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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 27 — Sep. 20, 2000
  • pp: 5040–5051

Supernumerary spacing of rainbows produced by an elliptical-cross-section cylinder. I. Theory

James A. Lock  »View Author Affiliations


Applied Optics, Vol. 39, Issue 27, pp. 5040-5051 (2000)
http://dx.doi.org/10.1364/AO.39.005040


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Abstract

A sequence of rainbows is produced in light scattering by a particle of high symmetry in the short-wavelength limit, and a supernumerary interference pattern occurs to one side of each rainbow. Using both a ray-tracing procedure and the Debye-series decomposition of first-order perturbation wave theory, I examine the spacing of the supernumerary maxima and minima as a function of the cylinder rotation angle when an elliptical-cross-section cylinder is normally illuminated by a plane wave. I find that the supernumerary spacing depends sensitively on the cylinder-cross-section shape, and the spacing varies sinusoidally as a function of the cylinder rotation angle for small cylinder ellipticity. I also find that relatively large uncertainties in the supernumerary spacing affect the rainbow angle only minimally.

© 2000 Optical Society of America

OCIS Codes
(080.1510) Geometric optics : Propagation methods
(290.0290) Scattering : Scattering
(290.4020) Scattering : Mie theory

History
Original Manuscript: March 2, 2000
Revised Manuscript: June 13, 2000
Published: September 20, 2000

Citation
James A. Lock, "Supernumerary spacing of rainbows produced by an elliptical-cross-section cylinder. I. Theory," Appl. Opt. 39, 5040-5051 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-27-5040

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