Why does light slow down in a medium?

[professorscot]

I was tutoring a student in an optics lesson the other day. We discussed the foundational concept, that light travels more slowly in a physical medium (such as air, water, or glass) than in vacuum. She asked, "Why? Because of friction?" and I said, "No, not friction," but then I had to admit, I didn't know what mechanism actually causes a light wave to slow down. It would seem more intuitive to me that a beam of light passing through a physical medium would lose energy / momentum (frequency).

But what causes it to slow down?

 

[Whovian]

If I remember correctly (which I can almost guarantee you I'm not,) this is caused by (we might need to consider light as a particle for the moment) the photons repeatedly being absorbed and re-emitted by the atoms in the medium.

 

[Quine!]

Great question, I might be wrong here, and I don't think this is a complete or satisfying answer by any means but:

the speed of light in a vacuum, c, is defined as

c = 1/√ε$_{0}$$\mu$$_{0}$

where ε$_{0}$ is the permittivity of free space aka the electric constant, and $\mu$$_{0}$ is the permeability of free space, aka the magnetic constant.


Importantly, these constants are the permittivity of free space and the permeability of free space, respectively. These values are larger in other media, which is why the speed of light is slows. They also drop the "naught" subscripts and are just called ε and $\mu$

As to what permittivity and permeability actually are, I'd love to hear an explanation.
I also have a question: Are ε$_{0}$ and $\mu$$_{0}$ what fixes the speed of light or is it the other way around? I.e., Is the answer to the question: "why is c ≈ 3 ×10^5 km/sec?" just "because ε$_{0}$ and $\mu$$_{0}$ are such and such values" ?

 

[jtbell]

https://www.physicsforums.com/showthread.php?t=511177

 

[professorscot]

Good responses

Quine: You're right, ε and μ are just numbers used to describe the slow-down of light, but they don't explain why in terms of principles. And the three values c, ε₀, and μ₀ are most likely three parameters with two degrees of freedom. If any two of them are determined, the third is fixed. Other than that, I don't know if there is any rhyme or reason to their particular values.

Whovian: I thought about the idea of photons being absorbed and re-emitted by atoms, but then the re-emission would be scattered in every direction (and, as the article points out, only in discrete frequencies.

JTBell: Thanks for the article. This makes me feel assured that it's complicated, so I'm not just being dumb, LOL. The explanation offered here only makes sense for solid media. I have to give my student kudos for asking a really astute question!

 

[vanhees71]

First of all you have to ask what you mean by "light slows down". If you refer to the fact that in regions of normal dispersion in media $n(\omega)>1$ and thus the phase velocity of wave modes at such frequencies is $c_{\text{matter}}=c/n(\omega)<c$, that's right, but there are as well regions of frequencies, where $n(\omega)<1$, and then the phase velocity is higher than the speed of light in vacuo.

This has been a puzzle in the early history of relativity and has been answered comprehensively by Sommerfeld in a famous very short reply to a corresponding question by Wien in 1907. Later on Sommerfeld and Brillouin have worked out the traveling of em. waves through media, using classical dispersion theory (in linear response approximation) which is quite close to the full quantum theory. As it turns out the wave front always travels with the vacuum-speed of light, and there is no contradiction with the causality structure of special relativity although in regions of anomalous dispersion, the phase velocity (and also the group velocity, which however loses its physical significance precisely in these region!) are greater than the vacuum-speed of light.

They carefully approximated, how the em. wave behaves close to the wave front and found very interesting phenomena (the Sommerfeld and Brillouin precursers). The corresponding chapter in Sommfeld's textbook (Lectures on Theoretical Physics, Vol. 4) is still very valuable for a deeper understanding of these phenomena. If you can read German, also the original papers by Sommerfeld and Brillouin are worth being studied:

Sommerfeld, A. Über die Fortpflanzung des Lichtes in dispergierenden Medien. Ann. Phys. (Leipzig) 349 (1914), 177–202.
http://dx.doi.org/10.1002/andp.19143491002

Brillouin, L. Über die Fortpflanzung des Lichtes in dispergierenden Medien. Ann. Phys. (Leipzig) 349 (1914), 203.
http://dx.doi.org/10.1002/andp.19143491003

 

[nasu]

The above mentioned articles can be found in English translation in Brillouin's book "Wave propagation and group velocity". There are several editions, I think.

 

[Antiphon]

This topic needs to be a sticky.

