Exact Result for the Grazing Angle of Specular Reflection from a Sphere
Abstract
The present paper shows that it is possible to exhibit the grazing angle of specular reflection as one of four angles derived from the zeros of a certain self-inversive quartic polynomial whose coefficients are complex. Thus the grazing angle may now be found deterministically, whereas heretofore it had to be computed either by approximations or numerical procedures. The preceeding analysis shows further that factoring, in a useful way, a quartic polynomial whose complex coefficients depend on even a small number of parameters, is not always a trivial matter, even though the methods of Cardan and Ferrari have been known for centuries.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 09, 1991
- Accession Number
- ADA239578
Entities
People
- Allen R Miller
- Emanuel Vegh
Organizations
- United States Naval Research Laboratory