Previous article Next article Exact Result for the Grazing Angle of Specular Reflection from a SphereAllen R. Miller and Emanuel VeghAllen R. Miller and Emanuel Veghhttps://doi.org/10.1137/1035091PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractAn exact formula is given for the grazing angle of specular reflection from a sphere by displaying the zeros of a certain self-inversive quartic polynomial.[1] W. T. Fishback, Simplified methods of field intensity calculations in the interface region, Report, 461, MIT Radiation Laboratory, 1943, Dec. Google Scholar[2] D. E. Kerr, Propagation of Short Radio Waves, McGraw-Hill, New York, 1951 Google Scholar[3] L. V. Blake, Radar Range-Performance Analysis, Lexington Books, Lexington, MA, 1980 Google Scholar[4] M. I. Skolnik, Radar Handbook, McGraw-Hill, New York, 1990 Google Scholar[5] A. R. Miller, , R. M. Brown and , E. Vegh, New derivation for the rough surface reflection coefficient and for the distribution of sea wave elevations, IEE Proc. Pt. H, 131 (1984), 114–116 Google Scholar[6] A. R. Miller and , E. Vegh, Family of curves for the rough surface reflection coefficient, IEE Proc. Pt. H, 133 (1986), 483–489 Google Scholar[7] A. R. Miller and , E. Vegh, Comparison of the rough surface reflection coefficient with specularly scattered acoustic data, J. Acoust. Soc. Amer., 82 (1987), 1836–1838 CrossrefISIGoogle Scholar[8] A. R. Miller and , E. Vegh, Computing the grazing angle of specular reflection, Internat. J. Math. Ed. Sci. Tech., 21 (1990), 271–274 CrossrefGoogle Scholar[9] D. Secrest, Problem 6602: Roots on the unit circle, Amer. Math. Monthly, 98 (1991), 176–177 CrossrefISIGoogle Scholar[10] S. Borofsky, Elementary Theory of Equations, Macmillan, New York, 1950 0041.35701 Google ScholarKeywordsself-inversive polynomialsroots of quarticsspecular reflection Previous article Next article FiguresRelatedReferencesCited ByDetails The Ptolemy–Alhazen Problem and Spherical Mirror ReflectionComputational Methods and Function Theory, Vol. 19, No. 1 | 15 December 2018 Cross Ref Improving quantum sensing efficiency with virtual modes12 May 2016 Cross Ref Volume 35, Issue 3| 1993SIAM Review359-550 History Submitted:07 November 1991Accepted:23 October 1992Published online:12 July 2006 InformationCopyright © 1993 Society for Industrial and Applied MathematicsKeywordsself-inversive polynomialsroots of quarticsspecular reflectionMSC codes30C15PDF Download Article & Publication DataArticle DOI:10.1137/1035091Article page range:pp. 472-480ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics