CAUSTIC SURFACES ACCOMPANYING THE REFLECTION OF HOMOCENTRIC PENCILS OF RAYS BY A SPHERE

This paper presents the results of theoretical studies of caustic surf aces. The equations of the caustics are obtained for the cases of refl ection of homocentric pencils of rays with an arbitrary location of th e source relative to a spherical reflector. It is established that, wh en the source is placed at infinity or on the surface of the sphere, t he parametric equation of the caustic curve turns into the equation of an ordinary epicycloid. It is proven that the involutes of the causti c curve are in phase with the lines of the radiation of a point source after reflection. A kinematic method is proposed for deriving the equ ations of the caustics. (C) 1998 The Optical Society of America.