Question

A ray of light travelling in air is incident on the plane of a transparent medium. The angle of incident is ${45}^0$ and that of refraction is ${30}^0$. The refractive index of the medium with respect to air is:

• A. $2$
• B. $\frac{1}{\sqrt{2}}$
• C. $2\sqrt{2}$
• D. $\sqrt{2}$

Answer 1

The correct option is D $\sqrt{2}$

Given:

Angle of incidence $\angle i={45}^0$
Angle of refraction $\angle r={30}^0$

Refractive index of transparent medium w.r.t. air is

${\mu }_{ma}=\frac{{\mu }_m}{{\mu }_a}=\frac{{\mu }_m}{1}={\mu }_m$

By Snell's Law,

${\mu }_m=\frac{sini}{sinr}=\frac{sin{45}^0}{sin{30}^0}=\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}=\sqrt{2}$