Question

A ray of light falls on a prism $ABC(AB=BC)$ and travels as shown in the figure. The refractive index of the material of prism should be at least :

• A. $\frac{4}{3}$
• B. $\sqrt{2}$
• C. $\frac{3}{2}$
• D. $\sqrt{3}$

Answer 1

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

This is a right angled isosceles triangle

$\angle A=\angle C={45}^{0}and\angle B={90}^0$

the total internal reflection takes places at critical angle $\theta$

$sin\theta \ge \frac{1}{\mu }\mu \ge \frac{1}{sin\theta }$

$\theta =criticalangle\left(incidentangle\right)$

here critical angle $\theta =i={45}^0$

thus $\mu \ge \sqrt{2}$

Option B is correct.