Question

A ray of light travelling in air is incident on the plane of a transparent medium with an angle of incidence ${45}^{\circ }$ and the angle of refraction ${30}^{\circ }$. Find the refractive index of the medium.

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

Answer 1

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

Given:
Angle of incidence, $i={45}^{\circ }$
Angle of refraction, $r={30}^{\circ }$

From snell's law, refractive index is given by:
$n=\frac{\sin i}{\sin r}$
$n=\frac{\sin {45}^{\circ }}{\sin {30}^{\circ }}$
$n=\frac{\left(\frac{1}{\sqrt{2}}\right)}{\left(\frac{1}{2}\right)}$
$n=\sqrt{2}$