Speed of Light in Media: Why Does It Vary?

[_PJ_]

Firstly, I must apologise if this thread is in the wrong place on the forums. I wasn't entirely sure where it might suit best.

My question arises from something taken pretty much as read without much thought. That light travels through varying edia at varying speeds.

I am curious as to why this is?

In the case of massive objects on larger-than-elementary scales, the concept of movement through matter being slowed make sense. Swimming, for example, there are water molecules that must be pushed aside, whereas in the air, there are more 'gaps' between molecules and the air molecules are 'easier' to push aside.

Yet for subatomic particles such as photons, passing through water, any incidents of contact would result in certain energy exchanges, whereas the photons that do not enter any contact or exchanges with particles would simply continue on unabated.

Is there simply a case where all (or an overwhelming majority) of photons DO collide and are then scattered and/or re-emitted, and it is the time taken between various particles emitting and absorbing photons in succession that results in the longer time takemn, therefore a slower OBSERVED speed, or perhaps, multiple scattering causes a greater distance until the photons finally reach the observer, again, indicating a slower OBSERVED speed?

Even if the two possibilities I could think of outlined above are responsible, it still implies a speed of 'c', where only the distance or time taken for an individual photon is inadequately assumed, so the result of a slower speed is in fact, incorrect.

 

[DaveC426913]

There is an FAQ on this:
https://www.physicsforums.com/showpost.php?p=899393&postcount=4

 

[_PJ_]

Thanks for the link, I must admit, I didn't search :(

The implication, then, is that absorption-reabsorption is responsible for a delay, this then agrees that ligt does NOT travel slower, but the time taken for its journey is incorrect?

However, since the virtual photon absorption and reabsorption cycles of the "quantum foam" of the universe is possible in the 'vacuum' of space, then maybe there is a similar delay here as well? Only this delay is so small, and, because it would be all-pervasive (in addition to any delay when traveling through other matter as well), that it is largely irrelevant and extremely likely to be immeasurable as well?

 

[Electrocuted]

Light indeed does not travel slower. The time taken for the journey is correct. The reason? What you are calculating is not the speed of light. You are actually tabulating the average of the speed of light and the time taken for photon exchange within the medium travelled. Thus, the time taken seems incorrect. You're actually including an additional value which shouldn't be included.

 

[Saw]

It seems to me that the delay is not only due to "the time taken for photon exchange". It must also be caused by the fact that the photon's direction is changed, once and again, as it finds its way through the looser atoms of a transparent material.

I mean, the "photon exchange" process is not that the photon is absorbed through the front door and reemitted through the back door, after following a straight line. Should that be the case, opaque materials would not be opaque. I suppose the photon will be re-emitted following the law of reflection (angle of incidence equals angle of reflection): if that happens in an opaque material (atoms closely packed-up), it means "external" reflection; if instead it happens in a transparent material (loose atoms, with interstices), it entails "internal" reflection and, ultimately, "transmission".

Or maybe I missed something?

 

[ZapperZ]

But you can falsify your own explanation here. If the direction is changed, then why would you see the same image in such a clear, coherent fashion AFTER light has passed through a piece of glass? We know what happens when light scatter off a medium in such a fashion - try shinning light through smoke or a fog! That's what happens when its scattered in a diffuse manner.

Is this what you see when it passes through glass?

Again, as stated in the FAQ, this has nothing to do with "atom" interaction or absorption.

Zz.

 

[Saw]

But you can falsify your own explanation here. If the direction is changed, then why would you see the same image in such a clear, coherent fashion AFTER light has passed through a piece of glass? We know what happens when light scatter off a medium in such a fashion - try shinning light through smoke or a fog! That's what happens when its scattered in a diffuse manner.

Is this what you see when it passes through glass?

First, you are the expert and I only speculate. But please let me argue a little more.

What the FAQ says about the "collective" behaviour of the body (rather than the individual characteristics of atoms) being relevant, looks very reasonable. But relevant for what purpose? For the purpose of determining whether a certain frequency is absorbed instead of reflected? That is OK, I can understand that: if the body as a whole has a certain resonance frequency or available phonon, it will tend to absorb analogous frequencies and reflect others.

But does the "collective" behaviour of the body also determine how the light is reflected, that is to say, in which direction? It seems to me that your explanation suffers from the same objection that you attribute to mine. A photon impinges upon a piece of glass. It goes through it in a straight line and so I see a clear-cut image of what is behind the glass. Why this straight line? Because the material has a certain resonance frequency? I don´t see the connection.

