Question

A ray of light travelling through a medium of refractive index $ \frac{5}{4} $ is incident on a glass of refractive index $ \frac{3}{2} $. Find the angle of refraction in the glass, if the angle of incidence at the given medium - glass interface is 30°

• A. \( \sin^{-1} \left( \frac{1}{2} \right) \)
• B. \( \sin^{-1} \left( \frac{1}{3} \right) \)
• C. \( \sin^{-1} \left( \frac{5}{12} \right) \)
• D. \( \sin^{-1} \left( \frac{6}{5} \right) \)

Hint:

Always use Snell's law to find the angle of refraction when light passes from one medium to another. Ensure to use the correct refractive indices for the media involved.

Answer 1

The Correct Option is C

Using Snell's Law: \[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \] where \( n_1 = \frac{5}{4} \), \( n_2 = \frac{3}{2} \), and \( \theta_1 = 30^\circ \). Substitute the known values: \[ \frac{5}{4} \sin 30^\circ = \frac{3}{2} \sin \theta_2 \] Since \( \sin 30^\circ = \frac{1}{2} \), we get: \[ \frac{5}{4} \times \frac{1}{2} = \frac{3}{2} \sin \theta_2 \] \[ \frac{5}{8} = \frac{3}{2} \sin \theta_2 \] \[ \sin \theta_2 = \frac{5}{8} \times \frac{2}{3} = \frac{5}{12} \] Now, \( \theta_2 = \sin^{-1} \left( \frac{5}{12} \right) \). Thus, the angle of refraction is \( \sin^{-1} \left( \frac{5}{12} \right) \), which corresponds to option (C).