Quasifocal Line and “Burning Curve”

  • Aleksandr Dvoretskii
  • Tetiana Denysova
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 809)


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.


Quasifocal line Burning curve Reflected surface Congruence Caustic 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Aleksandr Dvoretskii
    • 1
  • Tetiana Denysova
    • 1
  1. 1.The Crimean Federal University Named After V.I. VernadskySimferopolRussia

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