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Rainbows and Supernumerary Arcs

Date:Aug.,1989 Instrument:f=135mm
Place:BC/Canada Observer:S. Kohle

© Copyright by the observers

The image above shows a complex rainbow phenomenon including the primary and the secondary bow, as well as supernumerary arcs, which are located immediately below the blue edge of the primary bow.
Both, the primary and the secondary bow with its inverted colour-sequence, can be understood with classical optics, i.e. deflection and refraction of sunrays through water droplets. The rays which experience one deflection inside the droplet form the primary rainbow. Those which are deflected twice (which amounts only to about 10 percent of the total light) form the fainter secondary bow. The rays forming the primary bow have a minimum deviation of 138 - 140 degrees from their initial direction, depending on their wavelength: blue light is refracted more than red light. Measured from the virtual center of the rainbow the observer sees the blue edge of the primary bow on its inner side.

For the explanation of the supernumerary arcs, the principals of classical optics fail. The occurance of minima and maxima in the light distribution can be explained by interfering rays which experience a difference in the length of their paths while passing through the water droplet. Those rays which differ by half of their wavelengths interfer destructively and lead to the minima of light between the supernumerary arcs. However, also effects of polarization of deflected rays, sizes and oscillations of the water droplets have to be taken into account to properly model the supernumerary arcs.

More detailed information about rainbows can be found here.

See also:
M.G.J. Minnaert: "Light and Color in the Outdoors", Springer-Verlag
Nussenzveig H. M.: "The Theory of the Rainbow" in: Light from the Sky, Scientific American, 1977