Question: 19: A light ray falls on a glass surface of refractive index \sqrt{3}, at an angle 60^{\circ}. The angle between the refracted and reflected rays would be
(1) 90^{\circ}
(2) 120^{\circ}
(3) 30^{\circ}
(4) 60^{\circ}
Answer: Option (1)
Explanation:
The angle of incidence is given as i = 60^{\circ}. According to the law of reflection,
the angle of reflection is equal to the angle of incidence.
\angle \text{reflection} = 60^{\circ}.
Using Snell’s law for refraction,
n = \frac{\sin i}{\sin r},
where n = \sqrt{3} is the refractive index of glass.
Substituting the values,
\sqrt{3} = \frac{\sin 60^{\circ}}{\sin r}.
\sqrt{3} = \frac{\frac{\sqrt{3}}{2}}{\sin r}.
\sin r = \frac{1}{2}.
Thus, the angle of refraction is
r = 30^{\circ}.
The reflected ray makes an angle of 60^{\circ} with the normal on one side,
and the refracted ray makes an angle of 30^{\circ} with the normal on the other side.
The angle between the reflected and refracted rays is therefore
180^{\circ} - (i + r) = 180^{\circ} - (60^{\circ} + 30^{\circ}) = 90^{\circ}.
Hence, the angle between the refracted and reflected rays is 90^{\circ}.