Effects of sherically-symmetric gravitational lenses produced by galaxies and clusters

Images are considered which are produced by a spherically symmetric gravitational lens from a source of small angular size. Simple analytic expressions are derived to describe the position, amplification, shape distortion and time delay for these images provided the mass distribution of the lens corresponds to the King model. Possible types of images are analysed (single and triple images, as well as degenerate double ones at caustics) which may be formed at different positions of the observer relative to the light source and lens. The focal length of galaxies of different types is evaluated on the basis of the obtained results and the conditions are determined at which these galaxies may considerably affect the images of distant sources.