Instead the common explanation does overcome that objection. The examples you mention of diffuse images (smoke, fog) correspond to gases, where the atoms are looser than in a liquid like water or a solid like glass (which, after all, is a sort of solidified liquid). If I enter a little populated room (a gas) and start bumping around among its inhabitants, I may end up nobody knows where. But if I enter a room where there is a tighter crowd (a liquid or glass), I will bump around with immediate neighbours but never managing to stray off a basic straight line. At least that is my experience with crowds.

Putting the two things together, I would conclude:

- The collective behaviour has a bearing on which EM radiation is absorbed and which is not, id est, which is reflected.
- Assuming EM radiation has been reflected, the way the atoms are arranged inside the body (more loosely or more tightly) determines whether it admits or not internal reflection of such EM radiation and hence its transmission. The outcome of this process of internal reflection should be a straight path if the atoms of the body are loose enough (to allow transmission) but tight enough (so that changes of direction basically cancel out). Nevertheless, those changes of direction do exist and have an influence on the time that light takes to traverse the glass.

 

[Austin0]

First, you are the expert and I only speculate. But please let me argue a little more.

What the FAQ says about the "collective" behaviour of the body (rather than the individual characteristics of atoms) being relevant, looks very reasonable. But relevant for what purpose? For the purpose of determining whether a certain frequency is absorbed instead of reflected? That is OK, I can understand that: if the body as a whole has a certain resonance frequency or available phonon, it will tend to absorb analogous frequencies and reflect others.

But does the "collective" behaviour of the body also determine how the light is reflected, that is to say, in which direction? It seems to me that your explanation suffers from the same objection that you attribute to mine. A photon impinges upon a piece of glass. It goes through it in a straight line and so I see a clear-cut image of what is behind the glass. Why this straight line? Because the material has a certain resonance frequency? I don´t see the connection.

Instead the common explanation does overcome that objection. The examples you mention of diffuse images (smoke, fog) correspond to gases, where the atoms are looser than in a liquid like water or a solid like glass (which, after all, is a sort of solidified liquid). If I enter a little populated room (a gas) and start bumping around among its inhabitants, I may end up nobody knows where. But if I enter a room where there is a tighter crowd (a liquid or glass), I will bump around with immediate neighbours but never managing to stray off a basic straight line. At least that is my experience with crowds.

Putting the two things together, I would conclude:

- The collective behaviour has a bearing on which EM radiation is absorbed and which is not, id est, which is reflected.
- Assuming EM radiation has been reflected, the way the atoms are arranged inside the body (more loosely or more tightly) determines whether it admits or not internal reflection of such EM radiation and hence its transmission. The outcome of this process of internal reflection should be a straight path if the atoms of the body are loose enough (to allow transmission) but tight enough (so that changes of direction basically cancel out). Nevertheless, those changes of direction do exist and have an influence on the time that light takes to traverse the glass.

Actually it seems like light can be reflected and refracted amazingly coherently through passage through extremely diffuse mediums ,,, temperature/pressure differentials in plain old air. Eg. Mirages and like phenomena ?

 

[ZapperZ]

First, you are the expert and I only speculate. But please let me argue a little more.

What the FAQ says about the "collective" behaviour of the body (rather than the individual characteristics of atoms) being relevant, looks very reasonable. But relevant for what purpose? For the purpose of determining whether a certain frequency is absorbed instead of reflected? That is OK, I can understand that: if the body as a whole has a certain resonance frequency or available phonon, it will tend to absorb analogous frequencies and reflect others.

But does the "collective" behaviour of the body also determine how the light is reflected, that is to say, in which direction? It seems to me that your explanation suffers from the same objection that you attribute to mine. A photon impinges upon a piece of glass. It goes through it in a straight line and so I see a clear-cut image of what is behind the glass. Why this straight line? Because the material has a certain resonance frequency? I don´t see the connection.

Instead the common explanation does overcome that objection. The examples you mention of diffuse images (smoke, fog) correspond to gases, where the atoms are looser than in a liquid like water or a solid like glass (which, after all, is a sort of solidified liquid). If I enter a little populated room (a gas) and start bumping around among its inhabitants, I may end up nobody knows where. But if I enter a room where there is a tighter crowd (a liquid or glass), I will bump around with immediate neighbours but never managing to stray off a basic straight line. At least that is my experience with crowds.

