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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 12 — Dec. 1, 2012
  • pp: 2679–2687

Exact ray tracing formulas based on a nontrigonometric alternative to Snell’s law

Hassan A. Elagha  »View Author Affiliations

JOSA A, Vol. 29, Issue 12, pp. 2679-2687 (2012)

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In this work, Fermat’s principle is applied to derive a simple exact formula for refraction (reflection) in terms of the lengths of the incident and refracted rays. This formula is a nontrigonometric alternative to Snell’s law and is general for all optical surfaces. It is used to derive the paraxial optics equations in a more simple and direct way than that often used in the literature. It’s also applied to derive a new single, exact ray tracing formula for the nonparaxial refraction (reflection) at a single optical surface. The obtained formulas are used to develop a simple ray tracing procedure for meridional refraction through systems of spherical surfaces without the need to use any form of Snell’s law. Numerical examples are provided and discussed.

© 2012 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(120.5700) Instrumentation, measurement, and metrology : Reflection
(120.5710) Instrumentation, measurement, and metrology : Refraction
(080.1753) Geometric optics : Computation methods

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: September 21, 2012
Revised Manuscript: November 2, 2012
Manuscript Accepted: November 4, 2012
Published: November 29, 2012

Hassan A. Elagha, "Exact ray tracing formulas based on a nontrigonometric alternative to Snell’s law," J. Opt. Soc. Am. A 29, 2679-2687 (2012)

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