Question

A light ray is incident perpendicularly to one face of a ${90}^0$prism and is totally internally reflected at the glass-air interface.
If the angle of reflection is ${45}^0$, we conclude that the refractive index 'n' will be

Diagram

• 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 D $n>\sqrt{2}$

The angle of reflection is ${45}^0$
So the incident angle is also ${45}^0$
Incident angle > Critical angle,
$i>i_c$
$\therefore sini>sin{i}_c$
$sin{45}^0>sin{i}_c$
$sin{i}_c=\frac{1}{n}$
$sin{45}^0>\frac{1}{n}$
$\frac{1}{\sqrt{2}}>\frac{1}{n}\Rightarrow n>\sqrt{2}$