Refraction of Light: Quick Revision

A brief note on Refraction of Light. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• Light bends at a boundary because its speed changes.
• Into an optically denser material (larger $n$) it bends toward the normal; into a rarer one, away from it. Along the normal, it does not bend.
• Snell's law: $\dfrac{\sin i}{\sin r}$ is constant for two materials. From air, $\sin r = \dfrac{\sin i}{n}$.
• The refractive index $n = \dfrac{c}{v}$ has no unit and is never below $1$.
• A glass slab sends a ray out parallel to the way it came, shifted sideways.
• Looking straight down, water looks shallower: apparent depth $= \dfrac{\text{real depth}}{n}$.

The facts at a glance

A worked example

A ray goes from air into a clear liquid ($n = 1.36$) at $45^\circ$. Find the angle of refraction and the speed of light in the liquid.

1. The angle. $\sin r = \dfrac{\sin 45^\circ}{1.36} = \dfrac{0.707}{1.36} = 0.520$, so $r = 31.3^\circ$.
2. The speed. $v = \dfrac{3.00 \times 10^{8}\ \text{m/s}}{1.36} = 2.21 \times 10^{8}\ \text{m/s}$.
3. Check. The ray bends toward the normal, and the light is slower than in air.

Practice with new numbers

A program to try

The program finds the angle of refraction and the speed of light for a few materials.

Mistakes to avoid

• Measuring angles from the surface. Use the normal, as for mirrors.
• Dividing the angle by $n$. Divide its sine.
• 'Optically denser means heavier.' Kerosene floats on water but has the larger $n$.
• Multiplying the depth by $n$. Things under water look shallower, so divide.

Check yourself

1. Which bends a ray from air more: water or glass?

2. A material has $n = 1.25$. How fast is light in it?

3. A ray enters a glass slab at $47^\circ$. At what angle does it leave?

4. A tank $1.6\ \text{m}$ deep is full of water ($n = 1.33$). How deep does it look from straight above?