## Light as a Wave

We have spent some time looking at waves — and by now should be able to recognise a wave when we see one! In this chapter we look at evidence that a light beam behaves like a train of waves.

To help us predict how the wave properties of light should manifest themselves, we use a construction originally proposed by the Dutch mathematician Christiaan Huygens and based on the hypothesis that a train of waves continuously regenerates itself, each point on the wave acting as if it were a new source of secondary wavelets. Snell's law of refraction can be derived using Huygens' construction — circumstantial if not overwhelming evidence that light behaves a wave.

A more convincing argument is available. If we really believe that light is a wave, it should be possible to arrange an experiment in which light waves interfere destructively — in other words, light plus more light sometimes makes darkness.

When we send a beam of light through a very small aperture such as a thin slit, Huygens' construction gives a curious prediction. The walls of the slit will cut off some of the secondary wavelets and create an imbalance in the emerging beam. Not only will there be a sideways spread (diffraction), but the unmatched wavelets will interfere constructively and destructively, producing a characteristic pattern.

In a practical way, the wave nature of light sets a limit to the resolving power of optical instruments. It is not possible to make microscopes and telescopes of unlimited magnifying power. No matter how sophisticated the optical system is, we cannot use light waves to examine structures finer than the structure of the waves themselves.

In Young's experiment two thin slits act as coherent light sources. When their light comes together we get constructive and destructive interference, a pattern of dark lines within the diffraction pattern — an example of light + light = dark !

Interference between light from diffraction gratings, which contain very large numbers of slits, gives us the ability to investigate atomic structure. We can probe even more deeply using X-rays and we were fortunate that nature provided us with perfect diffraction gratings, in the form of crystalline solids.

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