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Why do the Supernumeraries of Secondary Rainbows Never Show up in Rainshowers?

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Abstract

At the last Topical Meeting, Fraser 1) offered an explanation for the paradoxical fact that supernumeraries of the primary rainbow are regularly visible in rainshowers, although the obvious broad droplet-size distribution should prevent such. The reason of their appearance is the flattened shape of falling drops, which causes the rainbow angle to increase with increasing (equivalent) drop-radius r, at least for solar heights h between 0 and 42°. Since therefore the positions of the Airy maxima as a function of r have a minimum, the supernumeraries still show up in rainshowers. However, the angular spacing between then contains hardly information about the drop-sizes in the showers any more, as they are determined by the places of these minima: if the drop-size distribution is broad enough, the separation between the first and second supernumerary is fixed at 0.7°.

© 1986 Optical Society of America

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