ABSTRACT
Lens systems can be computed in which, by the use of different kinds of glass, the ordinary purposes of most optical instruments can be achieved by the use of spherical, or nearly spherical surfaces. It is supposed that Descartes was the first to consider what kind of surfaces would result in freedom from aberration. The method of grinding and polishing parabolic surfaces has been described by Dourneau and Demarcq. Gleichen, gives a number of interesting notes on applications of non-spherical surfaces. He showed that for parallel incident rays, aplanatic imageformation can be effected by reflection at a cardioid in conjunction with reflection at a spherical surface. When a parallel beam of light is reflected from a spherical concave mirror the rays near the axis CA are brought to a focus F at a distance from the mirror surface equal to half its radius of curvature. Ordinary reflecting telescopes therefore use paraboloidal ones to receive the parallel rays.