Putting the two things together, I would conclude:

- The collective behaviour has a bearing on which EM radiation is absorbed and which is not, id est, which is reflected.
- Assuming EM radiation has been reflected, the way the atoms are arranged inside the body (more loosely or more tightly) determines whether it admits or not internal reflection of such EM radiation and hence its transmission. The outcome of this process of internal reflection should be a straight path if the atoms of the body are loose enough (to allow transmission) but tight enough (so that changes of direction basically cancel out). Nevertheless, those changes of direction do exist and have an influence on the time that light takes to traverse the glass.

You are using different explanation for different phenomenon, and then you conclude it doesn't work. OF COURSE it doesn't!

Reflection is a different mechanism. In metals, which makes the best mirrors for visible light, it is the PLASMON, i.e. the presence of conduction electrons, that is responsible for such an effect, not the phonon modes! It is entirely different!

You are using faulty reasoning for the wrong phenomenon, and then concluding it doesn't work! Of course not!

Zz.

 

[Saw]

You are using different explanation for different phenomenon, and then you conclude it doesn't work. OF COURSE it doesn't!

Reflection is a different mechanism. In metals, which makes the best mirrors for visible light, it is the PLASMON, i.e. the presence of conduction electrons, that is responsible for such an effect, not the phonon modes! It is entirely different!

You are using faulty reasoning for the wrong phenomenon, and then concluding it doesn't work! Of course not!

Well, then for sure you're right and my statement was not. But then let me learn where was the mistake. I confess I am at a loss. I've re-read the FAQ. Is this summary right: "there is a brief absorption and re-emission of the photon (which is what causes the delay) although not at the atomic level, but at the level of the lattice of ions and electrons"? Are there different lattices in one solid, so that the photon "jumps" from one to the other, or a single one? I understand that there are several, since you say that the photon may encounter one and then others. In any case, how is it that the photon impinges on one edge of the lattice and comes out by the other end? How does the info propagate along the lattice, at the speed of sound? Sorry for my ignorance.

 

[ZapperZ]

Well, then for sure you're right and my statement was not. But then let me learn where was the mistake. I confess I am at a loss. I've re-read the FAQ. Is this summary right: "there is a brief absorption and re-emission of the photon (which is what causes the delay) although not at the atomic level, but at the level of the lattice of ions and electrons"? Are there different lattices in one solid, so that the photon "jumps" from one to the other, or a single one? I understand that there are several, since you say that the photon may encounter one and then others. In any case, how is it that the photon impinges on one edge of the lattice and comes out by the other end? How does the info propagate along the lattice, at the speed of sound? Sorry for my ignorance.

I have no idea wha tyou mean by "photon jumps from one to the other". There are no "photon jumps". The phonon density of states is usually continuous. There are no "jumps".

If the vibrational mode isn't there (such as in a photonic band gap material), then the lattice simply cannot sustain that mode and re-emit the EM wave. That's it. That photon may encounter other lattice phonons along the way and the same process repeats.

Zz.

 

[I_am_learning]

If the vibrational mode isn't there (such as in a photonic band gap material), then the lattice simply cannot sustain that mode and re-emit the EM wave. That's it.

Re emit in which direction? --> Same direction from which it absorbed. How does the lattice Remember it(direction from which it absorbed)?

 

[ZapperZ]

Re emit in which direction? --> Same direction from which it absorbed. How does the lattice Remember it(direction from which it absorbed)?

Again, as stated in the FAQ, this is the NAIVE picture of the whole scenario. Note that the E-field polarity defines the direction of oscillation for the lattice, and that's the same direction that gets "replayed" upon transmission. What this means is that the phonon transition absorbs and energy AND momentum of the photon, and then re-emits it with the same energy and momentum, assuming that a direct transition is allowed.

Notice how this is no longer a thread about Relativity, but has become a thread on Condensed Matter physics.

Zz.

 

[Austin0]

Reflection is a different mechanism. In metals, which makes the best mirrors for visible light, it is the PLASMON, i.e. the presence of conduction electrons, that is responsible for such an effect, not the phonon modes! It is entirely different!

Zz.

Hi ZapperZ In the case of plasmons and reflection,, isn't it more a situation where plasmons are a consequence of photon interaction/reflection rather than being a factor in determining that reflection.
Reflection is a uniform occurence throughout a whole range of materials with exactly the same behavior. Angle of incidence equals angle of reflection. This applies to non-conductive relflectors with no free electrons , no?

