Physics To The Rescue

[Ecthy]

Oh Jon you're so nice thanks you're not KH.

[Jon Miller]

KH is good, he goes takes the time to explain things neatly and succinctly. (and completely)

Jon Miller

[Lorizael]

and sarcastically!

[Ecthy]

And insultingly. But he isn't around, so we're stopping this until he show up.

[Ramo]

Seriously though, why does light travel slower in a material? Lorizael's photon colliding explanation makes no sense. What's the real one? How does the epsilon-r gets into the Maxwell equations?

Let e be epsilon and m be mu for the spatially and temporally uniform medium, and ' denotes time derivitives:

Take the curl equations without any free charge or current (i.e. it's all bound in the polarization and magnetization of the material):

curl(E) = -mH'
curl(H) = eE'

Take the curl of the second:
curl(curl(H)) = e*curl(E') = e*[curl(E)]'

But curl(curl(H)) = -laplacian(H) + grad(div(H)) = -laplacian(H) since div(H) = 0

Substituting in the first equation, therefore, laplacian(H) = emH''

And the same thing with E if you curl the first equation and substitute in the second.

Therfore, the speed of light is sqrt(1/(em))

Edit: I'm assuming that the material is linear (i.e. polarization and magnetization are linearly related to the electric and magentic fields respectively), but the same basic idea (albeit a somewhat less elegant dependence) should hold for nonlinear materials. Dealing with nonlinear materials is messy.