Rainbows are caused by light ‘reflecting’ and ‘refracting’ (splitting in to colours) inside a water droplet. A second rainbow is caused when light is reflected twice inside the water droplet.
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So a second rainbow will always appear when there’s a rainbow but they are always fainter than the first rainbow so you can’t always see them.
If you looked closely, you might have noticed that the second rainbow has the colours in the opposite order because of the double reflection that Bradley mentioned!
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