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Rainbow on January 23rd, 2008

On January 23d, a red rainbow fragment appeared before sunrise, soon showing one, a few minutes later even two supernumeraries. These bows were not strictly concentric, the supernumeraries seemed to bend away from the primary. Later on, fragments of the upper part of the rainbow appeared, showing up to five supernumeraries. In all these fragments the spacing between the bows increased with elevation, producing a fan-like appearance. The secondary was rather faint.

Right hand side: Dawn on January 23rd, 2008.

It should be mentioned that apparently no rain reached the ground in the whole area. The ground was frozen and covered with hoarfrost.

Close to the ground, the rainbow was rather broad. The droplets must have been very small, otherwise no supernumeraries could have been formed at the base of the rainbow. The multiple supernumeraries at the top of the bow point to a very narrow drop size distribution.

Supernumeraries can only be observed under two conditions. Either the droplets are rather small and evenly-sized. Every droplet size creates its own supernumerary. If there are many different sizes, the supernumeraries are blurred. The smaller the droplets, the larger the primary bow. The spacing between the supernumeraries increases when the droplets get smaller.

But there is another mechanism capable of creating supernumeraries. While small droplets are roughly spherical, larger raindrops become oblate spheroids. The path of the light travelling through the droplet is slightly altered. This is why flattened droplets can form supernumeraries even when the droplets are not evenly-sized. The rainbow angle increases with the flattening of the drops. For light coming from the top of the bow, the scattering plane is vertical. It is horizontal at the base of the rainbow, the cross section is a circle. This is why supernumeraries normally occur near the rainbow top.

Further reading:

Günther P. Können, Appearance of supernumeraries of the secondary rainbow in rain showers. Journal of the Optical Society of Ameria A, Vol 4, No. 5, May 1987, pp. 810 - 816.

Alistar B. Fraser, Why can the supernumerary bows be seenin a rain shower? Journal of the Optical Society of America, Vol. 73, No. 12, December 1982, pp. 1626 - 1628.

Michael Vollmer, Lichtspiele in der Luft: Atmosphärische Optik für Einsteiger, Elsevier 2006.

Rainbow fragment with two supernumeraries. Nikon D80, processed with Adobe Photoshop Elements.

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