Question

The refractive index of the material of prism is $\sqrt{2}$ and its refracting angle is 30${}^{\circ }$. One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light enters the prism from the other surface and the ray retraces from the mirrored surface. The angle of incidence is :

• A. 30${}^{\circ }$
• B. 45${}^{\circ }$
• C. 60${}^{\circ }$
• D. 0${}^{\circ }$

Answer 1

The correct option is B 45${}^{\circ }$

By Snell's law,

Refractive index, $\mu =\frac{sini}{sinr}=\sqrt{2}$

$sini=\sqrt{2}sin\left({30}^{\circ }\right)$ $=\frac{1}{\sqrt{2}}$

$i={45}^{\circ }$

$\therefore$ Angle of incidence is ${45}^o$.