Question

A light ray is incident perpendicular to one face of a ${90}^{\circ }$ prism and totally internally reflected at the glass interface. If the angle of reflection is ${45}^{\circ }$. The refractive index is :

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

Answer 1

The correct option is B $n>\sqrt{2}$

The incident angle is ${45}^0$

Incident angle $>$ Critical angle

Therefore,

$sini>sin{i}_c$

or

$sin45>sin{i}_c$

$sin{i}_c=\frac{1}{n}$

$sin{45}^0>\frac{1}{n}$

or

$\frac{1}{\sqrt{2}}>\frac{1}{n}$

$⟹n>\sqrt{2}$