## Abstract

Glare points associated with the Airy caustics of once and twice
internally reflected rays are visible in the scattering by sunlit
icicles. Supporting color photographs include an image of the
far-field scattering. Relevant rays are analogous to the Descartes
rays of primary and secondary rainbows of drops; however, the caustic
conditions for the icicle are predicted to be affected by tilt of the
illumination relative to the axis of the icicle. A model for the
caustic evolution, given for a circular dielectric cylinder, manifests
a transition in which the Airy caustic (and associated glare
points) merge in the meridional plane at a critical tilt. At this
critical tilt the merged glare point is predicted to be very
bright. The calculations use the Bravais effective refractive index
and generalized ray tracing.

© 1998 Optical Society of America

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### Equations (10)

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(1)
$$n\prime \left(\mathrm{\gamma},n\right)={\left({n}^{2}-{sin}^{2}\mathrm{\gamma}\right)}^{1/2}/cos\mathrm{\gamma}\ge n.$$
(2)
$$n\prime sin\mathrm{\varphi}\prime =sin\mathrm{\varphi},$$
(3)
$$\mathrm{\theta}=180\xb0m\pm 2\left(\mathrm{\varphi}-p\mathrm{\varphi}\prime \right),0\le \mathrm{\theta}\le 180\xb0,$$
(4)
$${cos}^{2}{\mathrm{\varphi}}_{D}=\left(n{\prime}^{2}-1\right)/\left[\left(p-1\right)\left(p+1\right)\right].$$
(5)
$${\mathrm{\rho}}_{f}=a{cos}^{2}\mathrm{\varphi}\prime /\left(cos\mathrm{\varphi}\prime -n{\prime}^{-1}cos\mathrm{\varphi}\right).$$
(6)
$$h=2acos\mathrm{\varphi}\prime .$$
(7)
$${\mathrm{\gamma}}_{c}=\mathrm{arccos}\left\{{\left[\left({n}^{2}-1\right)/3\right]}^{1/2}\right\},$$
(8)
$$d=\frac{2a}{cosr}=\frac{2\mathit{na}}{{\left({n}^{2}-{sin}^{2}{\mathrm{\gamma}}_{c}\right)}^{1/2}}.$$
(9)
$${\left({\mathrm{\rho}}_{p}\prime \right)}^{-1}=\left(cosr-{n}^{-1}cos{\mathrm{\gamma}}_{c}\right)/a.$$
(10)
$${\left(180\xb0-{\mathrm{\theta}}_{D}\right)}^{2}=D{\left({\mathrm{\gamma}}_{c}-\mathrm{\gamma}\right)}^{3},$$