Question

If ${ϵ}_0$ and ${\mu }_0$ are, respectively, the electric permittivity and magnetic permeability of free space, $ϵ$ and $\mu$ the corresponding quantities in a medium, the index of refraction of the medium in terms of the above parameters is _________.

Answer 1

We know that the velocity of light in vacuum,
$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$
Also, the velocity of light in a medium, $v=\frac{1}{\sqrt{\mu ϵ}}$
$\therefore n=\frac{\text{Velocity of light in medium}}{\text{Velocity of light in vaccum}}=\frac{v}{c}$
$=\frac{1/\sqrt{{\mu }_0{ϵ}_0}}{1/\sqrt{\mu ϵ}}=\frac{\sqrt{\mu ϵ}}{\sqrt{{\mu }_0{ϵ}_0}}$.