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The Variety of Rainbows

Surely a rainbow is one of the most beautiful, if not the most beautiful, phenomenon of nature. It is also such an unexpected phenomenon. Although most humans have seen simple rainbows many times there are a number of more complex versions of rainbows that few have experienced.

A rainbow occurs because light rays enter water droplets and are refracted and reflected out at a different angle. This refractive angle, the difference in angle between the ray entering the ray leaving determines the angle in the sky at which the rainbow is observed, as is shown in the diagram below.

The determination of the refractive angles for rainbows is dealt with elsewhere.

A simple rainbow, called a primary rainbow, is one for which the refractive angle is about 42°. It is of the form shown below with red appearing at the top and blue indigo appearing at the bottom.

The primary rainbow and the refractive angle of 42° are associated with a light ray having one reflection before leaving the droplet. When there are two reflections the rainbow is called secondary. The refractive angle is about 50° The image below depicts the case of a primary and secondary rainbow appearing. The order of the colors in a secondary rainbow are the reverse of the order in the primary rainbow.

When there is a large body of water near the site of a rainbow the sun's rays may be reflected off the water and enter the water droplets from below. This results in a rainbow positioned differently from the unreflected rainbows. There may be a primary reflected rainbow in addition to the primary and secondary rainbows, as shown below.

Or, there may be both a primary and secondary reflected rainbow as shown below.

There may be three reflection of a light ray in a rain droplet before it leaves the droplet. The resulting rainbow is called a tertiary rainbow. Its refractive angle is about 172° and it is difficult to display it along with the primary and secondary rainbows.

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