|Geometry in the Skies imaged by Måns Hagberg August 13, 2008, Gärdhem, Trollhättan, Sweden.
©Måns Hagberg, shown with permission.
A single reflection inside spherical raindrops produces the inner primary bow. Although rainbows look bright, the process is not very efficient and most sunlight passes through the drops without being reflected. The 5% or so that is reflected once gets deviated 140° and more to form the bright edged rainbow disk of 42° radius.
Two internal reflections deflect sunlight through 231° and more to form lighter sky with a bright edged hole of 51° radius at its center - the secondary rainbow. More than two reflections?
Geometry does not completely rule. The coloured fringes, supernumerary bows, cannot be explained by geometric optics.