Properties of caustics from conic reflectors 1: Meridional rays

General relations for the caustic surfaces obtained by illuminating an ellipsoid, paraboloid, or hyperboloid reflector by a point-light source, lying along the principal axis of the reflector, were derived. A thorough study of the evolution of caustics with the particular type of reflector, as well as with the relative position of the point-light source and the reflector, was undertaken. Interesting laws for the shape, position, and properties of the caustics were derived, depending on the shape of the particular reflector used, its aperture, and the relative position of the light source and the reflector. These properties may be useful for the creation of wide angle all-reflective multimirror systems designed for definite limits of distances and which, by adjacent pairs of reflectors, present only a limited and reduced amount of third-order aberrations.