Question

An unpolarized light beam travelling in air is incident on a medium of refractive index 1.73 at Brewster's angle. Then:

• A. reflected light is partially polarized and the angle of reflection is close to \(30^\circ\)
• B. both reflected and transmitted light are perfectly polarized with angles of reflection and refraction close to \(60^\circ\) and \(30^\circ\), respectively
• C. transmitted light is completely polarized and the angle of refraction is close to \(30^\circ\)
• D. reflected light is completely polarized and the angle of reflection is close to \(60^\circ\)

Hint:

Remember that at Brewster's angle, the reflected light is completely polarized and the reflected and refracted rays are perpendicular to each other. The angle of incidence (Brewster's angle) is related to the refractive index by \( \tan i_B = \mu \).

Answer 1

The Correct Option is D

When unpolarized light is incident on a surface at Brewster's angle (\(i_B\)), the reflected light is completely polarized perpendicular to the plane of incidence. Brewster's angle is given by the relation: \[ \tan i_B = \mu \] where \( \mu \) is the refractive index of the medium. Given \( \mu = 1.73 \approx \sqrt{3} \), we have: \[ \tan i_B = \sqrt{3} \implies i_B = 60^\circ \] The angle of incidence at Brewster's angle is \( 60^\circ \). According to the law of reflection, the angle of reflection \( r \) is equal to the angle of incidence: \[ \text{Angle of reflection} = i_B = 60^\circ \] At Brewster's angle, the reflected light is completely polarized. The transmitted light is partially polarized. The angle of refraction \( r' \) can be found using Snell's Law: \[ \mu_1 \sin i_B = \mu_2 \sin r' \] Here, \( \mu_1 = 1 \) (air) and \( \mu_2 = 1.73 \): \[ 1 \times \sin 60^\circ = 1.73 \times \sin r' \] \[ \frac{\sqrt{3}}{2} = \sqrt{3} \cdot \sin r' \] \[ \sin r' = \frac{1}{2} \implies r' = 30^\circ \] So, at Brewster's angle of \( 60^\circ \), the reflected light is completely polarized, and the angle of reflection is \( 60^\circ \), while the angle of refraction is \( 30^\circ \).