Question

A ray incident at a point at an angle of incidence of $60^{\circ }$ enters a glass sphere of refractive index $\sqrt{3}$ and is reflected and refracted at the farther surface of the sphere. The angle between the reflected and refracted rays at this surface is

• A. $50^{\circ }$
• B. $60^{\circ }$
• C. $90^{\circ }$
• D. $40^{\circ }$

Answer 1

Answer: (C)

Refraction at $P$,
$\frac{sin60^{\circ }}{sin{r}_1}=\sqrt{3}$
$sin{r}_1=\frac{1}{2}$ or $r_1=30^{\circ }$
Since, $r_2=r_1$;
$\therefore r_2=30^{\circ }$
Refraction at $Q,\frac{sin{r}_2}{sin{i}_2}=\frac{1}{\sqrt{3}}$ or
$\frac{sin30^{\circ }}{sin{i}_2}=\frac{1}{\sqrt{3}}$ or
$i_2=60^{\circ }$
At point $Q,r_2^{\prime }=r_2=30^{\circ }$
$\therefore \alpha =180^{\circ }-(r_2^{\prime }+i_2)$
$=180^{\circ }-(30^{\circ }+60^{\circ })=90^{\circ }$