Refraction and wavelength-dependent interactions

The direction of bending depends on the change in speed:

• If the wave slows down, it bends towards the normal. Its angle to the normal becomes smaller.
• If the wave speeds up, it bends away from the normal. Its angle to the normal becomes larger.

For example, light bends towards the normal when travelling from air into glass, and away from the normal when travelling from glass into air.

If the wave travels along the normal, it continues straight ahead. Its speed still changes, but there is no change in direction.

Why a change in speed makes a wave turn

A wavefront joins points at the same stage of a wave's vibration; a line along a crest is one example. The direction of wave travel is perpendicular to the wavefront.

When a wavefront reaches a boundary at an angle, one end enters the new medium first. If the wave travels more slowly there, that end slows while the rest is still moving faster in the original medium. This turns the wavefront, changing the direction of travel towards the normal. When the new medium allows the wave to travel faster, the first end speeds up instead, and the wave turns away from the normal.

At normal incidence, the whole wavefront reaches the boundary at the same time. All parts change speed together, so the wavefront does not turn.

Speed and wavelength change, but frequency does not

The wave's frequency is the number of complete waves passing a point each second. Crossing a boundary does not change this rate: the source continues producing waves at the same frequency.

Wave speed, frequency and wavelength are linked by:

$$v = f\lambda$$

Since frequency stays constant, a decrease in speed means a decrease in wavelength. Successive wavefronts are therefore closer together in the slower medium. If the speed increases, the wavelength increases and the wavefronts are further apart.

Materials interact differently with different wavelengths — Higher tier

A wave meeting a substance may be transmitted, passing through it; absorbed, transferring energy to it; reflected, returning into the original medium; or refracted, changing speed and potentially direction as it crosses the boundary.

These processes are not necessarily alternatives. For instance, some light can be reflected at a glass surface while the rest enters the glass and is transmitted through it. The transmitted light may also be refracted.

How a substance behaves depends on the wave's wavelength. Glass provides a useful example: it can transmit and refract visible light, absorb ultraviolet radiation and reflect infrared radiation. The amount of each interaction depends on the type of glass and the particular wavelength; glass does not treat every wavelength within these groups identically.

The important connection is that being transparent to visible light does not mean a material transmits all electromagnetic waves. The same substance can allow one range of wavelengths through while absorbing or reflecting another.

Speed and wavelength change; frequency stays constant.

$$v = f\lambda$$

Lower speed means shorter wavelength; higher speed means longer wavelength.

Wavelength-dependent interactions — Higher tier

A substance may transmit, absorb, reflect or refract waves differently at different wavelengths. More than one interaction can occur.

Glass can transmit/refract visible light, absorb ultraviolet and reflect infrared; its behaviour depends on the glass and the wavelength.