A rainbow can be defined as a band of seven colors assembled as an arc that is formed by reflection and refraction (or bending) of the sun's rays inside raindrops. They appear when it is raining in one part of the sky and sunny in another.
What makes the colours of the rainbow?
The traditional description of the rainbow is that it is made up of seven colors - red, orange, yellow, green, blue, indigo, and violet. Actually, the rainbow is a whole continuum of colors from red to violet and even beyond the colors that the eye can see.
This implies that when we see a rainbow and its band of colors we are looking at light refracted and reflected from different raindrops.
What makes a double rainbow?
Not all of the energy of the ray escapes the raindrop after it is reflected once. A part of the ray is reflected again and travels along inside the drop to emerge from the drop. The rainbow we normally see is called the primary rainbow and is produced by one internal reflection; the secondary rainbow arises from two internal reflections.
Sources:
http://eo.ucar.edu/rainbows/
http://www.fi.edu/color/rainbow.html
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