Reflection, refraction and diffraction

Wavefronts and rays

To draw waves in two dimensions we use two pictures together:

• A wavefront is a line joining points that are in phase, such as a line along a crest. Neighbouring wavefronts are one wavelength apart.
• A ray is an arrow showing the direction the wave (and its energy) travels. Rays are always at right angles to the wavefronts.

A ripple tank shows these clearly. A light above the tank makes each crest act like a small lens, so crests appear as bright lines on a screen below. A straight bar dipping into the water makes straight (plane) wavefronts; a point dipper makes circular ones.

Reflection

When a wave meets a barrier it bounces back. Angles are measured between the ray and the normal, a line at right angles to the surface at the point where the ray hits.

$\theta_i = \theta_r$

The incident ray, reflected ray and normal all lie in the same plane. Reflection changes only the direction: the wave stays in the same medium, so its speed, frequency and wavelength are unchanged.

Echoes, sonar and ultrasound imaging all use reflection. A wave can reflect from any boundary where the medium changes, not just a hard wall: some ultrasound reflects at every boundary between tissues, which is how the image is built up.

Refraction

Refraction is the change in direction of a wave as it passes from one medium into another at an angle, caused by the change in speed. In a ripple tank, water waves travel more slowly in shallow water, so a sheet of glass on the tank floor makes a shallow region.

The reasoning HSC markers look for runs like this:

1. The frequency is set by the source, so it is the same on both sides of the boundary.
2. The speed changes because the medium changes.
3. From $\lambda = v/f$, the wavelength changes in proportion to the speed.
4. If the wavefront meets the boundary at an angle, the part that crosses first changes speed first, so the wavefront swings round and the direction changes.

Slowing down bends the ray towards the normal; speeding up bends it away from the normal. A wave that hits the boundary along the normal changes speed and wavelength but not direction. The same rule, with numbers, is Snell's law: $\dfrac{\sin\theta_1}{\sin\theta_2} = \dfrac{v_1}{v_2}$. You will use it for light on page 3H.

Refraction explains why waves line up with the beach. The part of each wavefront in shallower water slows first, so the whole front swings round until it runs almost parallel to the depth contours. Headlands get concentrated wave energy and bays get less, which is why surf breaks form off points.

Diffraction

Diffraction is the spreading of a wave as it passes through a gap or around the edge of an obstacle. Each point on a wavefront that gets through the gap acts as a source of new circular wavelets (Huygens' principle, which you will use again in Year 12), so the wave fans out into the region behind the barrier.

The amount of spreading depends on the ratio of wavelength to gap width:

• Gap much wider than $\lambda$: the wave passes almost straight through with a sharp "shadow" and only a little bending at the edges.
• Gap about equal to $\lambda$ or smaller: the wave spreads out in almost semicircular wavefronts.

Diffraction does not change the wave's speed, frequency or wavelength. It explains why you can hear someone around a corner but cannot see them: sound wavelengths (about 0.02 to 17 m) are comparable to doorways, while light wavelengths (about 400 to 700 nm) are millions of times smaller. It also explains why long-wavelength AM radio reaches valleys behind hills that FM signals miss.