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Fog bows and cloud bows
As no two trees are alike, so one rainbow differs from another. The greatest contrast exists between a magnificently coloured rainbow, as seen in a passing shower, and the dull white fog-bow, which is formed in minute drops of water.
The outward appearance of the rainbow changes as the drops of water become smaller and this can easily be established with a flower-syringe. The colours begin to overlap each other and the bow turns whitish with only a faint colouration along the edge. Its radius somewhat decreases and the supernumerary bows are farther away from the bow. It is usually more difficult to see secondary rainbows. Very small drops, as occur for instance in clouds, show the rainbow only as a slightly intensified brightness of the light at about 145º from the sun; the colours have completely disappeared. Only an experienced observer is able to establish the presence of the bow in clouds (photo 1).
photo 1: The extra brightness of the clouds in the centre of the photo is the result of
rainbow-scattering (by G.P. Können)
The tangential polarization of this cloud-bow is, however, still present, although it is somewhat weaker than in the case of big drops. The cloud-bow betrays its presence by this polarization: with a polarizing filter we can see that the-light of sunlit water-clouds at about 145º from the sun is Polarized to an abnormally high degree, certainly in comparison with ice-clouds! So, with the aid of a polarizing filter, everybody can easily observe the cloud-bow. Strange to relate, rainbows can be seen almost every day, though merely in the form of the inconspicuous cloud-bow.
fog bow (UK Crown Copyright)
In fog, the shape of the bow usually remains more easily recognizable, even frequently showing some red colourization at its outer edge so that without the aid of a polarizing filter the fog-bow can easily be found. It can also be observed in the steam of a bathroom shower when a thin ray of sunlight enters the room. Then, the bow is seen as a 'thickening' of this ray of light, which means a greater local brightness.
If the Tangential ly polarized fog-bow appears, the Radial ly polarized rings of the glory are usually visible near the observer's shadow. In Nature or in the bathroom, the simultaneous appearance of these oppositely polarized phenomena yields interesting observations.
source: Polarized light in Nature