Exact result for the grazing angle of specular reflection from a sphere. (English) Zbl 0783.30005

The determination of the specular angle is an important consideration in the design of radar by ray tracing methods. This angle is easily determined for a flat surface. However, the problem is more difficult for a sphere where numerical procedures exist – but no exact formula was known. The authors derive an exact formula for spherical specular reflection by displaying the grazing angle as one of four roots of a self-inversive quartic polynomial that arises from the geometry of the reflection.


30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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