# Why is the speed of light smaller in a medium?

fxdung
Why is speed of light in matter medium smaller than speed of light in vacuum?Are all photons must be absorbed by atoms and then the atoms re-emit radiations in matter?What is real picture of all photons in transparent medium?

Delta2

Mentor
Are all photons must be absorbed by atoms and then the atoms re-emit radiations in matter?
No.

Light is energy in electric and magnetic fields, where electric fields produce magnetic fields and vice versa. The propagation speed depends on how strong this conversion is, which depends on properties of the medium (or properties of the vacuum, without a medium). As soon as you have charges you'll get a slower propagation.

Technically there are three speeds to distinguish here, only in vacuum they are all identican. The phase velocity (relevant for diffraction), the group velocity (relevant for sending a light pulse) and the limit for the signal speed (relevant if you want to send information from A to B). The first one can easily exceed the speed of light in vacuum, the second one can do so only under exceptional conditions, the third one will never beat the speed of light.

Mentor
Why is speed of light in matter medium smaller than speed of light in vacuum?
If it were faster then you could get causality violations.

fxdung
Please tell me the detail about group speed(speed of transmiting energy) and signal speed.I think they would be the same.

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Why is speed of light in matter medium smaller than speed of light in vacuum?Are all photons must be absorbed by atoms and then the atoms re-emit radiations in matter?What is real picture of all photons in transparent medium?
Your question boils down to why materials have different electric permittivity and magnetic permeability than that of a vacuum.. The speed with which EM radiation (I.e. light) propagates through a medium depends directly on these quantities:

##c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}##

Is the speed of light in a vacuum. And

##v = \frac{1}{\sqrt{\epsilon \mu}}##

Is the speed of light in a material with electric permittivity ##\epsilon## etc.

For an explanation of why different materials have different electric permittivity you could look online for how this relates to Maxwell's equations. For example:

http://maxwells-equations.com/materials/permittivity.php

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No.

Light is energy in electric and magnetic fields, where electric fields produce magnetic fields and vice versa. The propagation speed depends on how strong this conversion is, which depends on properties of the medium (or properties of the vacuum, without a medium). As soon as you have charges you'll get a slower propagation.
The above is the classical explanation, where we assume the medium to be continuous. But no real medium is continuous, it consists of atoms or molecules and vacuum in the space between adjacent atoms/molecules. So photons travel in the vacuum between atoms with the full speed of light and they are "annihilated" when they "collide" with atoms. I am not sure what QED says when the photons are absorbed and reemitted by atoms, but I suspect there is a small delay between the absorb and the reemit of the photon and that's why the overall speed of photon seems to be smaller.

fxdung
I saw some where that the delay is 10^-8s to 10^-3s for spontanious emission of an excited atom.

And I do not understand this:Follow Compton picture a photon do not need to annihilated when collided an electron(with any energy level).But follow the Borh's model photon must be annihilated when collied with atom and atom only be excited when difference of two energy levels equal the energy of photon.So it seems contradict?

Mentor
Please tell me the detail about group speed(speed of transmiting energy) and signal speed.I think they would be the same.
As I said this is a rare case. You can have a pulse where the trailing part is damped more than the leading part. As a result the center of the pulse gets an apparent extra "motion" forward - without anything actually moving faster.
So photons travel in the vacuum between atoms with the full speed of light and they are "annihilated" when they "collide" with atoms.
That model has so many flaws everywhere and leads to so many misconceptions that it is best to not introduce it at all. There is no problem with approximating the material with a continuum in QED.
I saw some where that the delay is 10^-8s to 10^-3s for spontanious emission of an excited atom.
There we have an example of such a misconception.
That time is meaningful, but only for photons that are actually absorbed. Which is not a process that leads to slower light - it is a process that leads to scattering and absorption.

nasu, PeroK and weirdoguy
fxdung
And by the way,how about my question to the contradict between Compton and Borh's model?

Mentor
The Bohr model has been outdated for nearly 100 year now. It shouldn't be surprising that it doesn't lead to the correct result. Neither Compton nor Bohr describe what happens in solid objects where the electrons can form energy bands, by the way.

fxdung
But it seems that in the dilute gas the two descriptions still value.Because the theory of gas laser still uses the energy level in atoms(like Borh's model),so how to solve the question in case of independent atoms(gas)?

Mentor
Lasers are stimulated emission, not spontaneous.

fxdung
But in the pump process we excite an atom from one level to other level of energy(that is the likely Borh's model of atom).I mean the Borh's model is still value,so how can we solve the contradict between Borh and Compton picture.

