Question

A light ray passes from air (refractive index = 1) into water (refractive index = 1.33). If the angle of incidence is 30°, what is the angle of refraction in water?

• A. \( 22.2^\circ \)
• B. \( 30.0^\circ \)
• C. \( 23.0^\circ \)
• D. \( 17.0^\circ \)

Hint:

When light passes from a less dense medium to a more dense medium (like air to water), it bends toward the normal. Use Snell's law to calculate the angle of refraction.

Answer 1

The Correct Option is A

Using Snell's law: \[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \] Where: - \( n_1 = 1 \) is the refractive index of air, - \( n_2 = 1.33 \) is the refractive index of water, - \( \theta_1 = 30^\circ \) is the angle of incidence in air. Substituting the values: \[ 1 \times \sin 30^\circ = 1.33 \times \sin \theta_2 \] \[ \sin \theta_2 = \frac{\sin 30^\circ}{1.33} = \frac{0.5}{1.33} = 0.3759 \] \[ \theta_2 = \sin^{-1}(0.3759) = 22.2^\circ \] Thus, the angle of refraction in water is \( 22.2^\circ \).