A ray incident at a point at an angle of incidence of 60° enters a glass sphere of R.I. n = $\sqrt{3}$ and is reflected and refracted at the further surface of the sphere. The angle between the reflected and refracted rays at this surface is
Answer & explanation
Correct answer: option 3
Refraction at P.
$\frac{\sin 60°}{\sin r_1}=\sqrt{3}$
$⇒\sin r_1 = \frac{1}{2}$
$⇒r_1 = 30°$
Since $r_2 = r_1$
$∴ r_2 = 30°$
Refraction at Q, $\frac{\sin r_2}{\sin i_2}=\frac{1}{\sqrt{3}}$
Putting $r_2= 30°$ we obtain $i_2 = 60°$
Reflection at Q
$r'_2=r_2=30°$
$∴α=180°-(r'_2+i_2)$
= 180° - (30° + 60°)
= 90°