# Refractive index

The speed of light is determined by the medium (material) through which the light is travelling. Light travels faster in a vacuum than it does in any other medium.

Light changes speed as it passes from one medium to another. This is called refraction.

The frequency of light does not change as it refracts.

The refractive index of a material is a measure of the change in the speed of light as it passes from a vacuum (or air as an approximation) into the material.

$n=\frac{v_{1}}{v_{2}}$

In the equation above:

• $$n$$ is the refractive index of the material
• $$v_{1}$$ is the speed of light in a vacuum
• $$v_{2}$$ is the speed of light in a material

The bigger the refractive index, $$n$$, the slower the light travels in that material - ie the smaller $$v_{2}$$ is.

Question

Light of frequency $$4.6\times 10^{14}Hz$$ travels at a speed of $$1.24\times 10^{8}ms^{-1}$$ in diamond.

Calculate the refractive index of diamond for this colour of light.

$v_{diamond}=1.24\times 10^{8}ms^{-1}$

$c=3.0\times 10^{8}ms^{-1}$

$n=\frac{v_{1}}{v_{2}}$

$n_{diamond}=\frac{3\times 10^{8}}{1.24\times 10^{8}}$

$n_{diamond}=2.42$

Refractive index of diamond for this colour of light $$=2.42$$

Question

Now state the frequency of this light in air.

The frequency of this light in air $$=4.6\times 10^{14}Hz$$. (Frequency does not change when light passes from one material to another)