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°

Hint:

When unpolarized light is incident on a transparent medium, the reflected ray is completely polarized at Brewster's angle. The angle of refraction in the medium can be calculated based on this condition.

Answer 1

The Correct Option is A

Step 1: Brewster's Angle
According to Brewster's law, the angle of incidence \( \theta_i \) at which the reflected light is completely polarized is called Brewster's angle \( \theta_B \). Brewster's angle is given by: \[ \tan \theta_B = \frac{n_2}{n_1} \] where \( n_1 \) is the refractive index of the first medium (air) and \( n_2 \) is the refractive index of the second medium (the transparent medium). In air, \( n_1 \approx 1 \), so the equation simplifies to: \[ \tan \theta_B = n_2 \]
Step 2: Relationship Between Incident and Refracted Angles
According to Snell's law, the relationship between the angles of incidence and refraction is given by: \[ \frac{\sin \theta_i}{\sin \theta_r} = \frac{n_2}{n_1} \] where \( \theta_i = 60^\circ \), and \( \theta_r \) is the angle of refraction.
Step 3: Brewster's Angle for Complete Polarization
When the reflected ray is completely polarized, the angle of incidence \( \theta_i = 60^\circ \) must equal the Brewster's angle \( \theta_B \). Therefore, the angle of refraction \( \theta_r \) is: \[ \theta_r = 30^\circ \] Final Answer: The angle of refraction in the medium is \( 30° \).