high index there is a 180 phase change at reflection, but when going from high index to low there isn't. Also r^2+t^2 is not equal to 1. Unlike the sum of the intensities which take into account the different velocities of the fields in different media. I think that ignoring amplitudes is simpler but will lead to misunderstandings as the texts and many people refer to amplitudes. —Preceding unsigned comment added by Eranus ( talk • contribs) 16:16, 21 July 2008 (UTC)
-Shouldn't also be pointed out that the refractive index used for these equations is a complex number? --an anonymous Raptor 10:00,07/10/05 CET
I think the equation for p-polarization is wrong. From what I've seen in the literature, the following should be the equation:
—The preceding unsigned comment was added by 132.206.69.48 ( talk • contribs) .
Why not include the equations for both intensity and amplitude and make clear which is which and where each is used?- 4.232.0.63 17:06, 7 August 2006 (UTC)
Power ratio or intensity ratio? They are differnt!-- Antonysigma ( talk) 16:55, 1 May 2011 (UTC)
Please state somewhere that the incident theta angle is in the range [0,90] degrees, otherwise the trigonometric expressions are not valid. — Preceding unsigned comment added by Ed.fuentetaja ( talk • contribs) 01:57, 19 August 2019 (UTC)
All references at my disposal use z not s in all forms. -- 4.232.0.63 16:52, 7 August 2006 (UTC)
Some physics in the article are imprecise. Approximations or assumptions made for some formulae are not clearly spelled out (e.g. the paragraph on reflectivity of a dual-surface window and the next paragraph on Fabry-Perot interference directly contradict each other), and other assumptions may be misleading (i.e. mentioning dielectric materials, but neglecting parelectric materials). Contrary what is claimed in the article, Fabry-Perot interferometers cannot be used to create perfect mirrors or reflection-free lenses (causality, i.e. the Kramers-Kronig relations, dictates that there is always some absorption.)
I spent a while editing the article, but Wikipedia lost the edited version on trying to preview it. I'm not sure I want to go through that frustration again, so someone else has to correct the article. —Preceding unsigned comment added by 218.186.8.10 ( talk • contribs)
This article needs to include the phase shifts associated with reflection and transmission from these surfaces. —Preceding
unsigned comment added by
140.247.5.34 (
talk) 17:17, 27 November 2009 (UTC)
I think the Fresnel equations should be expressed in terms of the amplitude instead of intensity. This will bring out important features such as the phase shift upon reflection when going from a low to a high index material. —Preceding unsigned comment added by 74.104.44.203 ( talk) 19:34, 27 November 2009 (UTC)
This article, like almost every textbook ever, makes the assumption that the relative magnetic permeability equals 1. This is all fine until you are trying to compute the reflection on a iron plate. If you derive the Fresnel equations without neglecting the magnetic permeability, then you quickly notice that the refractive index is not what should appear in them. Instead, we should see admittances (for the perp case) or impedances (for the para case). Refractive index: ; admittance ; impedance . When equals 0, the admittance and the refractive index both look like (the gets simplified), hence the confusion that is repeated everywhere. But fundamentally, this is wrong. We obviously cannot correct the main equations since they're in every textbook (except Stratton's, he got it right, even though he used the weirdest notations ever), but having a paragraph for the case wouldn't hurt, especially since the formulas aren't even more complicated. Niriel ( talk) 00:25, 28 October 2014 (UTC)
Would it be okay to redirect a Fresnel's law page to this page? —The preceding unsigned comment was added by Wk muriithi ( talk • contribs) 13:03, 24 January 2007 (UTC).
The article says "For materials which absorb light, like metals and semiconductors, n is complex, and Rp does not generally go to zero." But don't clean metallic surfaces essentially not absorb light? Is this right? —Ben FrantzDale ( talk) 21:56, 30 April 2008 (UTC)
I've heard the term " optical coupling" and " wetting out" to describe what happens when optical films come in contact. I assume this is the transition from a film-air-film sandwich to a film-film sandwich as the air thickness starts to get well below the wavelength of the light. Could someone point me to more information on that? 155.212.242.34 ( talk) 14:16, 19 May 2008 (UTC)
Since the whole article deals with intensities, it is confusing that the picture deals with amplitudes (there is no negative intensity) I added the word amplitude in the caption of the article, I think the article requires more info on amplitudes. Eranus ( talk) 08:26, 22 July 2008 (UTC)
I don't think this is the case for an equation. I mean, none of the other non-inline equations in this article have period after them.-- Zipspeed ( talk) 14:02, 17 May 2009 (UTC)
I'm concerned that there appears to be a sign error in the numerator of the expression for Rp. Hecht (pp 114, 115, 4th ed) and Born and Wolf (p40, 3rd ed) both agree that the form should be:
Rp = n2Cos(θi) - n1cos(θt) / n2cos(θi) - n1cos(θt)
I'll attempt to make the change to make the formula for Rp agree with Hecht and Born and Wolf if I don't get any comments to the contrary.
