`Very beautiful it is in the brightness thereof. It compasses the heavens about with a glorious circle, and the hands of the Most High have bended it." Thus wrote the author of Ecclesiastes many centuries ago - and he was, of course, referring to the rainbow.
The rainbow was first convincingly explained by the French scientist Rene Descartes in the 17th century as being the result of reflection and refraction (or bending) of light by water drops. Some of the light that enters a water drop is reflected at the inner surface on the far side of the drop; since this light is also broken into its component colours by refraction, the rays leave the drop at angles decided by their colours - and an observer with his back to the sun sees a number of concentric coloured rings.
The appearance of the rings depends very much on the size of the raindrops which cause them. Very small drops - those with a diameter of about one twenty-fifth of a millimetre - give a wide and nearly colourless rainbow. Large drops - with diameters of about a millimetre or greater - produce a narrow, bright bow with sharp, well-defined colours.
But look more closely at a well-defined rainbow and you will notice that the total effect is rather more complex than just a simple coloured arc against the sky. You will see, for example, that its two "legs" near the ground appear to be much brighter than the zenith of the arc - particularly if the sun is low in the sky near the opposite horizon.
The difference arises because Descartes's theory of the rainbow is firmly based on the assumption that a raindrop is a sphere. In real life, however, a large falling raindrop is distorted by the flow of air around it; it resembles neither a sphere nor the traditional tear-drop depicted by cartoonists, but is more of a flattened sphere, a bunburger or, if you will, a horizontal tractor wheel.
Now rays of light from a low sun travel almost horizontally to hit a raindrop near the opposite horizon; at that angle the circular cross-section of a "horizontal tractor wheel" of water presents them with the curved shape they need to follow Descartes's plan - and we get a strong reflection. But a ray of sunlight heading upwards towards a drop that will contribute to the top of the rainbow encounters, at that angle, a volume of water whose opposite sides are flattened and almost parallel; Descartes's "spherical" theory breaks down.