Hyperbolic caustics of light rays reflected by hyperbolic front mirrors

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 rel...

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Bibliographic Details
Published in:European physical journal plus 2023-03, Vol.138 (3), p.266, Article 266
Main Authors: Tuncer, O. Oğulcan, Gök, İsmail
Format: Article
Language:English
Subjects:
Alkalies
Applied and Technical Physics
Atomic
Complex Systems
Condensed Matter Physics
Light
Light reflection
Light sources
Mathematical and Computational Physics
Mirrors
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Theoretical
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Summary: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.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-023-03891-9