## Supernumerary Spacing of Rainbows Produced by an Elliptical-Cross-Section Cylinder. I. Theory

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

**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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