Question

A ray of light incident normally on one of the faces of a right angle prism is found to be totally reflected as shown in figure. What is the minimum value of the refractive index of the material of the prism?

• A. $ \sqrt{2} $
• B. $ \sqrt{\frac{3}{2}} $
• C. $ \frac{4}{3} $
• D. None of these

Answer 1

Answer: (A)

For total internal reflection
$\theta \ge C$
Where $C$ is the critical angle
$\therefore \sin \,\theta \ge \sin \,C$
$ \sin\,\theta \,\frac{1}{4}\,\mu \,\ge \,\frac{1}{\sin\,45^{\circ}}$
$ \mu \,\ge \sqrt{2}$