Question

A ray of unpolarised light is incident on the glass surface of refractive index 1.73 at polarizing angle. The angle of refraction will be [Take \( \tan 60^\circ = 1.73 \)]

• A. 45°
• B. 15°
• C. 35°
• D. 30°

Hint:

At the polarizing angle, the angle of refraction is determined by Snell’s law. Use the refractive index and the polarizing angle to find the angle of refraction.

Answer 1

The Correct Option is D

Step 1: Polarizing angle.
The polarizing angle \( \theta_p \) is given by: \[ \tan \theta_p = \mu \] where \( \mu = 1.73 \) is the refractive index of the glass.
Step 2: Polarizing angle calculation.
Since \( \tan 60^\circ = 1.73 \), the polarizing angle is \( \theta_p = 60^\circ \).
Step 3: Angle of refraction.
For light incident at the polarizing angle, the angle of refraction \( \theta_r \) can be found using Snell's law: \[ \mu \sin \theta_p = \sin \theta_r \] Substituting \( \mu = 1.73 \) and \( \theta_p = 60^\circ \), we get: \[ 1.73 \times \sin 60^\circ = \sin \theta_r \] \[ 1.73 \times \frac{\sqrt{3}}{2} = \sin \theta_r \] \[ \sin \theta_r = 1 \] Thus, \( \theta_r = 30^\circ \).
Step 4: Conclusion.
The angle of refraction is 30°, which is option (D).