A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively.

The prism will be

For critical angle, $\mu =\frac{1}{\sin \mathrm{c}}$
The prism will have different refractive indices for different colours.

$\mu =\frac{1}{\sin {45}^{\circ }}=\sqrt{2}$
If the refractive index of a particular colour is less than $\sqrt{2}$, total internal refl ection takes place.
For red colour,
$\begin{array}{l}{\mu }_R=1.39\text{ and }\mu =\sqrt{2}=1.414\\ {\mu }_R<\mu \end{array}$
So, ${\mathrm{\theta }}_{\mathrm{c}}>{45}^{\circ }$so, it will pass through
${\mu }_a\text{ and }{\mu }_b>1.414\text{. }$
So  ${\theta }_c<{45}^{\circ }$
So total internal refl ection take place for blue and green.
$\therefore$ These rays refract

$\therefore$Red colour separates from blue and green.