Patrick ( talk) 04:23, 8 June 2009 (UTC)
I think someone needs to take a look at the Fresnel equations, with respect to definitions of amplitude coefficients and intensity, as it has the potential to confuse. I think the amplitude coefficents should be quoted, rather than the intensity, and then a note made that the intensity is simply the square of the amplitude. —Preceding unsigned comment added by Nheath555 ( talk • contribs) 09:28, 22 October 2009 (UTC)
I think a history section would be a nice addition. I can't find the original form of Fresnel equations when did Fresnel derive them, when where did he publish them? An hour on Google and Google scholar did not help me much in contrast to History of Young's double slit experiment, Snell's law, Fresnel propagation... which are well documented, I would appreciate any refferance anyone may have. Eranus ( talk) 17:48, 28 August 2009 (UTC)
I'm wondering if I'm the first one noticing that the formula with the difference of angles fails at normal incidence:
and
both resolve to zero for , i.e. normal incidence. This is clearly wrong.
The problem lies in the careless simplification of the correct expression (for , but similar arguments hold for the case of )
using Snell's law . Multiplying the numerator and denominator of with (e.g.) is only allowed if is not zero, which it of course is in the case of normal incidence.
The correct result for normal incidence is given further down on the page. My suggestion is to remove the terms with the difference of angles and just keep the following expressions, i.e. change
to
and correspondingly for .
Oliver Jennrich ( talk) 08:05, 23 April 2010 (UTC)
(The last expression is valid at non-normal incidence, but at normal incidence it equals 0/0.)
or something like that :-) -- Steve ( talk) 09:00, 23 April 2010 (UTC)
I suggest, if possible, that the autor of the graphics modifies them by plotting the coefficients for a refraction index of 1.5, more typical af a glass, which is the main material dealt with in the article. -- GianniG46 ( talk) 07:52, 15 June 2010 (UTC)
I suggest to include in the amplitude reflection coefficients the part beyond the critical angle of incidence for internal total reflection. I've quickly made this file:
but feel free to make a better one (which would perhaps include the transmission coeficients as well?) — Preceding unsigned comment added by Coussin00 ( talk • contribs) 15:20, 19 April 2021 (UTC)
I just wanted to direct your attention to a recent disambiguation implemented in transmittance involving Fresnel equations: see here. Thanks. Fgnievinski ( talk) 22:30, 9 March 2011 (UTC)
There is a sentence in the article:
This should be true *only if* R and T are defined in amplitudes.
However, the formula given in the article is in ratio of intensities:
i.e.
Although conservation of energy still applies (), the areas ,, are not the same. This means R+T should not be equal to 1! (except at normal incidence)
I wish to know what you think about it.-- Antonysigma ( talk) 16:05, 1 May 2011 (UTC)
The graphs shown are useful, but an index difference of n=1 to n=2 isn't very practical in real world situations. Practical examples with meaning to most readers will be 1/1.33 (air/water) or 1/1.5 (air/glass). Note that most practically common glasses occupy the narrow refractive index range between 1.45 and 1.55. In general, materials with refractive indices above 2 are very uncommon optical materials (though they of course exist). I suggest to redo the plots for 1/1.5 index contrast, if possible. — Preceding unsigned comment added by 13.2.16.151 ( talk) 18:00, 14 June 2011 (UTC)
Is there an error in the graph of Glass to Air amplitude coefficients? How can there be and in the portion of the graph corresponding to Total Internal Reflection? Kghandi ( talk) 03:35, 1 November 2016 (UTC)
I cleaned up the new material on amplitude equations, and rearranged things a bit, but have not checked the equations themselves against a reference. It's not clear to me that the coefficients and the associated beam and field geometries are adequately defined, nor that the equations properly capture the phase of r and t. The construction has problems, in that it divides vectors to get a scalar quantity. As written and both equal , which is clearly wrong. I think the E's are just missing subscripts, as in the captions on the new images.
I don't have time to work on this any more right now, and more pairs of eyes looking at it is probably a good idea anyway. I am on record above as being opposed to incorporation of the amplitude equations into this article, but am willing to give it a chance if we can get them explained clearly and correctly, with the geometry and sign conventions fully defined.
Also on the to-do list: verify that these equations actually describe ratios of electric field amplitudes, as claimed in the text, and not the square root of intensity or some other quantity. It's been too long since I looked at the Fresnel equations for me to do that off the top of my head, but I've seen derivations that use square root of intensity and call it "E". -- Srleffler ( talk) 08:47, 18 December 2011 (UTC)
It is requested that a physics diagram or diagrams be
included in this article to
improve its quality. Specific illustrations, plots or diagrams can be requested at the
Graphic Lab. For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images. |
-- Srleffler ( talk) 21:03, 18 December 2011 (UTC)
that is impossible for me to read (colorblind)... any way you can make it not red and blue? — Preceding unsigned comment added by 23.118.190.205 ( talk) 14:45, 16 June 2014 (UTC)
For a while the article has used the sign convention for rp where positive means that the magnetic field's orientation does not change. That means that rs and rp have opposite signs at normal incidence. There is nothing incorrect about this, since it's just a convention and the article is consistent as written. But I do think the opposite sign convention for rp is more common and we should follow whatever convention is most common. Also, you can easily find statements in references like "Reflected light will experience a 180 degree phase change when it reflects from a medium of higher index of refraction and no phase change when it reflects from a medium of smaller index." [5], which is a nice clean statement to make but only works with the opposite sign convention for rp. (Well, it still doesn't work for p-polarization at very oblique angles, but it works in every other case!)