 

[PhilDSP]

Quine: You're right, ε and μ are just numbers used to describe the slow-down of light, but they don't explain why in terms of principles. And the three values c, ε₀, and μ₀ are most likely three parameters with two degrees of freedom. If any two of them are determined, the third is fixed. Other than that, I don't know if there is any rhyme or reason to their particular values.

We need to remember though, that they're only numbers (constants) for source-less calculations. In isotropic media ε and μ become vectors and in anisotropic media they become tensors. They have physical meaning in relation to describing the impedance or conductivity of the vacuum or other EM media. They also have independent meaning in many physical situations. One fundamental limitation of Minkowski electrodynamics (and SR) is that ε and μ can only be dealt with in a passive sense and only as approximations, not as in classical EM where phenomena can be derived from their function and where the speed of EM propagation in any any situation can be decomposed.

 

[Vanadium 50]

This topic needs to be a sticky.

It is. It doesn't help.

 

[krd]

I was tutoring a student in an optics lesson the other day. We discussed the foundational concept, that light travels more slowly in a physical medium (such as air, water, or glass) than in vacuum. She asked, "Why? Because of friction?"

And in a way, she was completely correct.

and I said, "No, not friction,"

And you were completely wrong.

but then I had to admit, I didn't know what mechanism actually causes a light wave to slow down.

At least you admitted it.

It would seem more intuitive to me that a beam of light passing through a physical medium would lose energy / momentum (frequency).

Yes. That is what happens. Kind of.

But what causes it to slow down?

This is a great explanation Phil Moriarty Nottingham Sixty Symbols

When light enters a transparent medium, it becomes a phonon - it's no longer a photon traveling through a vacuum at the speed of light, it's a wave being propagated through a medium. So, there is a drag on the wave, and it slows down.


You would be surprised how many people have bluffed their way to a PhD without know this. Phil's explanation is good.

 

[PhilDSP]

When light enters a transparent medium, it becomes a phonon - it's no longer a photon traveling through a vacuum at the speed of light, it's a wave being propagated through a medium. So, there is a drag on the wave, and it slows down.

The problem with attaching either "drag" or "friction" to light traversing media is that it cannot be so. No momentum is lost. As the photon exits the media to again propagate through a vacuum it immediately assumes speed c and it's original frequency. The correct characterization of light entering media is called dispersion.

 

[PhilDSP]

I might add that because a wave packet that enters media is dispersed (its frequency components are no longer coherent) scattering can occur where different frequency components assume different trajectories. In that case, of course, the total momentum of the incoming packet will be divided into the total of all parts being scattered in different directions.

 

[harrylin]

I was tutoring a student in an optics lesson the other day. We discussed the foundational concept, that light travels more slowly in a physical medium (such as air, water, or glass) than in vacuum. She asked, "Why? Because of friction?" and I said, "No, not friction," but then I had to admit, I didn't know what mechanism actually causes a light wave to slow down. It would seem more intuitive to me that a beam of light passing through a physical medium would lose energy / momentum (frequency).

But what causes it to slow down?

Refraction is explained with scattering theory as light interacts with atoms.
- https://www.physicsforums.com/showthread.php?p=3772953
(more there in post #8)

 

[harrylin]

It is. It doesn't help.

The FAQ on it is not good enough, as I pointed out before.
To elaborate: while it does a good job in discussing collective behaviour, "re-emission" suggests earlier absorption which is wrong according to standard theory and that same FAQ. Moreover we can surely do better than providing a "naive" explanation.

I tried to do better in the aforementioned posts. Perhaps someone else who understands this stuff can rewrite the FAQ based on the existing FAQ and my textbook-based reply there.

 

[PhilDSP]

Scattering doesn't allows occur, I believe. (Unless you interpret scattering to include refraction and dispersion, which some apparently do) It might be best or clearest to separate the different concepts, then a person can walk through what occurs at what point and what causes each effect.

 

[harrylin]

Scattering doesn't allows occur, I believe. (Unless you interpret scattering to include refraction and dispersion, which some apparently do) It might be best or clearest to separate the different concepts, then a person can walk through what occurs at what point and what causes each effect.

Simultaneous with you I checked the dictionary and modified my phrasing to avoid the suggestion that the term "scattering" should include refraction - so we agree on that, and thanks anyway!

 

[andrien]

photons always travel with speed c.but when a light wave enters a medium, the electric field of the light shakes the electron of that medium which in turn create their own electric field(modified) the resultant of which appears as a phase shift which can be described by giving the light a speed c/n.