On phonons wrt refraction: It seems to me there are a bunch of real problems with phonons as a coherant explanation for refraction. IMO

1) It seems clear that phonon patterns are neccessarily going to be anisotropic.
Dependant on the molecular structure, degrees of freedom and structural bias of the medium.

As far as I know refraction is dependant only on the material index and the angle of incidence but is completely independant of the orientation with regard to the internal structure of the lattice. Is this incorrect?

2) Isn't it the case that there is not a singular uniform periodicity but rather a complex of waves with different orientations?

That the overall pattern is also temperature and momentum dependant and so not at all uniform.

That although the phenomenon has a wide, continuous, range of possible frequencies,
at anyone time there is only going to be a limited subset and yet there is uniformly consistent relative refraction through the frequency range of EM photons . Correct?

So is there something I am missing here?
Thanks PS isn't light as a phenomena ,its speed, etc a matter for SR?

 

[ZapperZ]

Again, I don't know why there is a propensity to use a mechanism for one particular phenomenon and using it for a DIFFERENT phenomenon. Since when is this about reflection and REFRACTION? Refraction is an INTERFACE phenomenon. There's no refraction while light is moving INSIDE a material! There is refraction when light goes through the interface between mediums with different index of refraction!

And this IS a condensed matter issue since it requires knowledge of how the material interacts with light. Optical conductivity inside a solid is a common condensed matter topic.

At this point, I think I'm getting quite tired of trying to explain something else that wasn't meant to be used in the first place. "Light travel in a media" is not reflection and is not refraction. You guys need to find another thread to for that.

Zz.

 

[Saw]

ZapperZ,

First, it seems you don´t want to discuss the subject. If you say so, for me that’s it and I will not post again in this thread.

Second, light travel in media is one of the typical subjects of SR. If you posted the FAQ, it must be because you shared that view. And if you included there an explanation based on condensed matter physics, then it should be because you thought that you weren’t deviating from the SR context. Now we’re only asking for clarifications of your explanation. Is the basic “naïve” explanation a matter of SR, while a sincere effort to understand it in more depth a non-SR related matter that must be ruled out of the forum?

Third, we all know what reflection, refraction, transmission and absorption are. The question is that, following the standard explanation, IF you think well of it, those four words or concepts reduce to only two: there is either reflection or absorption!

When a photon impinges on an atom, there are two possibilities: the frequency of the photon is “absorbable” or it is not; in the latter case the electron briefly jumps to a higher orbit (or energy state) only to the return soon to its original state and thus release the same energy it had acquired, i.e., it “reflects” the photon. This reflection will be outwards (if the material is opaque) or inwards (if it is transparent). If the reflection is inwards, there is a change of direction when light crosses the boundary between the two media and we call it “refraction” and if, on top of that, the photon manages to come out of the material (with or without other internal reflections), we talk about transmission.

This may be a way to put it that you have not heard, but I am pretty sure that it is consistent with the traditional explanation.

What the FAQ, instead, proposes is a different concept of “transmission”. It’s not only that the “collective behaviour of the atoms of the material” have relevance for the purpose of which frequencies are absorbable and which not (with which I have no problem). You go one step further: you say that the “lattice” (instead of the atom) gets the photon from one edge and expels it... (unlike the atom) by the other edge! Ok, that is a third possibility that was not in the standard explanation! That’s not absorption, of course, but it is not reflection, either. It is a third phenomenon. It may perfectly exist, but you should not be so surprised that we want to know the credentials of this new guest: how does it make the trick, how long does it take to do it…? And you should not be so surprised that we compare it with its predecessor in the role: reflection. Just repeating quite often that they are different phenomena is not a valid argument. Your “transmission through the lattice” should gain acceptance as a valid independent concept, vis-à-vis its competitor (“transmission by reflection”), if it proves that it works.

In this sense, there are some tests the new concept should pass:

- As thecritic put it, why is the photon re-emitted in the same direction?

Your answer was:

“Again, as stated in the FAQ, this is the NAIVE picture of the whole scenario. Note that the E-field polarity defines the direction of oscillation for the lattice, and that's the same direction that gets "replayed" upon transmission. What this means is that the phonon transition absorbs and energy AND momentum of the photon, and then re-emits it with the same energy and momentum, assuming that a direct transition is allowed.”

This triggers a new question:

- What is peculiar about transparent materials that allows their lattices to do this trick?

