Question

A ray of light is incident at $60^{\circ}$ on one face of a prism of angle $30^{\circ}$ and the emergent ray makes $30^\circ$ with the incident ray. The refractive index of the prism is

• A. $1.732$
• B. $1.414$
• C. $1.5$
• D. $1.33$

Answer 1

Answer: (A)

$1.732$

Answer 2

Here, $i = 60^{\circ}, A = 30^{\circ}, \delta= 30^{\circ}$
As $i+ e = A + \delta$
$e = A + \delta - i = 30^{\circ} + 30^{\circ} - 60^{\circ} = 0^{\circ}$
Hence emergent ray is normal to the surface.

$e= 0^{\circ}$
$\Rightarrow r_{2} = 0^{\circ}$
As $r_{1} +r_{2} = A$
$\therefore r_{1} = A -r_{2} = 30^{\circ} - 0^{\circ} = 30^{\circ}$
$\mu =\frac{ sin\, i}{sin \,r_{1}} = \frac{sin\, 60^{\circ}}{sin \,30^{\circ}}$
$= \frac{\sqrt{3}}{2}\times \frac{2}{1} = \sqrt{3}$
$= 1.732$