The above picture appears in Scrambles amongst the Alps by the English mountaineer Edward Whymper. It portrays a phenomenon that appeared during the first ascent of the Matterhorn above Zermatt, Switzerland, on July 14, 1865. It was seen soon after an accident when a rope broke and four members of the party fell to their deaths down the north face of the mountain. Only Whymper and his two Swiss mountain guides survived.

The tragedy caused quite a stir at the time: with the deaths of Lord Francis Douglas and the Rev Charles Hudson, The Times published a leader condemning mountaineering and Queen Victoria wondered about prohibiting it.

This is how Whymper described the apparition: “A mighty arch appeared, rising high into the sky, pale colourless, and noiseless, but perfectly sharp and defined, except where it was lost in the clouds, we watched with amazement the development of two vast crosses, one on either side.”

The climbers had their backs to the sun and there are several optical effects that can appear from this angle. The most familiar is the rainbow.

Rainbows are formed from the refraction and reflection of light through water droplets in rain. But the bow Whymper saw was colourless and it wasn’t raining. However, there was a mist below the men.

Some accounts refer to the apparition as a Brocken spectre, named after the Brocken, a mountain in Germany frequently shrouded in mist. This spectre forms when the observer’s shadow is cast on to the mist. Coloured rings called glories often form around the shadow’s head. Glories are much smaller than rainbows and form quite differently. They result from different parts of the light wave reflected back from individual water droplets in the mist interfering with each other: each colour forms a different ring size. This interference also accounts for the iridescent effect when looking at soap bubbles. Glories are not unusual in high mountains but this phenomenon is not compatible with Whymper’s description of a colourless and mighty arch.

Whymper himself claimed that what he saw was a form of fogbow, similar to a rainbow except that, with the much smaller water droplets held in mist, interference effects become significant. The individual coloured arcs making up the rainbow become broader and overlap, mixing up the colours so the bow becomes white.

What about the crosses? It is possible that Whymper exaggerated the story; in later correspondence the younger of the two guides claimed not to have seen the crosses. However, this would be out of character as Whymper was an engraver and his woodcuts and observations were usually accurate.

The apparition may have derived from a combination of a fogbow and haloes.

Haloes are generally white but are sometimes coloured; they are formed by the refraction and reflection of light through ice crystals in the atmosphere at cold temperatures.

Cirrus clouds, for example, consist of ice crystals. Sometimes the crystals form as flat hexagonal plates. These plates can become horizontal as they fall through the air, just as falling leaves do. Such aligned crystals give the most common halo effect: sun rays are refracted through two sides of the hexagons to give bright red and yellow patches of light, known as parhelia, on either side of the sun.

However, to give the Whymper effect, we need the haloes to appear opposite the sun, which requires some of the light to be reflected from the crystal faces too. Scientists used HaloSim3 software developed by Cowley and Schroeder (www.sundog.clara.co.ukatopticsphenom.htm) to produce simulations of what may have occurred. This allows us to track many sun rays through different types and orientations of ice crystals and simulate what kind of haloes would appear. As they fall through the air, ice crystals consisting of thin hexagonal cylinders tend to align with their axes horizontal: these give the central cross. To produce the side crosses which Whymper saw, some of these crystals need to be capped with pyramids and two opposite faces of the hexagonal cylinder aligned vertically. This alignment may seem unlikely ever to appear, but a similar alignment of hexagonal cylinders with two opposite faces horizontal explains some features of a halo observed by Captain WE Parry in 1820, during his search for the North West Passage.

John Hardwick is a physicist and manager of the lightning division of Culham Electromagnetics and Lightning. The December 2002 issue of Weather, the journal of the Royal Meteorological Society, includes an article by the author