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Rainbows from inhomogeneous transparent spheres: a ray-theoretic approach

Summary: Rainbows from inhomogeneous transparent spheres:
a ray-theoretic approach
John A. Adam and Philip Laven
A ray-theoretic account of the passage of light through a radially inhomogeneous transparent sphere has
been used to establish the existence of multiple primary rainbows for some refractive index profiles. The
existence of such additional bows is a consequence of a sufficiently attractive potential in the interior of
the drop, i.e., the refractive index gradient should be sufficiently negative there. The profiles for which
this gradient is monotonically increasing do not result in this phenomenon, but nonmonotone profiles can
do so, depending on the form of n. Sufficiently oscillatory profiles can lead to apparently singular behavior
in the deviation angle (within the geometrical optics approximation) as well as multiple rainbows. These
results also apply to systems with circular cylindrical cross sections, and may be of value in the field of
rainbow refractometry. 2007 Optical Society of America
OCIS codes: 080.2710, 080.0080.
1. Introduction
This paper uses geometrical optics to analyze the
scattering of light by inhomogeneous spheres in
which the refractive index is a function of the radius
only. The results may be of value in the field of rain-
bow refractometry and thermometry, which are opti-
cal techniques used to measure the refractive index


Source: Adam, John A. - Department of Mathematics and Statistics, Old Dominion University


Collections: Mathematics