Oftentimes after a storm, a rainbow is visible. Sometimes you may even see a double rainbow or no rainbow at all. How do these form? It all has to do with light!
After a storm, or even as one is still happening but moving out, there are water droplets in the air. The sunlight, as long as it is coming toward the storm at a low angle, will hit these water droplets and reflect back. This and the process that happens inside the droplet allows you to see a rainbow.
Inside of the droplet, the white light from the sun, which is made up of all different colors, is separated into different wavelengths. This is called refraction. This allows you to see the different colors of the rainbow that make up the white light, just like a prism. This happens thousands of times as the light hits the many water droplets in the air. The same process happens when you see a double rainbow, but the angle is different, allowing for a second reflection inside the droplet. This creates a secondary rainbow that is often lighter and less visible.
When the light bounces back toward us, we see it reflected back in the shape of a semi-circle, although a rainbow is actually a full circle. The way you perceive the rainbow has to do with the angle between you the sun and the water droplets. This is why a rainbow will appear to move when you move to a different location and why you can never find the end.