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Reflection

Waves, sound and light · level 5, lesson 4 of 6

A question to start

Ships measure the depth of the sea by sending a pulse of sound down and timing its echo. How does that work, and what law does a reflected wave follow?

The idea

When a wave hits a surface, it can reflect. Draw a line at right angles to the surface where the wave hits: the normal. Then the law of reflection is:

\[\text{angle of incidence} = \text{angle of reflection},\]

both measured from the normal.

Timing an echo gives a distance. The wave goes there and back, so

\[d = \frac{v t}{2}.\]

This is how sonar (sound in water) and radar (radio waves) measure distance.

depth = v × t ÷ 2pulse downsea floor

Worked examples

1. The angle. A ray hits a mirror at 30° to the normal. It reflects at 30° to the normal, on the other side.

2. Sonar. Sound travels at 1,500 m/s in seawater. The echo returns after 0.4 s: \(d = 1500 \times 0.4/2 = 300\) m.

3. Radar to the Moon. A radar pulse returns from the Moon after 2.56 s: \(d = 3.00\times10^8 \times 2.56/2 = 3.84\times10^8\) m, about 384,000 km.

Try it

  1. What is the normal?
  2. A light ray hits a mirror at 55° to the normal. At what angle does it reflect?
  3. A bat hears the echo of its squeak 0.02 s later, in air at 340 m/s. How far away is the moth?
  4. Why do you divide by 2 when you work out a distance from an echo?
Answers
  1. A line at right angles to the surface where the wave hits.
  2. 55° to the normal.
  3. \(340 \times 0.02/2 = 3.4\) m.
  4. The wave travels there and back, twice the distance.

Common mistake

Measuring angles from the surface. Angles of incidence and reflection are measured from the normal, not from the mirror.

Where it leads