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

Snell's law states that \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \). Given: - \( n_1 = 1 \) (refractive index of air) - \( n_2 = 1.33 \) (refractive index of water) - \( \theta_1 = 30^\circ \) (angle of incidence in air) Substituting these values into the equation: \[ 1 \times \sin 30^\circ = 1.33 \times \sin \theta_2 \] Solving for \( \sin \theta_2 \): \[ \sin \theta_2 = \frac{\sin 30^\circ}{1.33} = \frac{0.5}{1.33} = 0.3759 \] Therefore, the angle of refraction in water, \( \theta_2 \), is: \[ \theta_2 = \sin^{-1}(0.3759) = 22.2^\circ \] The angle of refraction in water is \( 22.2^\circ \).