Rainbows are so spectacular, but do you understand how rainbows occur? The explanation that it is the same effect as occurs when a shaft of light passes through a triangular glass prism and is dispersed into a spectrum of colors is true in some respects, but misses much of the story. It does not explain why the sky is darker on one side of the rainbow, nor the angles at which one sees rainbows, nor why sometimes one seems alternating purple and green bands on one side of the rainbow, nor why a rainbow in a fog bank is white (a fog bow). What is surprising is that rainbows provide evidence that the wavelength of light is finite, even though the wavelength is extremely small, of the order of microns (a micron is a millionth of a meter). An understanding of rainbows allows one to understand the halos that sometimes occur around the moon, and a detailed analysis accounts for glories such as those that ring the shadow of an aeroplane cast on a cloud. Rainbows are beautiful and so too is the mathematics which explains them.