Question

Angle of a prism whose one surface is ${30}^{\circ }$ and its refractive index is $\sqrt{2}$. At what angle of incidence, a ray should be incident on the surface so that after reflection from the silvered surface, it retraces its path

• A. 30°
• B. 60°
• C. 45°
• D.

Answer 1

The correct option is C 45°

Given: $\angle A$ = ${30}^{\circ }$ and $\mu =\sqrt{2}$

By Snell's law at surface AB
$\mu =\frac{sini}{sinr}$

For a ray to retraces its path, it should fall at ${90}^{\circ }$ on the silver surface.

In $\Delta AOM$
$\angle A+\angle O+\angle M={180}^{\circ }{90}^{\circ }-r+{30}^{\circ }+{90}^{\circ }={180}^{\circ }r={30}^{\circ }$

$\Rightarrow \sqrt{2}=\frac{sini}{sin{30}^{\circ }}\Rightarrow i={45}^{\circ }$