Index of refraction = sqrt dielectric constant

[Point Conception]

Can someone explain in terms of electric fields how the index of refraction squared = the dielectric constant of the material ?

 

[Hootenanny]

The index of refraction is defined as the ratio of the speed of light in vacuum to the speed of light in the medium. If one solves the wave equation for the electric (or magnetic) wave in a dielectric medium it turns out that the speed of propagation is,

$$v = \frac{1}{\sqrt{\varepsilon_0\mu_0\varepsilon\mu}}$$

And the speed of light in vacuum is,

$$c = \frac{1}{\sqrt{\varepsilon_0\mu_0}}$$

Hence, taking the ratio of the two yields,

$$n = \frac{c}{v} = \sqrt{\varepsilon\mu}$$

Note that $\mu\approx1$ for most materials with light in the optical range.