# Rainbows

By Marcus Wilson 03/12/2009 1

The sun poked out from behind the clouds on my way in to work this morning just long enough to produce a beautiful rainbow for a few seconds. Not sure when we’ll next see it.

I guess most of us studied rainbows at school, but I’ll throw in a couple of physics words with this comment that you may not have heard of. The light from the sun is, as we know, made up of a whole range of different colours. Each point in the spectrum is made up of light with a different wavelength (the distance between peaks of the wave); red is longer wavelength (I say long, but I mean about 700 nanometres, where one nanometre is a millionth of a millimetre); violet is shorter, about 400 nanometres.

Now, the key to making a spectrum (e.g. a rainbow) from white light is a dispersive material. Water is one example, as is glass (e.g. your prism). Physicists describe something as dispersive if it has different properties at different wavelengths. That means the red light interacts with it differently to the blue, so they get split up. One of the key things physicists like to know about waves of some kind moving through a medium (e.g. light in air, sound in water, waves on a violin string) is the dispersion relation. This describes the relationship between wavelength and frequency (the number of oscillations a second).  A non-dispersive medium has wavelength times frequency equal to a constant (the wave velocity). But, what they forget to tell you at school, is that, in general, this isn’t true. And it’s materials where it isn’t true that are way more interesting to work with.

No dispersion, no rainbows. That simple.