# Question #d49f8

May 19, 2016

As explained below.

#### Explanation:

The refractive index $\mu$ of an optical medium is defined as the ratio of the speed of light in vacuum to the phase velocity $v$ of light in that medium. Mathematically it can be written as

$\mu \equiv \frac{c}{v}$ ......(1)

The speed at which crests or the phase of the wave moves is its phase velocity. Speed of light in vacuum is a constant.

Extending the equation for red and violet lights
${\mu}_{\text{red"=c/v_"red}}$ and
${\mu}_{\text{violet"=c/v_"violet}}$
Dividing one with the other we obtain
${\mu}_{\text{red"/mu_"violet"=v_"violet"/v_"red}}$ ......(2)
or $\mu \propto \frac{1}{v} _ \text{colour}$

Look at the following figure which shows different refractive indecies of light of different colours.

The refractive index of red light is less than that of violet light, as its angle of refraction is less.

Follows that speed of light higher for red than violet in a particular medium other than vacuum.