# A question about the speed of Light in different media...

sophiecentaur
Gold Member
2020 Award
I don't know why we are having this conversation any more. The thread is classified with an I. Whether or not it is appropriate for the OP, we don't know but we should surely answer and discuss at that (I) level. I don't know at what stage you were educated about QM in any meaningful way but I have not come across many A level students who would be able to deal with Schrodinger and it's certainly not (as of a few years ago, at least - and certainly not in either of our educations) part of what they get taught.
The primary phenomena that are observable (by us and the 'ancients') are diffraction based and very easily explained by looking at the wave nature of light. Of course, wave theory is not enough to explain frequency reduction and your more advanced ideas need to be brought in.
If you want a higher level of conversation then why not either ask the OP directly if the change of agenda is OK or else start a new thread with the appropriate level. Alternatively if you have a way that 'explains' simple optics in terms of particles that doesn't involve statistics, QM, or harder Maths and which can yield the results of Young's Slits and how a lens works then go ahead.
Personally, I tend to use the simplest modelling level to explain phenomena that is available.
It all depends how "simple" you find the names and ideas that you include in that first paragraph in your post. Can you rely on a member who posts an 'I' level question finding it that simple? You'd wonder why Huygens and Maxwell ever got involved with waves, if particles make it so simple.

DrDu
Nevertheless, I think I learned an interesting piece of physics from this question and though it is not classical wave mechanics, you don't need to solve Schroedinger equations.
Here is little back of the enelope estimation, dropping all numerical constants, of the length a photon can travel in matter until it has lost
all its energy due to Compton scattering:
The density of electrons in ordinary matter is about 1 electron per cube of the Bohr radius ##a_0##, i.e. ##V=a_0^3##.
The scattering cross section for Compton scattering in the low energy range is about ##\sigma=r_e^2 ## with ##r_e## being the classical electron radius.
The change in wavelength per scattering event is about ##\lambda_e##, the Compton wavelength of the electron.
Now I can ask how many scattering events it takes for a photon with wavelength ##\lambda## to loose all its energy.
This is ##n=\lambda/\lambda_e##.
The mean free path length between scattering events is ##V/\sigma##, or the total path length till all energy is lost is
##l=\lambda V/(\sigma \lambda_e)##. Now the three length scales are all proportional to each other ##r_e=\alpha \lambda_e=\alpha^2 a_0## with ##\alpha=1/137## being the fine structure constant.
Hence
## l=\lambda /\alpha^5 ##.
For X rays this makes only some cm, but for visible light some dekameters.
This is an asymptotic result which should hold when wavelength is so high that electrons can be considered approximately free.
This is certainly reasonable for x-rays and maybe for UV light in metals above the plasma frequency.
For transparent media like glass it is probably still too small because the momentum transfer is suppressed by the electrons being bound to atoms. I would estimate this effect introducing another factor ##M/m_e## where M is the typical mass of the atoms. So light can travel several hundred kilometers in glass until it has been scattered completely by incoherent processes.

sophiecentaur
sophiecentaur
Gold Member
2020 Award
Nevertheless, I think I learned an interesting piece of physics
Me too.

"The speed of light in glass is approximately 200,000 kilometres (120,000 mi) /s, i.e, the speed of light changes as soon as the light enters from a different medium to glass...My question is that why, after this ''change'', the speed of light suddenly becomes constant for glass..., like why there is no constantly decreasing speed of light as the light propagates through glass????"

I understand your question. The term "speed of light" is somewhat of a misnomer, because what we are really talking about here is the rate of the exchange of information between adjacent participants in the propagating medium, which is a constant value that we know to occur over a distance of 186,000 miles in one second in the medium of air, wherein that determination is made. Denser mediums have more participants in the chain of information exchange over the same distance, therefore light will take longer to cross the denser medium for the same time frame, and when returned to the medium that is air, that distance increases with the decrease in density of the medium, and the apparent "speed of light" immediately returns to "normal".

nasu
Gold Member
The phase velocity changes as well when the wave (not necessarily EM wave) enters a different medium. The problem is not to distinguish between phase, group and signal velocities. They all change in a different medium.
I think the confusion comes from the fact that we use "velocity" for two slightly different things. The velocity of a moving particle is related to change in position of a material object over time. In the case of a wave we have a similar velocity for the particles of the medium, in the case of a mechanical wave. But what we call wave velocity does not describe quite the same thing.
No particle moves with that velocity. For phase velocity is the phase, an abstract concept, that change position. The concepts of accelerating and decelerating the wave does not apply to this type of velocity. The fact that there is a tendency to "jump" to photons before understanding properly the classic wave makes the confusion more likely.

I did not see any question about accelerating and decelerating sound waves when they go from air to water and vice-versa. Would that mean that the things are pretty clear for sound?

Drakkith
Staff Emeritus