Question

A ray incident at a point at an angle of incidence $\theta$ enters into a glass sphere placed in air which is reflected and refracted at the farther surface of the sphere as shown in the figure. The angle between reflected and refracted rays at this surface is ${90}^0$. If refractive index of the sphere is $\sqrt{3},$ the angle $\theta$ is :

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. $\frac{2\pi }{3}$

Answer 1

Answer: (A)

$\frac{\pi }{3}$

Applying Snell's law on the 2 surfaces,

$sin\theta =\sqrt{3}sinr$

Where, r is the angle of refraction.

Applying on the second surface,
$sinr=cos\theta$

Equating the 2 terms,

$sin\theta =\sqrt{3}cos\theta$

Thus, $tan\theta =\sqrt{3}$

Or, $\theta ={60}^0$