In 1997, Aza Raskin took this picture of a double rainbow over the Pacific. It was early morning, with the sun rising behind us. The low resolution is due to the primitive state of digital cameras in those ancient times. Especially interesting was that the entire sky to the outside of the rainbow was darker than the sky under the rainbow, as the picture accurately portrays.

A rainbow is a refraction from what is essentially a vertical screen of water droplets. I am sure you have seen many diagrams of how this works. At particular angles you see different colors. Under certain conditions light coming from behind the screen is refracted away from you if the angle between you and the screen is too great, thus, outside the rainbow the sky can appear dark. The same geometry that determines the rainbow gives the angle beyond which this effect happens. Inside the rainbow, the light coming toward you from the sky beyond is not refracted away.