Image Courtesy of Carlye Calvin/University Corporation for Atmospheric Research
Rainbows appear in the sky when there is bright sunlight and rain. Sunlight is known as visible or white light and is actually a mixture of colors. Rainbows result from the refraction and reflection of sunlight by these water droplets. It takes many droplets (each refracting and reflecting light back to our eyes at slightly different angles) to produce the brilliant colors of a rainbow.
You can only see a rainbow if the sun is behind you and the rain in front. You can even make your own rainbow with a garden hose or water sprinkler on a sunny day.
A double rainbow occurs when some of the light entering the raindrop is refracted into its component colors, reflected off the back interior wall of the drop, and refracted again as it exits the drop. In the second rainbow, the colors are reversed where blue is on the outside and red is on the inside. The dark area in between the two rainbows is called Alexander’s band.
source: Windows to the universe