Thus, for a 1-inch sphere (R = 0.5 inch) and a reflection of the Sun (f = 0.5° = 0.0087 radians), a reflection angle (6r) of 90° yields a glitter point 0.003 inches long. Thus, for a typical 6r, the gleam of a solar reflection will be smaller than 7300 the diameter of the sphere.
Similarly, we can obtain an expression for the short axis (v) of the bean. This dimension is obtained by perturbing Fig. F-1c around the average re-
Fig. F-1. The variables used to determine the size of the glitter reflected in a sphere.
flection angle, u = R
For the example situation, u is 0.0015 inch. The glitter point is about twice as wide as it is long.
For a nearly centered bounce with the gleam appearing near the middle of the sphere ( 6r = 0) and for a very small source angle (f, the expression for u is approximately
If we want to figure the size of the round gleam where the 1-inch reflective sphere is placed opposite to the Sun, we could use this approximation. The numbers are inserted this way (the angle must be in pure number format, i.e., radians):
The glitter size shrinks to about 1/450 the diameter of the sphere at its smallest aspect. The source of light is nearly behind the viewer's head and the reflection is approximately centered in the shiny sphere for this favorable condition to occur.
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