Wonders of the Universe. Andrew Cohen

them as being produced by the ‘light from the Sun as it is reflected by a cloud before reaching the eye’. This isn’t too far from the truth. The basis of our modern understanding was delivered by Isaac Newton, who observed that white light is split into its component colours when passed through a glass prism. He correctly surmised that white light is made up of light of all colours, mixed together. The physics behind the production of a rainbow is essentially the same as that of the prism. Light from the Sun is a mixture of all colours, and water droplets in the sky act like tiny prisms, splitting up the sunlight again. But why the characteristic arc of the rainbow?

      The first scientific explanation, which pre-dated Newton by several decades, was given by René Descartes in 1637. Water droplets in the air are essentially little spheres of water, so Descartes considered what happens to a single ray of light from the Sun as it enters a single water droplet. As the diagram opposite illustrates, the light ray from the Sun (S) enters the face of the droplet and is bent slightly. This is known as refraction; light gets deflected when it crosses a boundary between two different substances (point A), then when the light ray gets to the back surface of the raindrop, it is reflected back into the raindrop (point B), finally emerging out of the front again, where it gets bent a little more (point C). The light ray then travels from the raindrop to your eye (E).

      The key point is that there is a maximum angle (D) through which light that enters the raindrop gets bounced back. Descartes calculated this angle for red light and found it to be forty-two degrees. For blue light, the angle is forty degrees. Colours between blue and red in the spectrum have maximum angles of reflection of between forty-two and forty degrees. No light gets bounced back with angles greater than this, and it turns out that most of the light gets reflected back at this special, maximum angle. So, here is the explanation for the rainbow. When you look up at a rainbow, imagine drawing a line between the Sun, which must be behind you, through your head and onto the ground in front of you. At an angle of forty-two degrees to this line, you’ll see the so-called rainbow, or Descartes’ ray of red light. At an angle of forty degrees to this line, you’ll see the Descartes’ ray of blue light, and all the colours of the rainbow in between. There is some light reflected back to your eye through shallower angles, which is why the sky is brighter below the arc than above it. You don’t see the colours below the arc because all the rays merge to form white light. On the picture on the previous page, you can see the sky brightening inside the rainbow over the Victoria Falls, and the relative darkness of the sky outside it.

      So raindrops separate the white sunlight into a rainbow because each of the constituent colours gets reflected back to your eye at a slightly different maximum angle. But why the arc? In fact, rainbows are circular. Think of the imaginary line again between the Sun, your head and the ground. There isn’t just one place at which the angle between this line and the sky is forty-two degrees, there is a whole circle of points surrounding the line. The reason you can’t see a complete circle is that the horizon cuts it off, so you only see the arc. This is also why you tend to see rainbows in the early morning or late afternoon. As the Sun climbs in the sky, the line between the Sun and your head steepens and the rainbow, which is centred on this line, drops closer and closer to the horizon until at some point it will vanish below the horizon.