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Johann Bernoulli's brachistochrone solution using Fermat's principle of least time

Herman Erlichson

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Johann Bernoulli's brachistochrone problem is now three hundred years old. Bernoulli's solution to the problem he had proposed used the optical analogy of Fermat's least-time principle. In this analogy a light ray travels between two points in a vertical plane in a medium of continuously varying index of refraction. This solution and connected material are explored in this paper.


PACS

45.10.Db Variational and optimization methods

02.30.Xx Calculus of variations

42.25.Gy Edge and boundary effects; reflection and refraction

Subjects

Mathematical physics

Computational physics

Optics, quantum optics and lasers

Dates

Issue 5 (September 1999)

Received 8 April 1999



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