Question

The angle of polarisation for a medium is 60°. The critical angle for this will be \( \left( \tan 60^\circ = \sqrt{3} \right) \):

• A. \( \cos^{-1} (\sqrt{3}) \)
• B. \( \tan^{-1} (\sqrt{3}) \)
• C. \( \sin^{-1} (\sqrt{3}) \)
• D. \( \sin^{-1} \left( \frac{1}{\sqrt{3}} \right) \)

Hint:

The critical angle is determined using the refractive index and is given by \( \sin^{-1} \) or \( \tan^{-1} \) depending on the medium's properties.

Answer 1

The Correct Option is B

Step 1: Critical Angle Formula.
The critical angle \( \theta_c \) is given by the formula: \[ \sin \theta_c = \frac{1}{n} \] For a medium with polarisation angle \( 60^\circ \), the refractive index is related to the tangent of the angle. Thus, the critical angle is given by: \[ \theta_c = \tan^{-1} (\sqrt{3}) \] Step 2: Conclusion.
Thus, the critical angle is \( \tan^{-1} (\sqrt{3}) \).