Mentor
See above: The Bohr model has been outdated for a long time. "It has the concept of energy levels" doesn't save it. Okay, it has one element that didn't turn out to be wrong. So what?

fxdung
So the concept of energy level is still right, and it require photon has energy equal the difference between two levels of atom to excite the atom.But Compton effect says that the photon need not have the special value of energy to collide atom.How can we solve this seeming contradict?

Mentor
How can we solve this seeming contradict?
The solution is to discard the Bohr model

PeroK and vanhees71
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Indeed, the Bohr model works just for the hydrogen atom's energy levels (and also for the harmonic oscillator), which is just good look because of the very large dynamical symmetry of both systems. Even for the hydrogen atom it gets the wrong shape, a circular disk rather than a sphere in its ground state (modern quantum theory gets a "fuzzy sphere").

In all other cases (already for the He atom) it fails, and that's why the pressure on the theoretical physicists became large enough to develop within about 10 years modern QT in 3 different formulations at the same time: Born, Jordan, Heisenberg's matrix mechanics, Schrödinger's wave mechanics, and Dirac's "transformation theory".

PeroK and weirdoguy
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@vanhees71 may I ask you what modern QT says on why light slows down when propagating through a medium other than vacuum?
Because here all we got are answers from @mfb and @PeroK that reproduce the classical explanation (with electric permittivity and magnetic permeability of the medium e.t.c).

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The classical explanation is better than you might think. You get the correct formulae as with the semiclassical quantum mechanical treatment for the standard case that the wave length of the considered em. waves is much larger than the extension of the atoms (take as an example of the medium just an ideal gas to get the principle idea), as is the case for visible light. Then you consider the Hamiltonian in the form
$$\hat{H}=\hat{H}_{\text{atom}}+\hat{H}_{\text{int}},$$
where the interaction Hamiltonian is in dipole approximation
$$\hat{H}_{\text{int}}=\vec{E}_0 \cdot \hat{\vec{x}} \cos(\omega t),$$
where ##\vec{x}## is the position of the atom. Then you can do perturbation theory to first order to get the same formulae as in the classical theory with the important difference that the resonance frequencies are given by the difference of the energy levels of the atom, i.e., ##\omega_{mn}=(E_m-E_n)/\hbar##.

This has been already treated by Schrödinger in one of his 6 famous papers on wave mechanics.

Delta2
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I mean the Borh's model is still value,so how can we solve the contradict between Borh and Compton picture.
By realizing that the Bohr model can't explain Compton scattering. It also can't explain other things, like spectral line widths and transition times, you need a more general theory for that. Quantum theory, QED, or QFT, etc.

This is not surprising when you study the history. Bohr was trying to explain what the spectroscopists were seeing. It would be amazing if he got it all right on his first attempt.

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The Bohr model can explain by chance only some very simple examples for energy spectra (harmonic oscillator, simple hydrogen atom, rigid rotator). It fails in all other cases. It was very important historically to find "modern QT". The key issue to be solved were indeed the atomic spectra, including the anomalous Zeeman effect. The latter lead finally to spin.

Bohr also confused the issue with the Stern-Gerlach result: Stern started the whole endeavor of this technically very challenging experiment to disprove the space-quantization hypothesis made within the Bohr-Sommerfeld model. In short: With this model one would have expected three lines and one Bohr magneton for the magnetic moment of the Ag atom (Debye, Sommerfeld 1916). Remarkably, in his very gibberish way Bohr discussed the third line away somehow, given the facts from the anomalous Zeeman effect, where one gets a split in two lines in the alkali atoms instead of 3 as expected from the Bohr-Sommerfeld model.

See, e.g.,

N. Bohr, The Theory of Spectra and Atomic Constitution, Cambridge University Press (1922)

This "normal Zeeman" effect one gets for strong magnetic fields when the spin-orbit coupling is negligible compared to the interaction with the strong magnetic field, one can neglect the spin in the transitions altogether and one gets the split from the orbital angular momentum (for ##l=1## in a triplet) (Paschen-Back effect). For details, see the nice Wikipedia article:

https://en.wikipedia.org/wiki/Zeeman_effect
To Stern's surprise, he and Gerlach finally of course found the direction quantization and a split in only two not three lines.

The final resolution was of course the introduction of half-integer spin (spin 1/2 for the electron) and the gyrofactor 2, which resulted in the split into two lines rather than 3 but still with one Bohr-magneton for the interaction strength. So Bohr was just lucky once more with an ad-hoc hypothesis, and Stern congratulated him with a postcard showing the famous photograph of the two-line split in comparison to the single line when no magnetic field was applied. Somewhat later Stern and Gerlach also quantitatively verified the strength to be 1 Bohr magneton (with an error ##\lesssim 10\%##).

weirdoguy