I say so, because if the lattices of opaque materials could do the same, we would have invented a way to make visible light pass through wood and steel…

- There is another question you didn’t answer.

You said: “If the vibrational mode isn't there (such as in a photonic band gap material), then the lattice simply cannot sustain that mode and re-emit the EM wave.”

But the lattice will have a certain length. The photon comes one way with its unsustainable frequency and goes out by the other edge with that very same unsustainable frequency. How does the right edge know that it must re-emit the photon with a certain unsustainable frequency that came through the left edge? How is that information (“such frequency is unsustainable”) transmitted from one end to the other? At what speed?

- AustinO also raised interesting concerns in his post #14.

Come on… Take the challenge to answer. It’ll either help you refine the theory or put it under doubt, who knows? It’s fun, anyhow.

 

[Austin0]

ZapperZ,

Third, we all know what reflection, refraction, transmission and absorption are. The question is that, following the standard explanation, IF you think well of it, those four words or concepts reduce to only two: there is either reflection or absorption!
When a photon impinges on an atom, there are two possibilities: the frequency of the photon is “absorbable” or it is not; in the latter case the electron briefly jumps to a higher orbit (or energy state) only to the return soon to its original state and thus release the same energy it had acquired, i.e., it “reflects” the photon. This reflection will be outwards (if the material is opaque) or inwards (if it is transparent). If the reflection is inwards, there is a change of direction when light crosses the boundary between the two media and we call it “refraction” and if, on top of that, the photon manages to come out of the material (with or without other internal reflections), we talk about transmission.

- As thecritic put it, why is the photon re-emitted in the same direction?

You said: “If the vibrational mode isn't there (such as in a photonic band gap material), then the lattice simply cannot sustain that mode and re-emit the EM wave.”
.

Hi Saw very interesting. I certainly see the point and validity of all your questions.
I think there is a certain semantic ambiguity in this realm.
In my mind there is reflection [and diffraction], refraction, interference,absorbtion and emmission. Reflection is not neccessarily synonamous with re-emmission. This also is a highly problematic hypothesis. With the problem thecritic mentioned above, being only one of them.
Reflection is also, not neccessarily, limited to the complete path change as represented by surface reflection. This is the interpretation that ZapperZ is apparently operating under.
There is also the possibility of reflection of part of the photon wave form ,equivalent to a photon passing through a double slit and then self interfering. That self interference with reflected portions of its own waveform may be a normal component of photon interaction.
With this interpretation, internal reflection could be very relevant to the path traveled by a photon in a medium. Any medium. The basic question of this thread relating to relative speeds of light applies to all situations, even the atmosphere.
So it would seem that a more universal explanation is required than lattice structure or phonons. IMO Hope this thread keeps going Cia0

 

[Saw]

Reflection is not neccessarily synonamous with re-emmission. This also is a highly problematic hypothesis. With the problem thecritic mentioned above, being only one of them.

Well, yes, it may be that I have taken inadvertently for granted that the process of "creation" of a photon is equivalent to that of its "reflection", which may not be true or at least not what standard physics would consider as accepted theory. Is that why you call it "a highly problematic hypothesis"? If so, better to leave out that part.

But I think, and thank you for that, that you correctly grasped that the essence of the argument remains valid, anyhow: we know that photons, when interacting with matter, are either absorbed or reflected (interference happens between photons; diffraction..., yes, let me think of it). I had interpreted "transmission" as a form of "internal reflection", which would follow the law of reflection in terms of direction. If we add to that that the frequencies that a crystal may sustain (and thus absorb) is a "band" determined by collective behaviour of a lattice, that's easy to swallow. But if you also add that the lattice "transmits" the photon without following the law of reflection, that requires more explanation. What makes the crystal lattices so special?

 

[ZapperZ]

In condensed matter physics, there is a sub-area of study called "Optical Conductivity". They study how light behaves and interact in matter. This is not something that is UNKNOWN as if we are meandering in the dark. In fact, we know so much about such a process, we USE it to study various properties of the solid. Techniques such as Raman scattering, FTIR, etc.. are ALL studies of light interaction with matter. It includes both reflection and transmission. One could even study particular phonon modes using such techniques.

So if one thinks that such "questions" regarding light behavior with solids are interesting, I would seriously recommend you major in condensed matter physics in graduate school, and take up optical conductivity experiments. Knock yourself out.

Zz.

