Mechanical Snell’s Law

We investigate the motion of a massive particle constrained to move along a path consisting of two line segments on a vertical plane under an arbitrary conservative force. By fixing the starting and end points of the track and varying the vertex horizontally, we find the least-time path. We define t...

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Bibliographic Details
Published inJournal of the Korean Physical Society Vol. 76; no. 4; pp. 281 - 285
Main Authors Kim, KyungTae, Ee, June-Haak, Kim, Kyounghoon, Kim, U.-Rae, Lee, Jungil
Format Journal Article
LanguageEnglish
Published Seoul The Korean Physical Society 01.02.2020
Springer Nature B.V
한국물리학회
Subjects
Incidence angle
Mathematical and Computational Physics
Particle and Nuclear Physics
Physics
Physics and Astronomy
Refraction
Theoretical
물리학
Snell’s law
Mechanical index of refraction
Least-time path
Brachistochrone curve
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Summary:We investigate the motion of a massive particle constrained to move along a path consisting of two line segments on a vertical plane under an arbitrary conservative force. By fixing the starting and end points of the track and varying the vertex horizontally, we find the least-time path. We define the angles of incidence and refraction similar to the refraction of a light ray. It is remarkable that the ratio of the sines of these angles is identical to the ratio of the average speeds on the two partial paths as long as the horizontal component of the conservative force vanishes.
ISSN:0374-4884
1976-8524
DOI:10.3938/jkps.76.281