Speed of light in material

The speed of light in vacuum is $c^2 = \frac{1}{\mu_0 \epsilon_0}$. We will see that the speed of light in material may be lower. Consider a material consisting of electric dipoles, e.g. water.

Normally the electric dipoles are aligned randomly, but if we apply an external electric field the dipoles will align and create a polarized electric field opposite the external electric field (unrelated to polarized light).

Similarly, if we apply an external magnetic field to a material consisting of magnetic dipoles, they will align with the external field. In this case the magnetic dipoles (current loops) will create a polarized magnetic field in the direction of the external field, effectively amplifying it.

The speed of light in material is then $v^2=\frac{1}{\mu \epsilon}$ where $\epsilon$ is the permittivity in the material and $\mu$ is the permeability.