 

[nasu]

And in a way, she was completely correct.


When light enters a transparent medium, it becomes a phonon - it's no longer a photon traveling through a vacuum at the speed of light, it's a wave being propagated through a medium. So, there is a drag on the wave, and it slows down.

There are several confusing statements here, especially the part in blue.
What does it even mean? How does a photon "becomes" a phonon?

It is possible to have some interaction between photons and the phonons in the solid but I don't think this means that he phonon "becomes" a phonon.
At if it did then it won't contribute to the outgoing beam.

And the photon is a wave both outside and inside the medium, isn't it?

 

[PhilDSP]

photons always travel with speed c.but when a light wave enters a medium, the electric field of the light shakes the electron of that medium which in turn create their own electric field(modified) the resultant of which appears as a phase shift which can be described by giving the light a speed c/n.

The varying field created by the moving electron superimposes with the incident field variations to produce really a shift in frequencies that is different for each frequency. I think you'd have to consider that a continuously varying and very intense shift of many different phases. That's the essentials of dispersion and it occurs with all EM particles: free and semi-bound electrons, protons, atoms, molecules and arrays or groups of molecules.

Equations that give the results for more simple configurations of particle groups are the Lorentz-Lorenz formula and the Ewald-Oseen extinction theorem. It seems a bit problematic to still call the once-named photon a photon when it would be lengthened and fractured (by interaction with many particles at once). Maybe the name phonon is more appropriate.

 

[nasu]

Maybe the name phonon is more appropriate.

For electromagnetic wave propagating in a crystal?

 

[krd]

There are several confusing statements here, especially the part in blue.
What does it even mean? How does a photon "becomes" a phonon?

Light traveling through a vacuum is propagating itself - it's not being propagated through a medium - let's call that a photon. When it enters a transparent material - it is being propagated through a medium (through the electric fields of the atoms). If you see Adrien's note above. The light wave becomes a phonon. It will have the same frequency and wavelength, but will be moving slower. When it reaches the other end of the transparent material, it turns back into a photon.

It is possible to have some interaction between photons and the phonons in the solid but I don't think this means that he phonon "becomes" a phonon.

No. It's a phonon. I'll give you another example. All objects give off a continuous spectra of black body radiation. How that happens is the atoms in an object giggle with each other - the giggling causes their electric fields to move against each other - the resultant effect is phonons. And since it's mostly random, you get a broad spectra of wavelengths. Once those phonons reach the surface of the material, they turn into photons. Into light.

At if it did then it won't contribute to the outgoing beam.

Okay, something that's probably not the best example, but will give you an idea of what happens. If your neighbour starts blasting really loud hip hop late at night - the sound from his speakers will reach your dividing wall. When hits the wall, some will enter the wall - when it does it will become a phonon. And when that wave reaches the other side of the wall, it re-emerges as a sound wave in your house.

Light through a transparent material does something very similar. But light - heat leaving a body as light - from a body that is not transparent or even black - is doing the same thing.

And the photon is a wave both outside and inside the medium, isn't it?

The wave is the same. But it's not a photon. The wave will be dissipated. That's why it's pitch black at the bottom of the ocean.


I have only heard the use of the term phonon to describe light in a medium relatively recently. I had not seen it in textbooks. Phonon is also use to describe sound or shockwaves passing through a medium. But essentially they're the same thing.

 

[harrylin]

[..] I have only heard the use of the term phonon to describe light in a medium relatively recently. I had not seen it in textbooks. Phonon is also use to describe sound or shockwaves passing through a medium. But essentially they're the same thing.

I thought - and still think- that a phonon is by definition some kind of quantized sound wave, which thus propagates at the speed of sound. If so, that should not be confounded with refraction.

 

[krd]

I thought - and still think- that a phonon is by definition some kind of quantized sound wave, which thus propagates at the speed of sound.

If so, that should not be confounded with refraction.

I think you're confounded.

This is really neat and it will join up a lot of things for you that you may not have realized were so connected. Like black body radiation - how heat travels - even how sound can turn into heat (the shock wave from an explosion is sound).

The sound wave always needs to a medium to propagate through - it's always a phonon. Though in a gas it travels longitudinally and in a solid transverse. A major difference between the sound phonon and the light phonon is the light phonon is traveling at relativistic speeds. It's traveling near the speed of light, not near the speed of sound.

