Digital Library of Mathematical Functions
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9 Airy and Related Functions

Sidebar 9.SB1: Supernumerary Rainbows

Michael Berry
See accompanying text

The faint line below the main colored arc is a ‘supernumerary rainbow’, produced by the interference of different sun-rays traversing a raindrop and emerging in the same direction. For each color, the intensity profile across the rainbow is an Airy function. Airy invented his function in 1838 precisely to describe this phenomenon more accurately than Young had done in 1800 when pointing out that supernumerary rainbows require the wave theory of light and are impossible to explain with Newton’s picture of light as a stream of independent corpuscles. The house in the picture is Newton’s birthplace.

Photograph by Dr. Roy Bishop, Physics Department, Acadia University, Nova Scotia, Canada. See Bishop (1981). ©R. L. Bishop.