This summer I went on a family holiday to Cornwall, on the Helford River. The peninsula south of the river is, rather wonderfully, called The Lizard. Standing on its cliffs, you are at the southernmost point of mainland Britain. North of the river is the port of Falmouth, from where packet-ships kept the mail services of the British Empire running until 1851. The area is lush with the sort of half-tamed beauty that England does so well, and the boundary with the contrasting wildness of the Atlantic is never far away.
Walking home from a riverside pub one evening, I witnessed a stirring natural display. With the sun setting at our backs, a fantastically bright and complete double rainbow framed the river-opening leading out to the sea. I have always loved rainbows, and this was the best one I have seen. It even came in front of the horizon, past the trees on the riverbank opposite, and merged with its reflection in the river. It was an invitation and a dare to scientific understanding.
The image hovering in front of me was formed by sunlight streaming from behind us, internally reflected back towards us by myriad tiny suspended raindrops. When light meets an interface between air and water—the surface of a raindrop—some of it is reflected and some of it passes through. The angle of refraction depends both on the light’s wavelength and on the angle at which it hits the surface. Parallel rays entering a spherical raindrop bounce off the inside and come back towards us. The reflection angle from the back of the raindrop, combined with the two refractions (one as it enters the drop, and one as it leaves) conspire to concentrate each wavelength of light at a certain return angle. Wavelength corresponds to color, so the colors separate into the familiar bands.