Question

A ray of light passes through a glass slab with refractive index \( n = 1.5 \) at an angle of incidence of \( 30^\circ \). What is the angle of refraction inside the glass? (Use \( \sin 30^\circ = 0.5 \))

• A. \( 20^\circ \)
• B. \( 25^\circ \)
• C. \( 18^\circ \)
• D. \( 15^\circ \)

Hint:

When light passes from one medium to another, Snell's Law \( n_1 \sin i = n_2 \sin r \) allows you to find the angle of refraction, where the refractive index is key to the change in direction.

Answer 1

The Correct Option is A

We are given: - Refractive index of glass, \( n = 1.5 \), - Angle of incidence, \( i = 30^\circ \). The relationship between the angle of incidence \( i \) and the angle of refraction \( r \) is given by **Snell's Law**: \[ n_1 \sin i = n_2 \sin r \] Where: - \( n_1 \) is the refractive index of the medium from which the light is coming (air, \( n_1 = 1 \)), - \( n_2 \) is the refractive index of the second medium (glass, \( n_2 = 1.5 \)), - \( i \) is the angle of incidence, - \( r \) is the angle of refraction. Substituting the given values: \[ 1 \times \sin 30^\circ = 1.5 \times \sin r \] \[ 0.5 = 1.5 \times \sin r \] \[ \sin r = \frac{0.5}{1.5} = \frac{1}{3} \] \[ r = \sin^{-1} \left( \frac{1}{3} \right) \approx 19.47^\circ \approx 20^\circ \] Thus, the angle of refraction inside the glass is approximately \( 20^\circ \).