Question

A parallel beam of light is incident form air at an angle $\alpha$ on the side $PQ$ of a right angled triangular prism of refractive index $n =\sqrt{2}$. Light undergoes total internal reflection in the prism at the face $PR$ when $\alpha$ has a minimum value of $45^{\circ}$. The angle $\theta$ of the prism is

• A. $15^{\circ}$
• B. $22.5^{\circ}$
• C. $30^{\circ}$
• D. $45^{\circ}$

Answer 1

Answer: (A)

$\sin i_{c}=\frac{1}{\sqrt{2}}$
$i_{C}=45^{\circ}$
$1 \times \sin 45^{\circ}=\sqrt{2} \sin r$
$\sin r=\frac{1}{2}$
$r=30^{\circ}$
$\therefore \theta=180^{\circ}-120^{\circ}-45^{\circ}=15^{\circ}$