# The speed of light

Yesterday in my physics lesson we were covering electromagnetism and my teacher mentioned the speed of light in a material was equal to the reciprocal of the square root of the magnetic permeability and electric permittivity of the material. I'd come across this before but I had always assumed this was because any photon would be absorbed/emitted in a random fashion, increasing the time it took to propogate the material.

However my teacher said that this value was the actual, true speed of light and that the speed of light was only c in a perfect vacuum. I find this incredibly hard to believe as photons are massless and if you start out with Einstein's famous equation (the full one) you end up with f*lambda = c. Treating light as a wave then f*lambda = velocity of the wave and therefore the photon should travel at c, through a vacuum or through molasses or whatever.

So am I just deluded or was my teacher wrong?

Cheers,
Just some guy.

Galileo
Homework Helper
The 'true' speed of light is c (299 792 458 m/s), but note that it has nothing to do with light. It's the fundamental speed limit that counts and light just happens to travel at that speed in a perfect vacuum. But that's important to note for relativity.

You are right that the more accurate physical mechanism for a changing speed of light in a material like, say, glass is the absorbtion and emission of photons. But we're talking in the context of electromagnetism, which is a macroscopic theory and doesn't deal with quantization of matter, charges and fields (atoms, electrons and photons). When you talk about polarization of a material by an electric field, all kinds of things are happening on an atomic scale, but for the described purpose it's enough to know that the field due to this polarization is proportional to the electric field (only for linear dielectrics).
Same thing goes for the magnetic field.

In this context of homogeneous linear media with no free charges/currents, Maxwell's equations become identical to the ones in vacuum, but with only the permitivity and permeability of vacuum switched for those of the material. In this case it follows that waves propagate in media with the reciprocal of the square root of the magnetic permeability and electric permittivity of the material.

It looks lika very simple derivation, but what happens on a molecular scale here is amazing! Apparantly, an EM-wave going through the medium will polarize and magnetize the material causing dipoles to oscillate and emit fields of their own. The sum of the two fields combine in such a way as to create a single wave traveling with the reduced velocity but the same frequency!

Last edited:
HallsofIvy