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?

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

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

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.)