Wave speed depends on the substance

1. All electromagnetic waves travel through a vacuum at the same speed, about $3.0\times 10^{8}m/s$.
2. When an electromagnetic wave enters a transparent substance, it travels more slowly than it does in a vacuum.
3. The amount by which the wave slows down depends on the substance, so light has a different speed in air, water and glass.
4. Light in air travels at almost exactly its speed in a vacuum, so the two speeds are treated as equal in most calculations.
5. Light in water travels at about $2.25\times 10^{8}m/s$, which is roughly three quarters of its speed in air.
6. Light in glass travels at about $2.0\times 10^{8}m/s$, which is roughly two thirds of its speed in air.
7. A material in which light travels more slowly is often called optically denser, which is not the same as having a greater mass per cubic metre.
8. Other electromagnetic waves, such as microwaves, infrared and ultraviolet, also change speed when they pass from one substance into another.
9. A change of speed at an interface between two substances is the cause of several effects you can see every day, and the most important of these is refraction.

How a change of speed causes refraction

1. A beam of light can be pictured as a series of wavefronts, which are lines joining the crests of the wave drawn at right angles to its direction of travel.
2. Picture a set of straight wavefronts travelling through air and meeting the flat surface of a glass block at an angle.
3. One end of each wavefront reaches the glass first and slows down, while the other end is still moving at the faster speed in air.
4. For a short time the end inside the glass covers less distance than the end in the air, so each wavefront swings round.
5. When the whole wavefront is inside the glass, it is travelling in a new direction, and this change of direction is refraction.
6. The wavefronts inside the glass are also closer together than those in the air, because each one moves forward a smaller distance in the same time.
7. A wave that slows down as it crosses an interface bends towards the normal, so its angle of refraction is smaller than its angle of incidence.
8. A wave that speeds up as it crosses an interface bends away from the normal, so its angle of refraction is larger than its angle of incidence.
9. A wave that meets an interface along the normal changes speed but not direction, because every part of each wavefront reaches the new substance at the same moment.
10. Refraction depends entirely on the change of speed, so if two substances carried light at exactly the same speed a ray would cross the interface without bending.

Frequency stays the same but wavelength changes

1. The frequency of a wave is set by the source that produces it, so it does not change when the wave passes into a new substance.
2. Every wavefront that arrives at an interface must leave it on the other side, so the number of waves passing each second is the same in both substances.
3. Wave speed, frequency and wavelength are linked by the wave equation $v=f\lambda$.
4. If the frequency stays constant while the speed falls, the wavelength must fall by the same proportion.
5. Light passing from air into glass keeps the same frequency, but both its speed and its wavelength fall to about two thirds of their values in air.
6. Light passing from glass back into air speeds up again, so its wavelength returns to its original value.

Why white light splits into colours

1. In a vacuum every colour of light travels at the same speed, but in glass or water the speed depends slightly on the wavelength.
2. Violet light, which has the shortest wavelength in the visible spectrum, travels a little more slowly in glass than red light, which has the longest.
3. Violet light therefore has the largest change of speed at each surface of a prism and is refracted through the largest angle.
4. Red light has the smallest change of speed and is refracted the least, so the colours spread out into a spectrum.
5. This spreading of white light into its colours is called dispersion, and the same process inside raindrops produces a rainbow.

Everyday effects of changing wave speed

1. A straw standing in a glass of water looks bent or broken where it enters the water.
2. Light from the underwater part of the straw speeds up as it passes from water into air, so it bends away from the normal at the water surface.
3. Your brain assumes that light reaching your eye has travelled in a straight line, so it traces the ray straight back and places the underwater part of the straw higher than it really is.
4. A swimming pool looks shallower than it is for the same reason, because light from the bottom bends away from the normal as it leaves the water.
5. Seen from directly above, the bottom of a pool appears to be only about three quarters of its real depth.
6. A fish in a pond is deeper than it appears, so a kingfisher diving for it must aim below the position where it sees the fish.
7. In each case nothing has moved or bent, because only the path of the light has changed as its speed changed at the water surface.