Fermat’s Principle

  • Vasudevan Lakshminarayanan
  • Ajoy K. Ghatak
  • K. Thyagarajan


As mentioned in chapter 1, optics and mechanics have a number of analogies which have been used time and again to understand and appreciate concepts in either of the fields. One of the most basic analogy is between the Fermat’s principle in optics and the Hamilton’s principle of least action in classical mechanics [1]. As in classical mechanics, we can use either the Lagrangian or the Hamiltonian formulations to further study properties of light ray propagation. We will first develop the Lagrangian formulation which will be followed by the Hamiltonian formulation.


Optical Element Road Surface Hamiltonian Formulation Delay Function Basic Analogy 
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    H. Goldstein, Classical Mechanics, Chapter 2 and Appendix A.Google Scholar
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    C. Lanczos, The Variational Principle of Mechanics, Dover, New York, 1970, Chapter X.Google Scholar
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    R.J. Pegis, The modern development of Hamiltonian Optics, in Progress in Optics (Ed. E. Wolf) Vol. I, North Holland Pub. Co., Amsterdam, (1961).Google Scholar
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    S. Allen, The Gaussian formula and the elusive fourth principal ray, Am. J. Phys. 60 (1992) 160–163. See also D simmons, Perfer Form, Princeton University Press, Princeton, NJ (1996) for a detailed derivation.ADSCrossRefGoogle Scholar
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    M.G.J. Minnaert, Light and color in the outdoors, Springer-Verlag, New York, (1993). Chapter 4 discusses the effects of curvature of light rays in the atmosphere.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Vasudevan Lakshminarayanan
    • 1
  • Ajoy K. Ghatak
    • 2
  • K. Thyagarajan
    • 2
  1. 1.University of Missouri-St. LouisSt. LouisUSA
  2. 2.Indian Institute of TechnologyNew DelhiIndia

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