Question

A ray of light on a prism having one silvered surface, at an incident angle of ${45}^{\circ }$ as shown in figure. After refraction and reflection it retraces the path, then the refractive index of prism material is (prism angle is ${30}^{\circ }$)

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

Answer 1

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

$n_1=1;n_2=?;{\theta }_1={45}^0;{\theta }_2={30}^0$ (by using geometry)
we know
$n_{1}sin{\theta }_1=n_{2}sin{\theta }_2$
$n_2=\frac{sin{\theta }_1}{sin{\theta }_2}=\frac{sin{45}^0}{sin{30}^0}$
$n_2=1.414=\sqrt{2}$
hence, the refractive index of prism material is $\sqrt{2}$