Question

Obtain the relation between the critical angle and the refractive index of the denser medium.

Answer 1

The relation between the critical angle (C) and the refractive index (n) of the denser medium is derived using Snell’s Law.

At the critical angle:

Light travels from a denser to a rarer medium.

The angle of refraction is 90°.

Using Snell’s law:

n₁​ sin C = n₂​ sin 90°

n₁​ sin C = n₂

sin C = `n_2/n_1`

sin C = `1/n` ...(if rarer medium is air, i.e., n₂ ​= 1 and n_{1 ​}= n)

This indicates that the critical angle is inversely related to the refractive index of the denser medium.