{"title":"Refractive index for the mechanical refraction of a relativistic particle","authors":"Bikram Keshari Behera, Surendra Kumar Gour, Shyamal Biswas","doi":"10.1140/epjd/s10053-024-00849-z","DOIUrl":null,"url":null,"abstract":"<p>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.</p><p>Mechanical refraction from medium-1 to medium-2 for <span>\\(U2>U1\\)</span></p>","PeriodicalId":789,"journal":{"name":"The European Physical Journal D","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal D","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjd/s10053-024-00849-z","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
Mechanical refraction from medium-1 to medium-2 for \(U2>U1\)
期刊介绍：
The European Physical Journal D (EPJ D) presents new and original research results in:
Atomic Physics;
Molecular Physics and Chemical Physics;
Atomic and Molecular Collisions;
Clusters and Nanostructures;
Plasma Physics;
Laser Cooling and Quantum Gas;
Nonlinear Dynamics;
Optical Physics;
Quantum Optics and Quantum Information;
Ultraintense and Ultrashort Laser Fields.
The range of topics covered in these areas is extensive, from Molecular Interaction and Reactivity to Spectroscopy and Thermodynamics of Clusters, from Atomic Optics to Bose-Einstein Condensation to Femtochemistry.
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