Question

A light ray is passing from air (refractive index \( \mu_1 = 1.0 \)) into water (refractive index \( \mu_2 = 1.33 \)). If the angle of incidence in air is 30°, what is the angle of refraction in water?

• A. 22.5°
• B. 19.5°
• C. 25.0°
• D. 20.0°

Hint:

Snell's law helps us determine how light bends when transitioning between different mediums. Be sure to use the correct refractive indices for the given materials.

Answer 1

The Correct Option is A

We can use Snell's law to solve this problem: \[ \frac{\sin i}{\sin r} = \frac{\mu_2}{\mu_1} \] Where: - \( i = 30^\circ \) is the angle of incidence, - \( r \) is the angle of refraction, - \( \mu_1 = 1.0 \) (refractive index of air), - \( \mu_2 = 1.33 \) (refractive index of water). Substitute the known values: \[ \frac{\sin 30^\circ}{\sin r} = \frac{1.33}{1.0} \] \[ \frac{1/2}{\sin r} = 1.33 \] \[ \sin r = \frac{1/2}{1.33} \approx 0.375 \] \[ r = \sin^{-1}(0.375) \approx 22.5^\circ \] Thus, the angle of refraction in water is \( 22.5^\circ \).