We know her woof, her texture, Keats was moved to write about the rainbow: She is given in the dull catalogue of common things.
To form a rainbow, millions of little raindrops act like tiny mirrors. But rather than being reflected on the surface, the light passes into each drop to be reflected from the back, and the optical properties of a sphere of water are such the angle of reflection is always 42 degrees. The 42-degree angle limits the occurrence of the rainbow: none will appear unless the drops are located in the sky in precisely such a way that the eye can catch the light reflected at this angle. As a result, the bow is part of a circle which has an angular width of 42 degrees, the centre of the circle being the anti-solar point - a point on the continuation of an imaginary line joining the sun and the observer's head, and which is as far below one horizon as the sun is above the other.
A second consequence of reflection within the water drop is that the light, as it passes from air to water and out again, is separated into its constituent colours; the eye picks up different colours from different strategically placed drops, giving the rainbow its familiar pattern with violent on the inside and red on the outer edge.
Some rainbows, however - like Monday mornings, nascent rays of hope, and young men's prospects when they go a-wooing - are brighter than others. Their appearance depends on the size of the raindrops that reflect the sunlight. Very small drops give a wide and nearly colourless rainbow, while the large raindrops of a heavy shower produce a narrow, bright bow with sharp edges and colours well-defined.
Sometimes, when a ray of sunshine is reflected from the far side of a raindrop, not all the light succeeds in making its escape. Some of it is reflected a second time from the inner surface of the sphere of water, and only emerges from the raindrop at its next attempt. The geometry is such that this twice-reflected ray of light finally emerges from the drop at an angle of 51 degrees to the original ray of sunlight.
The result is that we sometimes see a larger secondary rainbow, concentric with the main, resulting from raindrops strategically placed so that our eyes can catch the light emerging from them at an angle of 51 degrees to the original sunbeams. This secondary bow, a larger, fainter, optical echo of the first, is a chromatic mirror image; its colours are reversed, with red inside and violet on the outer edge.