Imagine if I had a crystal - all the atoms being held in place by their electric fields - imagine these fields are made of some kind of elastic and flexible material. If I bob one atom against another, they'll giggle up and down. There will be a little oscillation. That oscillation will not be restricted to those two atoms, it will spread through electric fields of the nearby atoms, and they'll spread it to their neighbours. If it reaches the edge of the crystal, and escapes, it becomes light.

Something similar happens when you're heating soup on a stove.

The refraction of light can only happen in a medium, it can't happen in a vacuum. In a vacuum all wavelengths of light travel at the same speed, in a medium they can't - the path lengths of the wave are different.

Just to say something else - if I pass a sound wave of 60Hz through a wall - the other side of the wall must flutter at 60Hz for the sound to pass into the other room - it has to push and pull the air. I'm not sure, but I wonder would you see a 60Hz light too (I don't mean see - I mean I wonder if it's there)

 

[nasu]

I have only heard the use of the term phonon to describe light in a medium relatively recently. I had not seen it in textbooks.

Do you have a reference for this?

And maybe for the distinction between a wave "propagating" in vacuum and "being propagated" in a medium?

 

[nasu]

A major difference between the sound phonon and the light phonon is the light phonon is traveling at relativistic speeds. It's traveling near the speed of light, not near the speed of sound.

Are talking about phonons in optical branches when you say "light phonon"?
If you do, they may have group velocities even lower than these of the phonons in acoustic branches.
If you mean something else, I would appreciate some reference.

Imagine if I had a crystal - all the atoms being held in place by their electric fields - imagine these fields are made of some kind of elastic and flexible material. If I bob one atom against another, they'll giggle up and down. There will be a little oscillation. That oscillation will not be restricted to those two atoms, it will spread through electric fields of the nearby atoms, and they'll spread it to their neighbours. If it reaches the edge of the crystal, and escapes, it becomes light.

You mean that every piece of solid material glows due to this light?

Just to say something else - if I pass a sound wave of 60Hz through a wall - the other side of the wall must flutter at 60Hz for the sound to pass into the other room - it has to push and pull the air. I'm not sure, but I wonder would you see a 60Hz light too (I don't mean see - I mean I wonder if it's there)

What would be the meaning of "60 Hz light"? You mean an electromagnetic wave with 60 Hz frequency? Or light (visible) modulated with a 60 Hz frequency?

PS. Is it possible that when you say that photons "become" phonons you may be referring to "polaritons" in a dielectric material (describing the coupling between optical phonons and photons)?

 

[harrylin]

[..] The sound wave always needs to a medium to propagate through - it's always a phonon. Though in a gas it travels longitudinally and in a solid transverse.
A major difference between the sound phonon and the light phonon is the light phonon is traveling at relativistic speeds. It's traveling near the speed of light, not near the speed of sound. [..]

What you say sounds neat but also sounds as if it's your own theory - and at first sight it flatly contradicts light scattering theory. As explained in the other thread, the effective speed of light in a medium is considered to be the result of light propagating at the vacuum speed through the medium, whereby the secondary electromagnetic waves that are created by mainly the oscillating electrons cause an effective delay of the resulting, compound light wave. In contrast, the literature describes photons - even those called "optical phonons" - as mechanical vibrations of the atoms. Electromagnetic waves and mechanical waves can be coupled, but are by far not the same thing.

 

[krd]

What you say sounds neat but also sounds as if it's your own theory - and at first sight it flatly contradicts light scattering theory. As explained in the other thread, the effective speed of light in a medium is considered to be the result of light propagating at the vacuum speed through the medium, whereby the secondary electromagnetic waves that are created by mainly the oscillating electrons cause an effective delay of the resulting, compound light wave. In contrast, the literature describes photons - even those called "optical phonons" - as mechanical vibrations of the atoms. Electromagnetic waves and mechanical waves can be coupled, but are by far not the same thing.

The medium is not a vacuum. If you think of the electrons are tiny points spinning around the atom, and most of their path is empty space most of the time - you might think it's a vacuum. But it's not it's - in a crystal lattice between the atoms is an electric field. That electric field is the medium.

In contrast, the literature describes photons - even those called "optical phonons" - as mechanical vibrations of the atoms.

And what is the mechanism of those mechanical vibrations of the atoms?

Electromagnetic waves and mechanical waves can be coupled, but are by far not the same thing.

If they're not the same thing, what are they?

