Secondary Supernumeraries
By Tym Altman (images, rainbow) at Vancouver, Canada.   At right an Intense primary from one reflection inside the raindrops. At left, the fainter reversed colour secondary from two reflections. At further left a very rare sight indeed - the purple bands of supernumeraries from the secondary bow. ©Tym Altman, shown with permission

Primary supernumeraries, purple and green arcs inside the rainbow are a common sight whenever raindrops are small as towards the end of a shower. Those outside the secondary bow are almost never seen except when manufactured by hosepipes and lawn sprinklers.

Interestingly, there are only faint traces of a supernumerary inside this primary rainbow. The visibility, or not, of supernumeraries depends critically on the local concentration, raindrop size and raindrop size distribution. These can change quickly.

Right: Supernumeraries as we never see them - from a sun shrunk to a point to avoid blurring and raindrops all 0.75mm diameter. A calculation by AirySim.

Above: Primary supernumerary formation, ones outside the secondary bow are made in the same way.

A any point of a rainbow two classical ray paths contribute the light. But light is a wave phenomenon and the wave crests of the two emerging waves can coincide or otherwise be out of phase depending on the viewing angle. When the crests coincide there is a bright arc, a supernumerary bow.

Whether the supernumeraries are visible depends on the drop size, small drops have more widely spaced supernumeraries, and the drop size distribution - wide distributions blur out the supernumeraries.

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