I actually switched it a while ago and was reverted, with the comment that we need to discuss on the talk page. So let's discuss! What do other people think? -- Steve ( talk) 13:24, 5 June 2015 (UTC)
Update: I checked 6 mainstream textbooks, and I found 3 of each convention!
So I was incorrect when I said above that the rp<0 convention is "more common". Sorry! :-P
Hecht is a widely used and respected textbook, as Glrx rightly points out, but then again so is Griffiths, and Feynman, and Jackson for that matter. I think it's more-or-less a tie.
Srleffler: When light in air reflects off glass at normal incidence, the electric field switches sign (or you could say, it changes phase by pi), while the magnetic field keeps the same sign (or you could say, it changes phase by 0). Related to this, there are two ways to define the relative phase of oppositely-propagating light beams, the one based on whether the magnetic field is in phase or not, and the one based on whether the electric field is in phase or not. These two conventions line up with the two possible signs of rp.
Is one convention better than the other? Normally we care a lot more about the relative phase of the electric field, not magnetic field, because the electric field plays a much bigger role in light-matter interaction. The change I'm proposing is consistent with that preference. After that change, at normal incidence, we would be describing light as out-of-phase or in-phase based on the electric field, whereas with the current sign convention it's based on the magnetic field.
However, at glancing angle, that's no longer true. At glancing angle, the convention currently in the article is clearly superior to the one I'm proposing...
Given that, I'm starting to think that the convention in the article is best after all. Never mind. Thanks for the feedback :-D -- Steve ( talk) 21:59, 10 June 2015 (UTC)
Why do you think that the convention used is superior to the one you actually proposed at glancing angle? Somehow I'm also confused since Hecht 4th Edition states in (Eq. (4.38)) that there is no phase shift for normal incidence for the E-field. Am I mixing something up? Asdfawer2 ( talk) 22:51, 26 July 2015 (UTC)
Again, I just mean not even in Hecht the formulas seem consitent (from my point of view).
Looking at Eq. 4.32 for normal incidence at an interface from lower to higher refractive index he states , since . Eq. 4.38 yields . Since Hecht defines the reflection coefficients including the phaseshift, as there may only be a phaseshift of pi or 0, resulting in . For me its not clear how you would argue that you could infer a phase relation for any angle. Of course I agree with you in the extreme cases its obvious how the signs should look like, I just mean we could state more precisely what each reflection coefficient stands for, e.g. , in the currently used convention, which from my point of view does ""not"" agree with Hecht.
I hope I could clarify my point.
Asdfawer2 (
talk) 00:11, 5 August 2015 (UTC)
Edit
Asdfawer2 (
talk) 00:57, 5 August 2015 (UTC)
Why is there an empty section called "Special cases"? — Preceding unsigned comment added by 129.242.204.238 ( talk) 07:47, 25 October 2016 (UTC)
I disagree with this edit. The s and p should not be given "math" formatting when they appear in plain text, because they are not mathematical objects notwithstanding the fact that they appear in the equations as labels on variables. "S polarization" and "p polarization" are simply the English names for these two characteristics. I prefer them in italics, per Italic type#Usage, "Using a letter...mentioned as itself", but I'm open to arguments that that doesn't apply here because the s and p are not truly referring to themselves in this case. They should still be in italics in their first appearance in the text, however, as "Introducing or defining terms, especially technical terms or those used in an unusual or different way."-- Srleffler ( talk) 02:17, 14 November 2016 (UTC)
The u and the epsilon are missing identification in the equations of reflectance. I assume u is the magnetic moment and the epsilon is the dielectric constant. Also, in the portion between reflectance for magnetic and magnetic materials can we say..... " for materials that are repeled by a magnetic field" instead of "materials that are not magnetic". Both are technically correct but all materials have magnetic properties so it might be less confusing if we chose to incorporate something like "materials that repel a magnetic field." TerpeneOtto ( talk) 00:24, 21 January 2017 (UTC)
On 2017-11-05 I have replaced the plots for coefficients versus angle of incidence for air to glass and vice versa, for both amplitude and power coefficients, with substantially improved ones. The old plots by Ulflund (power coefficients) were very good, but showed only the values for reflection. The old plots by Kohlik17 showing the modulus of the amplitude coefficients were of low resolution and, in the case of glass-to-air, suffered from a limited vertical range hiding the important t>1 regime, and showed nonzero transmission in the TIR regime, which is just wrong physics. The new plots add power transmission, Brewster's angle for power plots, as well as expressions for the normal incidence limit as a function of . I tried to keep as many of the good things from Ulflund's plots as possible. Numerically, the new plots agree with the old ones by Ulflund, and for the amplitude coefficients I have checked them against 4th Ed. of Hecht. They are submitted in SVG format. The generating Python code will be shared when I get around to it.
