Image formation with a concave spherical mirror

The author presents an elementary theory of image formation by a concave spherical mirror, elaborated for arbitrary angles of incidence and wide beams of rays. The image formation of a point source is either real, virtual or mixed according to the position of the source with respect to the mirror. If the ratio of the diameter of the mirror to its radius is at least 2∶3, the mirror does not provide virtual image formation. Point sources, the image formation of which is virtual (or mixed), form regions definable by simple constructions. At large angles of incidence it can happen that after reflection from the mirror the rays fall on the same mirror. A confuse image is produced. Some results on image formation with a concave spherical mirror can be extended to cylindrical and rotational surfaces with general meridian curves. Some formulae are derived for tangential image formation with a mirror having a parabolic meridian.