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In a piece on rainbows in the LRB in 2002, Peter Campbell wrote:

There are also rare phenomena to take account of, like cloud bows, which are the very pale rainbows you might see from the window of a plane, and things which are hard to see, like supernumerary rainbows. Should you be lucky enough to be somewhere where it is possible to see the never-photographed tertiary bow you would have to look back over your shoulder towards the sun, or turn round to face it.

As reported on the BBC, the current issue of Applied Optics carries

what is believed to be the first photographic recording of a quaternary rainbow in nature. It appears on the Sun side of the sky with its red arc at a radius of about 45° from the Sun. The original pictures have been subjected to various forms of image processing to reveal the tertiary rainbow as well as the quaternary rainbow.

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