Question

Two media A and B are separated by a plane boundary. The speed of light in medium A and B is \( 2 \times 10^8 \, \text{ms}^{-1} \) and \( 2.5 \times 10^8 \, \text{ms}^{-1} \), respectively. The critical angle for a ray of light going from medium A to medium B is:

Answer 1

Using Snell’s law for the critical angle \( \theta_c \): \[ n_A \sin \theta_c = n_B \sin 90^\circ = 1 \] Hence, \[ \sin \theta_c = \frac{v_A}{v_B} = \frac{2 \times 10^8}{2.5 \times 10^8} = \frac{4}{5} \] Thus, the critical angle is: \[ \theta_c = \sin^{-1} \left(\frac{4}{5} \right) \] Thus, the correct answer is: \[ \text{(B) } \sin^{-1} \left(\frac{4}{5} \right) \]