Glitter in a Shiny Sphere

Figure F-1a shows a reflection in a small sphere. In its most general form, it is roughly shaped like a kidney bean, longer in the azimuthal direction than in the radial direction. Since the long axis of the bean is the limiting factor, an expression for this angle is derived first.

We wish to calculate u, the long axis of the glitter. If the glitter is far enough from the center, its approximate length is given by u/2 (fj

with x being the radius of the circle containing the glitter seen in perspective and ( being the angle of the source of light. If we turn the sphere to view the situation from the side (Fig. F-1c), the radius x is obtained from the great circle radius of the sphere R and the light diversion angle dr as in

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