I hope this edit is in line with how things are done here! Otherwise, please do let me know. Suggestions for further improvement welcome. Sbergjohansen ( talk) 11:50, 5 November 2017 (UTC)
Notice: Having added the "History" section, I'm now working on a "Derivation" section, covering both the "more general" case and the non-magnetic case. — Gavin R Putland ( talk) 09:07, 16 May 2018 (UTC).
[Above exchange moved from earlier on this page] Interferometrist ( talk) 16:29, 17 May 2018 (UTC)
P.S.: If my "Appendix: Theory" and its title are going to survive, it might be desirable to redirect "Derivation of Fresnel equations" and "Derivation of the Fresnel equations" to that appendix. — Preceding unsigned comment added by Gavin R Putland ( talk • contribs) 07:25, 20 May 2018 (UTC)
P.P.S: I am still suffering afterthoughts. Neither the old text nor my new appendix is yet consistent with the convention that the real part of the Poynting vector is related to average power. My appendix is also loose in its use of the term "magnitude". I shall attend to these matters ASAP. — Gavin R Putland ( talk) 15:29, 20 May 2018 (UTC).
but by (13) and (21) we will still have some reflection at non-normal incidence
So, for the incident, reflected, and transmitted H fields, let the respective components in the −z direction be Hi , Hr, Ht .
@ Gavin R Putland: and anyone else listening: I'm a bit busy and will respond quickly to some of your points:
For linear polarization, a complex vector is unnecessarily general; it suffices to use a constant unit vector multiplied by a complex scalar.
OTOH, some people expect that x is to the right and y is up. But I can change two diagrams if I have to.
I did it that way in order to re-use the red arrows.
.... especially when that breaks the last subsection.
OK, but one doesn't solve that problem by deleting the one subsection that refers to impedance
The formulae after ‘Making this substitution, we obtain equations using the refractive indices:’ seem to me to only depend on n = n₂ / n₁ and not on n₁ and n₂ separately.
Could you be a bit more specific? Can't you divide by n₁ above and below the division lines in the expressions for Rs and Rp?
Please add a photo on 's and p polarization' to describe it. Himadrichakrabortydip ( talk) 15:05, 15 May 2022 (UTC)
Overview
In overview section, it is said "The equations assume the interface between the media is flat and that the media are homogeneous and isotropic. The incident light is assumed to be a plane wave, which is sufficient to solve any problem since any incident light field can be decomposed into plane waves and polarizations".
However, I think it is important to add this content in order to have a more complete explanation:
Also, media are non-absorbing, meaning that the refractive index is a real value. the methodology below is a great approximation for weak absorbing media however, at strong absorbing media (as plasmas) different expressions are valid, known as generalised Fresnel Equations [1].
Complex amplitude reflection and transmission coefficients
In complex amplitude reflection and transmission coefficients section it is said that "The equations consider a plane wave incident on a plane interface at angle of incidence, a wave reflected at angle , and a wave transmitted at angle. In the case of an interface into an absorbing material (where n is complex) or total internal reflection, the angle of transmission does not generally evaluate to a real number. In that case, however, meaningful results can be obtained using formulations of these relationships in which trigonometric functions and geometric angles are avoided; the inhomogeneous waves launched into the second medium cannot be described using a single propagation angle."
I think that is important to add this sentence:
The more complete theory must be used, which considers two different angles: one for the equi-phase versor (wave propagation direction) and the other for the equi-amplitude versor (wave attenuation direction) [2].
Multiple surfaces
To a more complete Multiple surfaces section, from published research work, this content is important to be here:
Moreover, the decomposition of the rays propagation into a geometric series allow us to use novel methods as the ones presented in [1] [3]
[1].
[3].
[2].
WhoIsD ( talk) 15:42, 10 May 2023 (UTC)
References
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help)
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help)
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help)
In the "Complex amplitude reflection and transmission coefficients" section, the given equation for power transmission coefficients for complex media is
But I don't think this equation can be correct. If
Based on my own derivation, I believe the correct expression (applicable to either polarization) is
I'm hesitant to change the page based on my derivation alone, but in the books I have and the bit of googling I did, I didn't find anything on this topic. I don't have access to the source quoted here ( [1]).
Would anyone else have any sources that confirm (or deny) my assertion? Perhaps someone has a copy of that Hecht book and could double-check what it says. I'd be happy to post my derivation here if anyone would like to see it. Homm2trschell ( talk) 17:11, 14 July 2023 (UTC)
References
This
level-5 vital article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
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There seems to be an incoherence on this page: while in the linked articles the transmission and reflection coeficient are defined as ratios of Amplitudes (in this case of the E-Field), the equations in this article seem to describe a ratio of intensities.