If you take a piece of wire - and repeatedly bend it - warm it up through mechanical action. Then put it under a camera that can see the infrared spectrum - you'll see more light coming from it than before you warmed it up through bending it.

 

[Ghassan99]

Because the speed of the light depends on the Optical density ..Vacuum has no Optical density while other mediums as water and air have .

 

[krd]

Are talking about phonons in optical branches when you say "light phonon"?
If you do, they may have group velocities even lower than these of the phonons in acoustic branches.
If you mean something else, I would appreciate some reference.

Somewhere in this forum there is post with a much better description than I have. Unfortunately - I don't have the link.

You mean that every piece of solid material glows due to this light?

Yes. Every piece of solid material glows due to this light - it's black body radiation. I'm not saying it's the only means of light production - but for black body radiation it is.

What would be the meaning of "60 Hz light"? You mean an electromagnetic wave with 60 Hz frequency? Or light (visible) modulated with a 60 Hz frequency?

I was just thinking - if I vibrated a solid material at 60Hz, would I get a 60Hz light emission from the surface of the material As well as the push pull on the air. Because I would be vibrating the electric field of the material at 60Hz. Unfortunately, I'm nowhere near a lab or a well equip lab, where I could give it a go. Maybe if I went up into KHz I might be able to detect a radio wave.

PS. Is it possible that when you say that photons "become" phonons you may be referring to "polaritons" in a dielectric material (describing the coupling between optical phonons and photons)?

Ultimately, it's the same idea. You could describe it as the coupling of phonons with phonons. And the dielectric material gives you a polarised phonon. And similarly, a transparent medium like water, doesn't give you polarised phonons because it's not a dielectric material.

 

[nasu]

Somewhere in this forum there is post with a much better description than I have. Unfortunately - I don't have the link.

Do you need a link to explain what you mean by "light phonon"?

Yes. Every piece of solid material glows due to this light - it's black body radiation. I'm not saying it's the only means of light production - but for black body radiation it is.

OK, so when you say "light" you mean any electromagnetic radiation.
And your theory is that the black body radiation is just phonons that reach the boundary of the solid and get converted to outgoing photons?

Ultimately, it's the same idea. You could describe it as the coupling of phonons with phonons. And the dielectric material gives you a polarised phonon. And similarly, a transparent medium like water, doesn't give you polarised phonons because it's not a dielectric material.

You mean coupling of phonons with photons, right?

Water is not a dielectric? What do you consider it to be? A conductor? Is glass (transparent medium) a dielectric? Are there "polarized phonons" in glass? How about in (transparent) sodium chloride crystals?

 

[harrylin]

[..] And what is the mechanism of those mechanical vibrations of the atoms? [..]

Yes the mechanical vibrations are coupled to electromagnetic waves as those mechanical vibrations are based on a kind of electromagnetic springs. The point here was that the speed with which mechanical vibrations propagate depends on such things as the atom mass while the speed with which electromagnetic radiation propagates depends on vacuum permittivity and permeability - and as already explained in this thread and elsewhere, without interference from secondary electromagnetic (and not mechanical) waves, that speed would be even c inside glass.
- http://en.wikipedia.org/wiki/Vacuum_permittivity

It looks essential to me that we clearly distinguish between certain mechanical vibrations and the secondary electromagnetic waves that result from (other) mechanical vibrations. If you think otherwise, please try to explain -preferably based on reliable references- why light propagates with an effective speed of several 100'000 km/s in glass, and not with several km/s.

 

[wilbye]

So what happens if you initiate a beam of light and split it into two. Pass one split through a piece of glass and let the other pass unhindered. Do the two beams arrive at a single target at exactly the same time or does the one that passed through the glass arrive after the unhindered one?

 

[Whovian]

So what happens if you initiate a beam of light and split it into two. Pass one split through a piece of glass and let the other pass unhindered. Do the two beams arrive at a single target at exactly the same time or does the one that passed through the glass arrive after the unhindered one?

Depends on the setup.

 

[harrylin]

So what happens if you initiate a beam of light and split it into two. Pass one split through a piece of glass and let the other pass unhindered. Do the two beams arrive at a single target at exactly the same time or does the one that passed through the glass arrive after the unhindered one?

Hi welcome to physicsforums.
The classical explanation is that (mainly) the electrons in the glass atoms interact with the light wave so that they emit secondary waves which are slightly behind in phase and which interfere with the primary wave and each other. As a result the piece of glass delays the light beam; at equal distances that beam will arrive later. You can find more detailed explanations in earlier posts.