Question

The critical angle of a medium having the refractive index \( \sqrt{2} \) is:

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Hint:

Remember that the critical angle is defined when the angle of refraction is \( 90^\circ \), and it depends on the refractive index of the medium.

Answer 1

The Correct Option is B

The critical angle \( \theta_c \) is the angle of incidence for which the angle of refraction is \( 90^\circ \). It is given by the formula: \[ \sin \theta_c = \frac{1}{n} \] Where: - \( n \) is the refractive index of the medium. For a medium with refractive index \( \sqrt{2} \), we substitute \( n = \sqrt{2} \) into the formula: \[ \sin \theta_c = \frac{1}{\sqrt{2}} \] \[ \sin \theta_c = \frac{\sqrt{2}}{2} \] \[ \theta_c = \sin^{-1} \left( \frac{\sqrt{2}}{2} \right) \] \[ \theta_c = 45^\circ \] Therefore, the critical angle for a medium with refractive index \( \sqrt{2} \) is \( 45^\circ \).