I see two possibilities to correct this:
with the intensities of the incident light and if the reflected light.
with the corresponding amplitudes of the electric field
I would prefer the second possibility since it corresponds to the majority of the literature I have at hand - but I don't have time to check and replace the graphs right now - I'll be back when I have more time and take care of this if nobody else has until then...—The preceding unsigned comment was added by Nanomage ( talk • contribs) .
I also think that the equations for the reflection and transmission coefficients of the electric field should be given, further more their relation to the intensities should be emphasized and not only linked to. Some people care about phase, for example when going from low index to high index there is a 180 phase change at reflection, but when going from high index to low there isn't. Also r^2+t^2 is not equal to 1. Unlike the sum of the intensities which take into account the different velocities of the fields in different media. I think that ignoring amplitudes is simpler but will lead to misunderstandings as the texts and many people refer to amplitudes. —Preceding unsigned comment added by Eranus ( talk • contribs) 16:16, 21 July 2008 (UTC)
-Shouldn't also be pointed out that the refractive index used for these equations is a complex number? --an anonymous Raptor 10:00,07/10/05 CET
I think the equation for p-polarization is wrong. From what I've seen in the literature, the following should be the equation:
—The preceding unsigned comment was added by 132.206.69.48 ( talk • contribs) .
Why not include the equations for both intensity and amplitude and make clear which is which and where each is used?- 4.232.0.63 17:06, 7 August 2006 (UTC)
Power ratio or intensity ratio? They are differnt!-- Antonysigma ( talk) 16:55, 1 May 2011 (UTC)
Please state somewhere that the incident theta angle is in the range [0,90] degrees, otherwise the trigonometric expressions are not valid. — Preceding unsigned comment added by Ed.fuentetaja ( talk • contribs) 01:57, 19 August 2019 (UTC)
All references at my disposal use z not s in all forms. -- 4.232.0.63 16:52, 7 August 2006 (UTC)
Some physics in the article are imprecise. Approximations or assumptions made for some formulae are not clearly spelled out (e.g. the paragraph on reflectivity of a dual-surface window and the next paragraph on Fabry-Perot interference directly contradict each other), and other assumptions may be misleading (i.e. mentioning dielectric materials, but neglecting parelectric materials). Contrary what is claimed in the article, Fabry-Perot interferometers cannot be used to create perfect mirrors or reflection-free lenses (causality, i.e. the Kramers-Kronig relations, dictates that there is always some absorption.)
I spent a while editing the article, but Wikipedia lost the edited version on trying to preview it. I'm not sure I want to go through that frustration again, so someone else has to correct the article. —Preceding unsigned comment added by 218.186.8.10 ( talk • contribs)
This article needs to include the phase shifts associated with reflection and transmission from these surfaces. —Preceding
unsigned comment added by
140.247.5.34 (
talk) 17:17, 27 November 2009 (UTC)
I think the Fresnel equations should be expressed in terms of the amplitude instead of intensity. This will bring out important features such as the phase shift upon reflection when going from a low to a high index material. —Preceding unsigned comment added by 74.104.44.203 ( talk) 19:34, 27 November 2009 (UTC)
This article, like almost every textbook ever, makes the assumption that the relative magnetic permeability equals 1. This is all fine until you are trying to compute the reflection on a iron plate. If you derive the Fresnel equations without neglecting the magnetic permeability, then you quickly notice that the refractive index is not what should appear in them. Instead, we should see admittances (for the perp case) or impedances (for the para case). Refractive index: ; admittance ; impedance . When equals 0, the admittance and the refractive index both look like (the gets simplified), hence the confusion that is repeated everywhere. But fundamentally, this is wrong. We obviously cannot correct the main equations since they're in every textbook (except Stratton's, he got it right, even though he used the weirdest notations ever), but having a paragraph for the case wouldn't hurt, especially since the formulas aren't even more complicated. Niriel ( talk) 00:25, 28 October 2014 (UTC)
Would it be okay to redirect a Fresnel's law page to this page? —The preceding unsigned comment was added by Wk muriithi ( talk • contribs) 13:03, 24 January 2007 (UTC).
The article says "For materials which absorb light, like metals and semiconductors, n is complex, and Rp does not generally go to zero." But don't clean metallic surfaces essentially not absorb light? Is this right? —Ben FrantzDale ( talk) 21:56, 30 April 2008 (UTC)
I've heard the term " optical coupling" and " wetting out" to describe what happens when optical films come in contact. I assume this is the transition from a film-air-film sandwich to a film-film sandwich as the air thickness starts to get well below the wavelength of the light. Could someone point me to more information on that? 155.212.242.34 ( talk) 14:16, 19 May 2008 (UTC)
Since the whole article deals with intensities, it is confusing that the picture deals with amplitudes (there is no negative intensity) I added the word amplitude in the caption of the article, I think the article requires more info on amplitudes. Eranus ( talk) 08:26, 22 July 2008 (UTC)
I don't think this is the case for an equation. I mean, none of the other non-inline equations in this article have period after them.-- Zipspeed ( talk) 14:02, 17 May 2009 (UTC)
I'm concerned that there appears to be a sign error in the numerator of the expression for Rp. Hecht (pp 114, 115, 4th ed) and Born and Wolf (p40, 3rd ed) both agree that the form should be:
Rp = n2Cos(θi) - n1cos(θt) / n2cos(θi) - n1cos(θt)
I'll attempt to make the change to make the formula for Rp agree with Hecht and Born and Wolf if I don't get any comments to the contrary.
