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I don't think the second bow is a supernumerary. As Harald Edens
has already mentioned, a supernumerary (interference) bow so well
separated from the primary requires very small droplets and it would
have very pale colours. It would be, or almost be, a fogbow. Take a
look at http://www.sundog.clara.co.uk/droplets/fogdrpsz.htm for the
way supernumerary bows widen and separate as the drop size gets
smaller.
The double bows could be produced by mixtures of different water drop
*shapes*. Namely, small round drops and large oval or oblate ones.
It's
the shapes that matter, not the sizes except that surface tension holds
smaller droplets much more tightly spherical. Harald has explained how
they might occur in storms. Only geometric optics is needed, no
diffraction
effects have to be invoked.
To get distinct double bows requires that there be two distinct shapes
of drop. A mixture of many drop shapes would merely produce a
whitish mush - i.e. no rainbow! Perhaps that is why doubles are
rare.
The attached simulation is for a 50/50 mixture of spherical drops and
oblate
ones which departed from sphericity by only 2.5%. Even this small
departure
makes well separated bows. The non-sphericity of the photographed bows
must have been even smaller.
The simulation traced 15 million rays through the drops using program
developed by Michael Schroeder and myself. It's a bit rough and ready
because there wasn't time this morning to trace more rays. And of course
it doesn't rule out other ways of making a double bow!
Les Cowley
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