Here's an explanation of all things rainbow, courtesy of New Scientist's Jeff Hecht:
Rainbows form when light is reflected to our eyes from inside falling raindrops. A single reflection inside the drop produces a bright primary rainbow, which appears on the opposite side of the sky from the sun. Two reflections inside the drop form the fainter secondary bow, which is outside the primary rainbow, but still on the same side of the sky, opposite the sun. Although very beautiful, such double rainbows are fairly common.
By contrast, three reflections inside the drop produces the tertiary rainbow, which are much fainter and so rarely seen - and because those reflections take the light most of the way around the drop, it appears on the same side of the sky as the sun (this also makes it even harder to see).
Four reflections produce the fourth-order rainbow, close to - but even fainter than - the tertiary rainbow. Because this photo is taken into the sun, it must be a third and fourth order rainbow - as Theusner reports [in the latest issue of Applied Optics].
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