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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • 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)
http://dx.doi.org/10.1364/JOSAA.29.002679


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Abstract

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

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

Citation
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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-12-2679


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References

  1. R. P. Feynman, R. B. Leighton, and M. L. Sands, “Optics: the principle of least time,” in The Feynman Lectures on Physics(Addison Wesley Longman, 1970), Vol. 1, Chap. 26.
  2. F. L. Pedrotti and L. S. Pedrotti, “Geometrical optics,” in Introduction to Optics (Prentice-Hall, 1993), pp. 34–36.
  3. P. Mouroulis and J. Macdonald, “Rays and foundations of geometrical optics,” in Geometrical Optics and Optical Design (Oxford University, 1997), pp. 11–13.
  4. R. Kingslake and R. B. Johnson, “Meridional ray tracing,” in Lens Design Fundamentals (Academic, 2010), pp. 25–45.
  5. D. Malacara and Z. