Wave refraction

A wave can change speed when it enters a different region. If it crosses the boundary at an angle, the change in speed also changes its direction. This change in direction is called refraction.

A wavefront is a line joining points at the same stage of a wave, such as points along a crest. When a wavefront reaches a boundary at an angle, one part enters the new region before the rest. That part changes speed first, causing the wavefront to turn. The direction of travel, which is perpendicular to the wavefront, turns with it.

The normal is an imaginary line perpendicular to the boundary. A wave that slows down bends towards the normal; a wave that speeds up bends away from it. At normal incidence, the wave travels along the normal and its wavefront reaches the boundary all at once. Its speed changes, but its direction does not.

Refraction: Frequency and wavelength

The wave’s frequency remains unchanged as it crosses the boundary. Wave speed, frequency and wavelength are related by:

Here $$v$$ is wave speed, $$f$$ is frequency and $$\lambda$$ is wavelength. Since frequency stays the same, a wave that slows down has a shorter wavelength; a wave that speeds up has a longer wavelength. This change in wavelength occurs even at normal incidence, when the direction does not change.

Refraction in a ripple tank

In a ripple tank, water waves travel more slowly in shallow water than in deep water. As waves enter a shallower region, their frequency stays the same but their wavelength decreases, so successive wavefronts are closer together.

If the wavefronts meet the change in depth at an angle, the part entering the shallow water first slows first. The wavefronts turn, and the waves bend towards the normal. If they meet the boundary at normal incidence, they slow down and their wavelength decreases, but they continue in the same direction.