https://doi.org/10.1140/epjd/s10053-024-00849-z
Regular Article - Optical Phenomena and Photonics
Refractive index for the mechanical refraction of a relativistic particle
1
School of Physics, University of Hyderabad, C.R. Rao Road, 500046, Gachibowli, Hyderabad, India
2
Department of Physics, Indian Institute of Technology Guwahati, 781039, Guwahati, Assam, India
Received:
2
January
2024
Accepted:
15
April
2024
Published online:
17
May
2024
We have analytically determined the refractive index for the mechanical refraction of a relativistic particle for its all possible speeds. We have critically analysed the importance of Descartes’ metaphysical theory and extended it in this regard. We have considered the conservation of the tangential component of the relativistic momentum and the relativistic energy of the particle in the process of the mechanical refraction within the optical-mechanical analogy. Our result for the mechanical refractive index exactly matches with the forms of both the Fermat’s result on Snell’s law of optical refraction at the ultra-relativistic limit and the Descartes’ metaphysical result on the pseudo-Snell law of optical refraction at the non-relativistic limit.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
