# Why does light slow down in a medium?

1. Jun 12, 2012

### 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?

2. Jun 12, 2012

### 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.

3. Jun 12, 2012

### 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" ?

4. Jun 12, 2012

### Staff: Mentor

Last edited by a moderator: May 6, 2017
5. Jun 13, 2012

### 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!

6. Jun 13, 2012

### 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

7. Jun 13, 2012

### 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.

8. Jun 13, 2012

### Antiphon

This topic needs to be a sticky.

9. Jun 14, 2012

### PhilDSP

Re: Good responses

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.

Last edited: Jun 14, 2012
10. Jun 17, 2012

Staff Emeritus
It is. It doesn't help.

11. Jun 17, 2012

### krd

And in a way, she was completely correct.

And you were completely wrong.

Yes. That is what happens. Kind of.

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.

Last edited by a moderator: Sep 25, 2014
12. Jun 19, 2012

### PhilDSP

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.

Last edited: Jun 19, 2012
13. Jun 20, 2012

### 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.

14. Jun 20, 2012

### harrylin

Refraction is explained with scattering theory as light interacts with atoms.
(more there in post #8)

Last edited: Jun 20, 2012
15. Jun 20, 2012

### harrylin

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.

Last edited: Jun 20, 2012
16. Jun 20, 2012

### 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.

17. Jun 20, 2012

### harrylin

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!

18. Jun 20, 2012

### 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.

19. Jun 20, 2012

### nasu

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?

20. Jun 20, 2012

### PhilDSP

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.

Last edited: Jun 20, 2012