 

[Saw]

So if one thinks that such "questions" regarding light behavior with solids are interesting, I would seriously recommend you major in condensed matter physics in graduate school, and take up optical conductivity experiments.

I may not have time for that.

Knock yourself out.

I may not feel like that.

But I did have time for and felt like consulting the Encyclopædia Britannica Article on Light. It says that, as a light beam goes through transparent glass, light waves are “reradiated”. (I had guessed “reflected”.) As a consequence of this, logically, they are SCATTERED.

Since you hold that they are NOT SCATTERED, but

Note that the E-field polarity defines the direction of oscillation for the lattice, and that's the same direction that gets "replayed" upon transmission. What this means is that the phonon transition absorbs and energy AND momentum of the photon, and then re-emits it with the same energy and momentum, assuming that a direct transition is allowed.

then your “question” was:

If the direction is changed, then why would you see the same image in such a clear, coherent fashion AFTER light has passed through a piece of glass? We know what happens when light scatter off a medium in such a fashion - try shinning light through smoke or a fog! That's what happens when its scattered in a diffuse manner. Is this what you see when it passes through glass?

Britannica’s answer is that “the reradiated waves within the glass interfere destructively in all directions except the original propagation direction of the beam, resulting in little or no light's being scattered out of the original beam.”

 

[ZapperZ]

Since when is "re-radiated" means scattered?

That in itself invalidates your whole post.

I really hate having to keep repeating myself. You are under no obligation to accept anything that I've said here.

Zz.

 

[Saw]

Since when is "re-radiated" means scattered?

That in itself invalidates your whole post.

The whole quote is:

"Through interference effects, the superposition of the reradiated waves from all of the participating atoms determines the net outcome of the scattering interactions. Two examples illustrate this point. As a light beam passes through transparent glass, the reradiated waves within the glass interfere destructively in all directions except the original propagation direction of the beam, resulting in little or no light's being scattered out of the original beam. Therefore, the light advances without loss through the glass."

The message is clear: when the waves are re-emitted or "re-radiated", they do not follow their original direction, as you held, but change direction (they are "scattered"), as one would normally expect.

I really hate having to keep repeating myself. You are under no obligation to accept anything that I've said here.

You are reading my thoughts! I fully suscribe it. Let's leave it like this. Regards.

 

[_PJ_]

Sorry for such a long delay in replying.

What reasons are given or theorized for the delay between absorption/emission, are there any specific formulae/equations used in calculating the delay based on some property of the material?

 

[asheg]

"Feynman lectures in physics: Volume1 Lecture 31" has good answers to your question. The lecture exactly begins with your question and so your question is important one in this field.

About your main question that why speed of light should be lower. It effectively (summation of field itself with field re-emitted by atoms behaves so) but the field itself moves with speed of light anywhere.

 

[_PJ_]

Excellent, thanks so much, Asheg!

 

[Claude Bile]

Sorry for such a long delay in replying.

What reasons are given or theorized for the delay between absorption/emission, are there any specific formulae/equations used in calculating the delay based on some property of the material?

The delay between absorption and emission is governed by the upper state lifetime.

Given the thread topic though, I can't help but suspect you are alluding to the relationship between absorption/emission and light propagation through a solid. The atomic origin of the refractive index is the degree to which the atoms within a solid or fluid can be polarized, which in turn is determined mainly by the structure of the valence electrons of the solid (i.e. how the bonds within the solid are arranged).

The Lorentz-Lorenz formula relates the refractive index to the solid-state properties of a material.

Claude.

 

[obama5493]

Light indeed does not travel slower. The time taken for the journey is correct. The reason? What you are calculating is not the speed of light. You are actually tabulating the average of the speed of light and the time taken for photon exchange within the medium travelled. Thus, the time taken seems incorrect. You're actually including an additional value which shouldn't be included.

It seems to me that the delay is not only due to "the time taken for photon exchange". It must also be caused by the fact that the photon's direction is changed, once and again, as it finds its way through the looser atoms of a transparent material.

I mean, the "photon exchange" process is not that the photon is absorbed through the front door and reemitted through the back door, after following a straight line. Should that be the case, opaque materials would not be opaque. I suppose the photon will be re-emitted following the law of reflection (angle of incidence equals angle of reflection): if that happens in an opaque material (atoms closely packed-up), it means "external" reflection; if instead it happens in a transparent material (loose atoms, with interstices), it entails "internal" reflection and, ultimately, "transmission".
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