Quasifocal Lines

The article proved that the highest concentration of reflected rays from the surface of the reflector is located along the quasifocal line. The quasifocal line belongs to the caustic surface of the congruence of reflected rays. The parameters of the shape and position of the quasifocal lines are described by equations. Computer visualization of reflecting surfaces, congruences of reflected rays and their caustics, quasifocal lines and maps of isolines of local concentrations on the surface of the receiver of reflected rays are presented.

Magnification Cross Sections for the Elliptic Umbilic Caustic Surface

In gravitational lensing, magnification cross sections characterize the probability that a light source will have magnification greater than some fixed value, which is useful in a variety of applications. The (area) cross section is known to scale as μ − 2 for fold caustics and μ − 2.5 for cusp caustics. We aim to extend the results to higher-order caustic singularities, focusing on the elliptic umbilic, which can be manifested in lensing systems with two or three galaxies. The elliptic umbilic has a caustic surface, and we show that the volume cross section scales as μ − 2.5 in the two-image region and μ − 2 in the four-image region, where μ is the total unsigned magnification. In both cases our results are supported both numerically and analytically.