Question

A light ray is incident perpendicular to one face of a ${90}^{\circ }$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is ${45}^{\circ }$, we conclude that the refractive index n

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

Answer 1

Answer: (B)

$n>\sqrt{2}$

Given,

The incident angle is $i={45}^{\circ }$

The critical angle is ${\theta }_c$

It can be observed that

$i>{\theta }_c$

Hence,

$\sin i>\sin {\theta }_c$

The critical angle is given as

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

Where $n$ is the refractive index of prism

Therefore,

$\sin i>\frac{1}{n}$

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

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

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

$n>\sqrt{2}$ .