Patrick ( talk) 04:23, 8 June 2009 (UTC)
I think someone needs to take a look at the Fresnel equations, with respect to definitions of amplitude coefficients and intensity, as it has the potential to confuse. I think the amplitude coefficents should be quoted, rather than the intensity, and then a note made that the intensity is simply the square of the amplitude. —Preceding unsigned comment added by Nheath555 ( talk • contribs) 09:28, 22 October 2009 (UTC)
I think a history section would be a nice addition. I can't find the original form of Fresnel equations when did Fresnel derive them, when where did he publish them? An hour on Google and Google scholar did not help me much in contrast to History of Young's double slit experiment, Snell's law, Fresnel propagation... which are well documented, I would appreciate any refferance anyone may have. Eranus ( talk) 17:48, 28 August 2009 (UTC)
I'm wondering if I'm the first one noticing that the formula with the difference of angles fails at normal incidence:
and
both resolve to zero for , i.e. normal incidence. This is clearly wrong.
The problem lies in the careless simplification of the correct expression (for , but similar arguments hold for the case of )
using Snell's law . Multiplying the numerator and denominator of with (e.g.) is only allowed if is not zero, which it of course is in the case of normal incidence.
The correct result for normal incidence is given further down on the page. My suggestion is to remove the terms with the difference of angles and just keep the following expressions, i.e. change
to
and correspondingly for .
Oliver Jennrich ( talk) 08:05, 23 April 2010 (UTC)
(The last expression is valid at non-normal incidence, but at normal incidence it equals 0/0.)
or something like that :-) -- Steve ( talk) 09:00, 23 April 2010 (UTC)
I suggest, if possible, that the autor of the graphics modifies them by plotting the coefficients for a refraction index of 1.5, more typical af a glass, which is the main material dealt with in the article. -- GianniG46 ( talk) 07:52, 15 June 2010 (UTC)
I suggest to include in the amplitude reflection coefficients the part beyond the critical angle of incidence for internal total reflection. I've quickly made this file:
but feel free to make a better one (which would perhaps include the transmission coeficients as well?) — Preceding unsigned comment added by Coussin00 ( talk • contribs) 15:20, 19 April 2021 (UTC)
I just wanted to direct your attention to a recent disambiguation implemented in transmittance involving Fresnel equations: see here. Thanks. Fgnievinski ( talk) 22:30, 9 March 2011 (UTC)
There is a sentence in the article:
This should be true *only if* R and T are defined in amplitudes.
However, the formula given in the article is in ratio of intensities:
i.e.
Although conservation of energy still applies (), the areas ,, are not the same. This means R+T should not be equal to 1! (except at normal incidence)
I wish to know what you think about it.-- Antonysigma ( talk) 16:05, 1 May 2011 (UTC)
The graphs shown are useful, but an index difference of n=1 to n=2 isn't very practical in real world situations. Practical examples with meaning to most readers will be 1/1.33 (air/water) or 1/1.5 (air/glass). Note that most practically common glasses occupy the narrow refractive index range between 1.45 and 1.55. In general, materials with refractive indices above 2 are very uncommon optical materials (though they of course exist). I suggest to redo the plots for 1/1.5 index contrast, if possible. — Preceding unsigned comment added by 13.2.16.151 ( talk) 18:00, 14 June 2011 (UTC)
Is there an error in the graph of Glass to Air amplitude coefficients? How can there be and in the portion of the graph corresponding to Total Internal Reflection? Kghandi ( talk) 03:35, 1 November 2016 (UTC)
I cleaned up the new material on amplitude equations, and rearranged things a bit, but have not checked the equations themselves against a reference. It's not clear to me that the coefficients and the associated beam and field geometries are adequately defined, nor that the equations properly capture the phase of r and t. The construction has problems, in that it divides vectors to get a scalar quantity. As written and both equal , which is clearly wrong. I think the E's are just missing subscripts, as in the captions on the new images.
I don't have time to work on this any more right now, and more pairs of eyes looking at it is probably a good idea anyway. I am on record above as being opposed to incorporation of the amplitude equations into this article, but am willing to give it a chance if we can get them explained clearly and correctly, with the geometry and sign conventions fully defined.
