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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 34 — Dec. 1, 2008
  • pp: H11–H13

Geometric optics and rainbows: generalization of a result by Huygens

John A. Adam  »View Author Affiliations

Applied Optics, Vol. 47, Issue 34, pp. H11-H13 (2008)

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In 1652 Huygens derived a formula specifying the rainbow angle for the primary bow ( k = 1 ) in terms of the refractive index only. A generalization of this result for any k 1 is outlined, along with an alternative representation. The details of the derivation can be found in (Adam, Mathematics Magazine, 2008, under review), but the results as stated may be of interest to the atmospheric optics community.

© 2008 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.3870) General : Mathematics
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(080.2720) Geometric optics : Mathematical methods (general)

Original Manuscript: February 21, 2008
Revised Manuscript: April 11, 2008
Manuscript Accepted: May 9, 2008
Published: June 4, 2008

John A. Adam, "Geometric optics and rainbows: generalization of a result by Huygens," Appl. Opt. 47, H11-H13 (2008)

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  1. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge University Press, 1992). [CrossRef]
  2. J. A. Adam, “Noah's Arc: Asine in the Sky,” Mathematics Magazine (under review) (2008).
  3. See http://en.wikiversity.org/wiki/Waves_in_composites_and_metamaterials/Rainbows
  4. R. T. Wang and H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106-117(1991). [CrossRef] [PubMed]
  5. M. Vollmer, Lichtspiele in der Luft: Atmosphärische Optik für Einsteiger, (Elsevier, Spektrum Akademischer Verlag, 2006), Chap. 5, pp. 121-122.
  6. W. E. Weisstein, “Multiple-angle formulas,” from MathWorld--a Wolfram Web Resource . http://mathworld.wolfram.com/Multiple-AngleFormulas.html

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