Secondary rainbow

Rainbows may be seen during showers when the sun is behind the observer the direction of the sunlight determines the forward direction (or line of sight). The angular positions of the primary and secondary rainbows relative to the observer s line of sight are 180° — 137.9° = 42.1° and 180° — 129.1° = 50.9°, respectively. The fraction of the total rainbow that can be seen depends on the solar elevation. When the sun is greater than about 51° above the horizon, no rainbow can be seen even though conditions are otherwise favorable. On the other hand, the complete rainbow—one that forms a complete circle—may be seen from an airplane. 

Were it not for dispersion—the refractive index depends upon wavelength— the aesthetic appeal of rainbows would be greatly diminished. Indeed, the word rainbow used in everyday speech evokes images of a profusion of colors—the colors of the rainbow—rather than just an intensely bright arc in the sky. If we take m = 1.343 as the refractive index of violet light (X — 0.4 jam) and m = 1.331 as the refractive index of red light (X = 0.65 jam) (Irvine and Pollack, 1968), then the angular widths of the primary and secondary rainbows are about 1.7° and 3.1°, respectively. 

Furthermore, if one repeats this analysis for light rays which enter the lower half of the sphere and are reflected not once, but twice before emerging, one finds a maximum deflection angle of 129.08°. These angles are in excellent agreement with the angles at which the primary and secondary rainbows are observed. 

Handy, R. D. and Eddy, F. B. (1991). The absence of mucus on the secondary lamellae of unstressed rainbow trout, Oncorhynchus mykiss (Walbum), J. Fish Biol., 38, 153-155. 

In the region of backscatter the intensity of secondary refraction is only dominant in a narrow range above the Rainbow angle for perpendicular polarization. The optimum location of the receiving optics however strongly... 

Descartes analysis was a remarkable feat, but was deficient in two main respects. It said nothing about the colors of the rainbow nor about the supernumerary rainbows which sometimes appear faintly in the interior of the primary bow and on the exterior of the secondary bow. Newton resolved the problem of the colors,but the supernumerary rainbows are a wave interference effect and their explanation came more than 100 years later. 

RAIDA MK, BUCHMANN K. Innate immune response in rainbow trout Oncorhynchus mykiss) against primary and secondary infections with Yersinia ruckeri Ol. Dev Comp Immunol 2009,33,35-45. 

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