Also on the to-do list: verify that these equations actually describe ratios of electric field amplitudes, as claimed in the text, and not the square root of intensity or some other quantity. It's been too long since I looked at the Fresnel equations for me to do that off the top of my head, but I've seen derivations that use square root of intensity and call it "E". -- Srleffler ( talk) 08:47, 18 December 2011 (UTC)
It is requested that a physics diagram or diagrams be
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-- Srleffler ( talk) 21:03, 18 December 2011 (UTC)
that is impossible for me to read (colorblind)... any way you can make it not red and blue? — Preceding unsigned comment added by 23.118.190.205 ( talk) 14:45, 16 June 2014 (UTC)
For a while the article has used the sign convention for rp where positive means that the magnetic field's orientation does not change. That means that rs and rp have opposite signs at normal incidence. There is nothing incorrect about this, since it's just a convention and the article is consistent as written. But I do think the opposite sign convention for rp is more common and we should follow whatever convention is most common. Also, you can easily find statements in references like "Reflected light will experience a 180 degree phase change when it reflects from a medium of higher index of refraction and no phase change when it reflects from a medium of smaller index." [5], which is a nice clean statement to make but only works with the opposite sign convention for rp. (Well, it still doesn't work for p-polarization at very oblique angles, but it works in every other case!)
I actually switched it a while ago and was reverted, with the comment that we need to discuss on the talk page. So let's discuss! What do other people think? -- Steve ( talk) 13:24, 5 June 2015 (UTC)
Update: I checked 6 mainstream textbooks, and I found 3 of each convention!
So I was incorrect when I said above that the rp<0 convention is "more common". Sorry! :-P
Hecht is a widely used and respected textbook, as Glrx rightly points out, but then again so is Griffiths, and Feynman, and Jackson for that matter. I think it's more-or-less a tie.
Srleffler: When light in air reflects off glass at normal incidence, the electric field switches sign (or you could say, it changes phase by pi), while the magnetic field keeps the same sign (or you could say, it changes phase by 0). Related to this, there are two ways to define the relative phase of oppositely-propagating light beams, the one based on whether the magnetic field is in phase or not, and the one based on whether the electric field is in phase or not. These two conventions line up with the two possible signs of rp.
Is one convention better than the other? Normally we care a lot more about the relative phase of the electric field, not magnetic field, because the electric field plays a much bigger role in light-matter interaction. The change I'm proposing is consistent with that preference. After that change, at normal incidence, we would be describing light as out-of-phase or in-phase based on the electric field, whereas with the current sign convention it's based on the magnetic field.
However, at glancing angle, that's no longer true. At glancing angle, the convention currently in the article is clearly superior to the one I'm proposing...
Given that, I'm starting to think that the convention in the article is best after all. Never mind. Thanks for the feedback :-D -- Steve ( talk) 21:59, 10 June 2015 (UTC)
Why do you think that the convention used is superior to the one you actually proposed at glancing angle? Somehow I'm also confused since Hecht 4th Edition states in (Eq. (4.38)) that there is no phase shift for normal incidence for the E-field. Am I mixing something up? Asdfawer2 ( talk) 22:51, 26 July 2015 (UTC)
Again, I just mean not even in Hecht the formulas seem consitent (from my point of view).
Looking at Eq. 4.32 for normal incidence at an interface from lower to higher refractive index he states , since . Eq. 4.38 yields . Since Hecht defines the reflection coefficients including the phaseshift, as there may only be a phaseshift of pi or 0, resulting in . For me its not clear how you would argue that you could infer a phase relation for any angle. Of course I agree with you in the extreme cases its obvious how the signs should look like, I just mean we could state more precisely what each reflection coefficient stands for, e.g. , in the currently used convention, which from my point of view does ""not"" agree with Hecht.
I hope I could clarify my point.
Asdfawer2 (
talk) 00:11, 5 August 2015 (UTC)
Edit
Asdfawer2 (
talk) 00:57, 5 August 2015 (UTC)
Why is there an empty section called "Special cases"? — Preceding unsigned comment added by 129.242.204.238 ( talk) 07:47, 25 October 2016 (UTC)
I disagree with this edit. The s and p should not be given "math" formatting when they appear in plain text, because they are not mathematical objects notwithstanding the fact that they appear in the equations as labels on variables. "S polarization" and "p polarization" are simply the English names for these two characteristics. I prefer them in italics, per Italic type#Usage, "Using a letter...mentioned as itself", but I'm open to arguments that that doesn't apply here because the s and p are not truly referring to themselves in this case. They should still be in italics in their first appearance in the text, however, as "Introducing or defining terms, especially technical terms or those used in an unusual or different way."-- Srleffler ( talk) 02:17, 14 November 2016 (UTC)
The u and the epsilon are missing identification in the equations of reflectance. I assume u is the magnetic moment and the epsilon is the dielectric constant. Also, in the portion between reflectance for magnetic and magnetic materials can we say..... " for materials that are repeled by a magnetic field" instead of "materials that are not magnetic". Both are technically correct but all materials have magnetic properties so it might be less confusing if we chose to incorporate something like "materials that repel a magnetic field." TerpeneOtto ( talk) 00:24, 21 January 2017 (UTC)
On 2017-11-05 I have replaced the plots for coefficients versus angle of incidence for air to glass and vice versa, for both amplitude and power coefficients, with substantially improved ones. The old plots by Ulflund (power coefficients) were very good, but showed only the values for reflection. The old plots by Kohlik17 showing the modulus of the amplitude coefficients were of low resolution and, in the case of glass-to-air, suffered from a limited vertical range hiding the important t>1 regime, and showed nonzero transmission in the TIR regime, which is just wrong physics. The new plots add power transmission, Brewster's angle for power plots, as well as expressions for the normal incidence limit as a function of . I tried to keep as many of the good things from Ulflund's plots as possible. Numerically, the new plots agree with the old ones by Ulflund, and for the amplitude coefficients I have checked them against 4th Ed. of Hecht. They are submitted in SVG format. The generating Python code will be shared when I get around to it.
