https://doi.org/10.1140/epjp/s13360-023-03891-9
Regular Article
Hyperbolic caustics of light rays reflected by hyperbolic front mirrors
1
Department of Mathematics, Hacettepe University, 06800, Beytepe, Ankara, Turkey
2
Department of Mathematics, Ankara University, 06100, Beşevler, Ankara, Turkey
Received:
24
September
2022
Accepted:
12
March
2023
Published online:
23
March
2023
In plane, the caustic by reflection of a curve mirror with respect to a light source is the envelope of the rays, emitted from the light source, after reflection in the mirror. By this definition, a caustic of a curve relative to a point light source is the evolute of the orthotomic of the curve relative to the same point light source. In this paper, we generalize this definition of caustics to the hyperbolic 2-space and to front mirrors that may have singularities, and we investigate caustics of light rays on the hyperbolic 2-space reflected by hyperbolic front mirrors. For this investigation, we first introduce hyperbolic orthotomics of spacelike frontals in the hyperbolic 2-space and investigate properties of these hyperbolic orthotomics. Then, we provide some geometric properties of hyperbolic caustics in terms of hyperbolic orthotomics and front mirrors. Finally, we present local diffeomorphic images of hyperbolic caustics.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
