A beam of light consisting of 3 colours is incident on a right angled prism, as shown. The refractive indices of the material of the prism for these colours are $1.40,1.45$ and $1.48$ respectively. At least one colour is to be separated from the others. Find the minimum value of the angle of prism for this to happen :

One face $AB,\angle i=0and\angle r=0,PQwilltravelundeviated.$

At face $AC,$ angle of incidence = angle of prism $=i$ For one colour to be separated, $TIR$ should take place.

$i>{\theta }_c, \sin i>\sin {\theta }_C Or \sin >\frac{1}{\mu } Or \mu \ge \frac{1}{\sin i}$

For $i={30}^0,\mu \ge 2$

No colour will be separated.

For $i={45}^0,\mu \ge \sqrt{2}\ge 1.414$

The colour for which refractive index of prism is 1.40 will be separated. This colour will be transmitted, while others will be reflected.