Question

When unpolarized light is incident at an angle of 60° on a transparent medium from air. The reflected ray is completely polarized. The angle of refraction in the medium is

• A. 30°
• B. 60°
• C. 90°
• D. 45°

Answer 1

Answer: (A)

30°

Answer 2

According to Brewster’s law, the reflected ray is completely polarized when the angle of incidence $\theta_p$ satisfies:

$\tan \theta_p = n,$

where $n$ is the refractive index of the medium relative to air.

Given $\theta_p = 60^\circ$, we have:

$n = \tan 60^\circ = \sqrt{3}.$

Using Snell’s law $n_1 \sin \theta_1 = n_2 \sin \theta_2$, with $n_1 = 1$ (for air) and $\theta_1 = 60^\circ$:

$\sin \theta_2 = \frac{\sin 60^\circ}{\sqrt{3}} = \frac{\sqrt{3}/2}{\sqrt{3}} = \frac{1}{2}.$

Therefore, $\theta_2 = 30^\circ$.