The behavior of electromagnetic waves in matter

Question

In vacuum, the $\vec{E}$ and $\vec{B}$ field are always perpendicular, in phase, and they travel at the speed of light $c=3\times 10^8 \text{m/s}$. I would like to know what happens in matter ? Do the same rules apply ?

Answer 1

The wave equation $$\frac{\partial^2 \mathbf E}{\partial t^2} = c^2 \frac{\partial^2 \mathbf E}{\partial \mathbf x^2}$$ can be obtained from the Maxwell equations, for no charges or currents.

In vacuum, $c^2 = \frac{1}{\mu_0\epsilon_0}$.

For a transparent and isolant material as glass, with no free charges or currents, the same derivation is possible.

The only difference is that $\mu_0$ is replaced by $\mu$ and $\epsilon_0$ by $\epsilon$. So the wave speed changes, and is smaller than $c$.