A-level Physics (Advancing Physics)/Refraction/Worked Solutions

'''1. A ray of light is reflected from a mirror. Its angle to the normal when it reaches the mirror is 70°. What is its angle of reflection?'''

The angles of reflection on both sides of the normal are always equal, so the angle of reflection is 70°.

'''2. The speed of light in diamond is 1.24 x 108 m/s. What is its refractive index?'''

$$n = \frac{v_1}{1.24 \times 10^8}$$

Assuming the speed of light in the reference medium is 3 x 108:

$$n = \frac{3 \times 10^8}{1.24 \times 10^8} = \frac{3}{1.24} \approx 2.42$$

'''3. The refractive index of ice is 1.31. What is the speed of light in ice?'''

$$1.31 = \frac{3 \times 10^8}{v_2}$$

$$v_2 = \frac{3 \times 10^8}{1.31} \approx 2.29 \times 10^8 \mbox{ ms}^{-1}$$

'''4. A ray of light passes the boundary between air and a transparent material. The angle of refraction is 20°, and the angle of incidence is 10°. What is the speed of light in this material? Why is it impossible for this material to exist?'''

$$\frac{3 \times 10^8}{v_2} = \frac{\sin{10}}{\sin{20}} \approx 0.508 $$

$$v_2 \approx \frac{3 \times 10^8}{0.508} \approx 5.91 \times 10^8 $$

This is greater than the speed of light in a vacuum (3 x 108), and so is impossible.

5. What is the critical angle of a beam of light leaving a transparent material with a refractive index of 2?

$$\sin{C} = \frac{1}{2}$$

C = 30° (using the sin−1 button on a scientific calculator - this means 'inverse sine', often denoted arcsine or asin for short.)

Introdução à Física/Refração da luz/Exercícios