I hope this edit is in line with how things are done here! Otherwise, please do let me know. Suggestions for further improvement welcome. Sbergjohansen ( talk) 11:50, 5 November 2017 (UTC)
Notice: Having added the "History" section, I'm now working on a "Derivation" section, covering both the "more general" case and the non-magnetic case. — Gavin R Putland ( talk) 09:07, 16 May 2018 (UTC).
[Above exchange moved from earlier on this page] Interferometrist ( talk) 16:29, 17 May 2018 (UTC)
P.S.: If my "Appendix: Theory" and its title are going to survive, it might be desirable to redirect "Derivation of Fresnel equations" and "Derivation of the Fresnel equations" to that appendix. — Preceding unsigned comment added by Gavin R Putland ( talk • contribs) 07:25, 20 May 2018 (UTC)
P.P.S: I am still suffering afterthoughts. Neither the old text nor my new appendix is yet consistent with the convention that the real part of the Poynting vector is related to average power. My appendix is also loose in its use of the term "magnitude". I shall attend to these matters ASAP. — Gavin R Putland ( talk) 15:29, 20 May 2018 (UTC).
but by (13) and (21) we will still have some reflection at non-normal incidence
So, for the incident, reflected, and transmitted H fields, let the respective components in the −z direction be Hi , Hr, Ht .
@ Gavin R Putland: and anyone else listening: I'm a bit busy and will respond quickly to some of your points:
For linear polarization, a complex vector is unnecessarily general; it suffices to use a constant unit vector multiplied by a complex scalar.
OTOH, some people expect that x is to the right and y is up. But I can change two diagrams if I have to.
I did it that way in order to re-use the red arrows.
.... especially when that breaks the last subsection.
OK, but one doesn't solve that problem by deleting the one subsection that refers to impedance
The formulae after ‘Making this substitution, we obtain equations using the refractive indices:’ seem to me to only depend on n = n₂ / n₁ and not on n₁ and n₂ separately.
Could you be a bit more specific? Can't you divide by n₁ above and below the division lines in the expressions for Rs and Rp?
Please add a photo on 's and p polarization' to describe it. Himadrichakrabortydip ( talk) 15:05, 15 May 2022 (UTC)
Overview
In overview section, it is said "The equations assume the interface between the media is flat and that the media are homogeneous and isotropic. The incident light is assumed to be a plane wave, which is sufficient to solve any problem since any incident light field can be decomposed into plane waves and polarizations".
However, I think it is important to add this content in order to have a more complete explanation:
Also, media are non-absorbing, meaning that the refractive index is a real value. the methodology below is a great approximation for weak absorbing media however, at strong absorbing media (as plasmas) different expressions are valid, known as generalised Fresnel Equations [1].
Complex amplitude reflection and transmission coefficients
In complex amplitude reflection and transmission coefficients section it is said that "The equations consider a plane wave incident on a plane interface at angle of incidence, a wave reflected at angle , and a wave transmitted at angle. In the case of an interface into an absorbing material (where n is complex) or total internal reflection, the angle of transmission does not generally evaluate to a real number. In that case, however, meaningful results can be obtained using formulations of these relationships in which trigonometric functions and geometric angles are avoided; the inhomogeneous waves launched into the second medium cannot be described using a single propagation angle."
I think that is important to add this sentence:
The more complete theory must be used, which considers two different angles: one for the equi-phase versor (wave propagation direction) and the other for the equi-amplitude versor (wave attenuation direction) [2].
Multiple surfaces
To a more complete Multiple surfaces section, from published research work, this content is important to be here:
Moreover, the decomposition of the rays propagation into a geometric series allow us to use novel methods as the ones presented in [1] [3]
[1].
[3].
[2].
WhoIsD ( talk) 15:42, 10 May 2023 (UTC)
References
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In the "Complex amplitude reflection and transmission coefficients" section, the given equation for power transmission coefficients for complex media is
But I don't think this equation can be correct. If
Based on my own derivation, I believe the correct expression (applicable to either polarization) is
I'm hesitant to change the page based on my derivation alone, but in the books I have and the bit of googling I did, I didn't find anything on this topic. I don't have access to the source quoted here ( [1]).
Would anyone else have any sources that confirm (or deny) my assertion? Perhaps someone has a copy of that Hecht book and could double-check what it says. I'd be happy to post my derivation here if anyone would like to see it. Homm2trschell ( talk) 17:11, 14 July 2023 (UTC)
References