Question

If polarising angle is \( \theta_1 \), and critical angle is \( \theta_2 \), then:

• A. \( \tan \theta_1 = \sin \theta_2 \)
• B. \( \tan \theta_1 = \cos \theta_2 \)
• C. \( \cot \theta_1 = \sin \theta_2 \)
• D. \( \cot \theta_1 = \cos \theta_2 \)

Hint:

Brewster's law states that the polarising angle \( \theta_1 \) is related to the critical angle \( \theta_2 \) by \( \tan \theta_1 = \sin \theta_2 \).

Answer 1

The Correct Option is A

In optics, the polarising angle \( \theta_1 \) is the angle of incidence at which light reflected from a surface is completely polarised. The critical angle \( \theta_2 \) is the angle of incidence at which total internal reflection occurs when light passes from a denser to a rarer medium.
Brewster's law gives the relation between the polarising angle \( \theta_1 \) and the critical angle \( \theta_2 \), which is:
\[ \tan \theta_1 = \sin \theta_2 \] This relationship arises because at the polarising angle, the reflected and refracted rays are perpendicular to each other, and the angle of refraction is the critical angle. The derivation uses the fact that the refracted light at the critical angle makes an angle of \( 90^\circ \) with the reflected light.
Thus, the correct relationship between the polarising angle \( \theta_1 \) and the critical angle \( \theta_2 \) is:
\[ \tan \theta_1 = \sin \theta_2 \] Hence, the correct answer is option (A) \( \tan \theta_1 = \sin \theta_2 \).