Question

The angle of incidence for an equilateral prism of refractive index $\sqrt{3}$ so that the ray is parallel to the base inside the prism is

• A. $30^{\circ}$
• B. $20^{\circ}$
• C. $60^{\circ}$
• D. $45^{\circ}$
• E. $75^{\circ}$

Answer 1

Answer: (C)

Given, $\mu=\sqrt{3}$
Here, $r=\frac{A}{2}=\frac{60^{\circ}}{2}=30^{\circ}$ $(\because$ equilateral prism )
So, $ \frac{\sin\, i}{\sin\, r}=\mu$
$\sin\, i=\sqrt{3} \,\sin \,30^{\circ}$
$\sin\, i=\sqrt{3} \times \frac{1}{2}$
$\sin\, i=\frac{\sqrt{3}}{2}$
$i=\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)$
$i=60^{\circ}$