A remarkable rainbow imaged by Denis Betsch near Strasbourg, Alsace, France. ©Denis Betsch, shown with permission
Supernumerary arcs are narrow coloured fringes sometimes seen close to the inner purple edge of a primary rainbow. One or two fringes are a common sight but this rainbow with 7-8 arcs is rare indeed.
|At left, supernumerary fringes and their primary rainbow are computed using a theory developed by British Astronomer Royal George Biddell Airy (1801-1892). His theory makes assumptions about the algebraic form of the outgoing waves from the drop. Although it is approximate it is near enough to simulate supernumeraries and far quicker then the later, fully accurate but computationally laborious Mie-Lorentz theory.
The top slice shows supernumerary fringes from a point source and monosized drops 0.7mm diameter.
The lower slice is for of the same mean size but a spread of diameters plus a 'real' sun 0.5° diameter. Both changes blur the intricate supernumerary interference structure to our eyes.