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 in:Journal of the Korean Physical Society 2020, 76(4), , pp.281-285
Main Authors: Kim, KyungTae, Ee, June-Haak, Kim, Kyounghoon, Kim, U.-Rae, Lee, Jungil
Format: Article
Language:English
Subjects:
Incidence angle
Mathematical and Computational Physics
Particle and Nuclear Physics
Physics
Physics and Astronomy
Refraction
Theoretical
물리학
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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