Question

A prism with a refracting angle $30^{\circ}$, made of material of refractive index 1.732, has one of its faces silvered. A ray of light incident at a certain angle on the other face retraces the path after getting reflected at the silvered face. The angle of incidence is

• A. $30^{\circ}$
• B. $45^{\circ}$
• C. $60^{\circ}$
• D. $15^{\circ}$

Answer 1

Answer: (C)

$60^{\circ}$

Answer 2

Refracting angle of prism, $A = 30^{\circ} \, \mu = 1.732, i = ?$
$r = 90^{\circ} - 60^{\circ} = 30^{\circ}$
Using Snell's law at point $P$,
$1 .\sin i = \mu \sin r$
$\sin i = 1.732 \times \sin 30^{\circ} = \frac{1.732}{2} = \sin 60^{\circ}$
or, $i = 60^{\circ}$