Quasifocal Line and 'Burning Curve'

摘要

The caustic curve as a "burning curve" corresponds to its name only for a planar problem (2D). This is observed in flat sections of the congruence of reflected and refracted rays, when the normals to the surface lie in the cutting plane. For the congruence of reflected rays, i.e. for the 3D problem, the zone of maximum concentration is the quasifocal line. The surface of the caustic is the focal surface of the reflected ray congruence, but is not a zone of maximum concentration. To investigate the reflecting properties of surfaces of revolution, the congruence of reflected rays is stratified into a one-parameter set of reflected surfaces. It is proved that the quasifocal line remains an invariant of the reflecting surface for any stratification of the reflected ray congruence. The search of a zone of the greatest concentration of the rays, reflected by the surface has practical interest and can be used in designing solar installations for converting solar energy into thermal or electrical energy, in construction of reflecting surface of lamps and also in the designing the interior and exterior of buildings. That is why the quasifocal line theory will be proposed.