Rainbows are formed by light reflecting from rain drops. Often we see only one rainbow, called the primary bow, but sometimes we can see a second, outer rainbow, called the secondary bow.
When sunlight strikes a raindrop, some of the light is refracted at the first surface, internally reflected from the back surface, and refracted again on exiting the rain drop.
For each colour there is a maximum angle of deviation of the light. So, in rain drops there is a minimum angle, for each colour, between the incident and exit rays. For red, this is 42° and for violet it is 40°. The nature of internal reflection is such that many rays will emerge near this minimum angle.
Hence the sunlight will appear to be concentrated over a small region of the sky in a narrow range of angles from 40° to 42° and separated into colours, from blue to red.
Some of the sunlight is also refracted at the first surface, but is reflected twice internally from the back surface, and refracted again on exiting the rain drop.
Again there is the same maximum angle of deviation for each colour, but now the double internal reflection leads to a minimum angle between the incident and exit rays of 50.5° for red and 54° for violet. The bow is at a higher angle, and so will appear higher in the sky. And the colours are reversed, going from red to blue.
The amount of rainbow you see depends on the angles between you, the sun, and the raindrops. As the sun rises, less and less of the rainbow is visible. As you climb a mountain, you see more and more of the rainbow.
Reference: M Fogiel (Ed.), The Optics Problem Solver®, Research and Education Association, NJ (1990), pp 130-1.
First published on the web: 16 October 2000.
Author: Richard Payling