Question

The refractive index of glass with respect to air is 2. The critical angle at their interface is

• A. 90°
• B. 60°
• C. 45°
• D. 30°

Answer 1

The Correct Option is D

The critical angle $\theta_c$ is the angle of incidence for which the angle of refraction is 90°. It is given by the formula: $$\sin \theta_c = \frac{n_2}{n_1}$$ where $n_1$ is the refractive index of the denser medium (glass) and $n_2$ is the refractive index of the rarer medium (air). Given that the refractive index of glass with respect to air is 2, we have: $$\sin \theta_c = \frac{1}{2}$$ Now, solving for $\theta_c$: $$\theta_c = \sin^{-1} \left( \frac{1}{2} \right) = 30^\circ$$

The correct option is (D): $30°$