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1: Sidebar 9.SB1: Supernumerary Rainbows
Sidebar 9.SB1: Supernumerary Rainbows
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. …
2: 9.16 Physical Applications
The use of Airy function and related uniform asymptotic techniques to calculate amplitudes of polarized rainbows can be found in Nussenzveig (1992) and Adam (2002). … In the case of the rainbow, the scattering amplitude is expressed in terms of Ai ( x ) , the analysis being similar to that given originally by Airy (1838) for the corresponding problem in optics. …
3: 36.14 Other Physical Applications
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4: About Color Map
To provide an easily interpreted encoding of surface heights, a rainbow-like mapping of height to color is used. …
5: Bibliography B
  • M. V. Berry (1966) Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.
  • M. V. Berry (1975) Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces. J. Phys. A 8 (4), pp. 566–584.
  • R. L. Bishop (1981) Rainbow over Woolsthorpe Manor. Notes and Records Roy. Soc. London 36 (1), pp. 3–11 (1 plate).
  • 6: Bibliography
  • J. A. Adam (2002) The mathematical physics of rainbows and glories. Phys. Rep. 356 (4-5), pp. 229–365 (English).
  • 7: Bibliography M
  • P. L. Marston (1999) Catastrophe optics of spheroidal drops and generalized rainbows. J. Quantit. Spec. and Rad. Trans. 63, pp. 341–351.