# 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?

${\displaystyle n={\frac {v_{1}}{1.24\times 10^{8}}}}$

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

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

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

${\displaystyle 1.31={\frac {3\times 10^{8}}{v_{2}}}}$

${\displaystyle v_{2}={\frac {3\times 10^{8}}{1.31}}\approx 2.29\times 10^{8}{\mbox{ ms}}^{-1}}$

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?

${\displaystyle {\frac {3\times 10^{8}}{v_{2}}}={\frac {\sin {10}}{\sin {20}}}\approx 0.508}$

${\displaystyle v_{2}\approx {\frac {3\times 10^{8}}{0.508}}\approx 5.91\times 10^{8}}$

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?

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

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