Rainbow-enhanced forward and backward glory scattering

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When the refractive index m of a sphere is such that rainbows occur in the forward or backward direction, the glory scattering becomes exceptionally strong. A number of these refractive-index values have been determined from the geometry of ray paths. A physical-optics model of the scattering leads to an a2x4/3 dependence in the scattered irradiance, where a is the radius of the sphere, and x = ka is the size parameter. Normal glory scattering gives an irradiance proportional to x. Mie theory computations illustrate the presence of rainbow glories at predicted m values and the x4/3 irradiance factor. As in normal glory scattering, the rainbow-enhanced glory light contains a strong cross-polarized component. Experiments using single glass spheres immersed in liquids show the predicted cross-polarized scattering with a sensitive dependence on m.