rainbow after the rain?

Actually, you can see rainbow before (or without) rain. It is common phenomena near waterfalls or fountains in bright sunny day. All you have to have to see (natural) rainbow is, water drops in the air and shiny sun. When the sun shines at the water droplets from behind you, you can see the rainbow right in front of you. To understand how rainbow get colors, you have to understand the path the light from the sun travel through the water droplet. It is first refracted as it enters the droplet then reflected against itself in the droplet and then got refracted back as it exit the droplet. The amount of light refracted in the droplet is what form the color of the rainbow. Since blue light has shorter wavelength, it is refracted at an angle greater than red light, hence you see the rainbow forms colors from red at the outside (due to reflection of the refraction) to blue at the inside ring. An interesting point to note about rainbow is, it does not actually exist in physical sense at any area of the sky. It is just an optical illusion. So, its position and form depends on where the observer is and how he is looking at it