Question

A ray falls on a prism ABC (AB = BC) and travel as shown in figure. The least value of refractive index of material of the prism should be

• A. 1.5
• B. $\sqrt{2}$
• C. 1.33
• D. $\sqrt{3}$

Answer 1

The correct option is (C) $\sqrt{2}$

It is given that

AB = BC,

So, $\angle A=\angle C={45}^{\circ }$

If the angles are of ${45}^0$

Then,

At each reflection $i={45}^{\circ }$

We know,

For total internal reflection incidence angle shouyld be greater than the critical angle

Or, $i>i_c$

Or,

$sini>sin{i}_c$

Angle is ${45}^0$

$sin45>sin{i}_c$

After solving

$sin{i}_c>\frac{1}{\sqrt{2}}$

we know $\mu =\frac{1}{sin{i}_c}$

So,

or $\mu >\sqrt{2}$

Refractive index should be greater than or equal to the $\sqrt{2}$