# Why does light slow down in a medium?

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?

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.

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
Mentor

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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
Gold Member
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
Gold Member
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.

This topic needs to be a sticky.

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.

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Staff Emeritus
This topic needs to be a sticky.

It is. It doesn't help.

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.

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 travelling 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.

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When light enters a transparent medium, it becomes a phonon - it's no longer a photon travelling 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.

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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.

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.
(more there in post #8)

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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.

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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.

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!

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
Gold Member
And in a way, she was completely correct.

When light enters a transparent medium, it becomes a phonon - it's no longer a photon travelling 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?

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.

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TonyClifton
nasu
Gold Member
Maybe the name phonon is more appropriate.

For electromagnetic wave propagating in a crystal?

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

Light travelling 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 text books. Phonon is also use to describe sound or shockwaves passing through a medium. But essentially they're the same thing.

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

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 realised 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 travelling at relativistic speeds. It's travelling 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)

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nasu
Gold Member
I have only heard the use of the term phonon to describe light in a medium relatively recently. I had not seen it in text books.
Do you have a reference for this?

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