Image caption The third (l) and fourth (r) rainbows appear closer to the sun, rather than opposite it as with the first and second, which would have been behind the photographer

Scientists have captured the first image of a "quaternary" rainbow - the fourth rainbow caused by the bending of light through water in the air.

This refraction frequently creates a visible second rainbow, but until now, no-one had caught sight of the fainter third and fourth arcs that the process creates in a different part of the sky.

The first tertiary, or third, rainbow has only just been caught on film.

Digitally-enhanced pictures of the two effects appear in Applied Optics.

Unfortunately, the pictures are not as striking as more familiar images of double rainbows - and some image processing was the only way to make the arcs visible at all.

That is principally due to the fact that the tertiary and quaternary rainbows are by definition far fainter than their more familiar cousins.

What forms a normal rainbow is the collective action of rays of sunlight bending through raindrops; the constituent colours of the white light are slightly separated in the process because they travel at slightly different speeds in water.

Much of that bent and separated light then exits the drops, appearing for a given observation point to focus in an arc opposite the Sun.

However, some of the light takes another bounce within the drop, being bent at a different angle as it passes, creating the second rainbow.

Even smaller proportions make a third and a fourth bounce, and exit in a direction close to the source of the incoming light.

The rainbows that these bounces produce are the faint tertiary and quaternary arcs that, until now, have never been captured on film.

Bow hunt

A renewed hunt for the elusive rainbows started with Raymond Lee, a meteorologist at the US Naval Academy, who combed 250 years of scientific literature for the only recorded evidence of tertiary rainbows: he found just five examples.

Image caption The first photo of a tertiary rainbow still requires a close look

He studied the conditions in which those five occurred and came up with a recipe for spotting them, also published in Applied Optics.

He recommended trying to find them against dark clouds after a storm with evenly sized drops - and he challenged rainbow hunters to seek out those conditions.

Michael Grossmann of Arbeitskreis Meteore, the German association for the observation of atmospheric phenomena, went hunting for the tertiary effect in May this year, and found it after a storm in Kaempfelbach in south-western Germany.

Because the effect is so faint, a number of shots had to be taken and averaged after the fact, along with a digital enhancement known as unsharp masking, to show evidence of the tertiary rainbow.

Then in June, another rainbow hunter, Michael Theusner, caught another tertiary rainbow and its adjacent quaternary counterpart near Bremerhaven in northern Germany - after processing the images in the same way.

Unfortunately, the rare conditions that lend themselves to a nearly visible tertiary or quaternary rainbow, along with the post-production needed to make them apparent, mean that amateur skygazers are unlikely as ever to catch sight of one.

But after 250 years of scattered reports, the record finally holds a picture of them.