Image Formation of a Reflecting Cone for an Off-Axis Source*

Abstract

For a point source placed in front of a reflecting cone, expressions have been found for the shape of the virtual image and for the amplitude of the real-image field. Both the virtual and the real images have the same axis of symmetry, which passes through the vertex of the cone and lies in the plane containing the point source and the cone axis. The angle between the axis of symmetry and the axis of the cone is equal in magnitude but opposite in sign to the angle between the latter and the line joining the point source and the cone vertex. The projection of the virtual image onto a plane perpendicular to the axis of symmetry is an ellipse. Both the real and virtual images have two planes of symmetry that are the planes containing, respectively, the major and minor axes of the virtual image. The irradiance distribution along the axis of symmetry in the real-image field varies as the square of a Bessel function of zero order and of the first kind. The analytical expression found for the real-image field gives the expected behavior of the field when the cone becomes a plane. It also obeys the energy-conservation law.