Angular distribution of the solid angle at a point subtended by a circular disk

Abstract

The formula to estimate the angular dependence of the solid angle at a point subtended by a circular disk in the cylindrical coordinate system is derived. This formula is integrated with respect to the polar angle to obtain expressions for numerical and analytical calculations of the solid angle values. These expressions are given as single integrated superpositions of elementary functions and as complete elliptic integrals of the first and third and third kinds. In both cases the solid angle functions depend on the disk radius, separation of the point to the plane covering the surface of the disk, lateral distance from the point to the polar axis and the angle at the point determined between the direction made by conical sheets, which cross the circular disk, and the direction parallel to the polar axis. Combining solid angle formulas with expressions for Fresnel's refraction coefficient, the angular distribution of the flux of the light emitted isotropically from a point source and transmitted through a thin circular refractive medium has been estimated. A similar consideration for the flux of the light reflected by a circular nonconductor has been also presented. Some examples of graphs are given.