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We have all seen rainbows in our lives. But the other day, I saw a double rainbow! How rare are double rainbows and what causes them to appear?

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    $\begingroup$ Not particularly rare where I live in Northern Indiana. I usually see several each year. $\endgroup$ – L.B. Jun 5 '16 at 16:14
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A normal single arc rainbow is caused when sunlight enters a raindrop with a light-path refracted>reflected>refracted. A double rainbow occurs when sunlight hits a part of the raindrop at a different angle of incidence, at which the light-path is refracted>reflected>reflected>refracted. Some energy is lost with each reflection, so the double internal reflection emerges as less bright than the primary arc. Also, because there is another internal reflection the colours are inverted. So every rainbow has a primary and seconday arc. Hence the question becomes: 'Is the observer in a position to see the secondary arc', which is a matter of geometry between the sun, raindrop and observer.

So the answer to your question is 'no', it isn't rare at all, in fact a secondary arc is always present somewhere, but is not always visible to the observer for reasons of geometry and background light intensity.

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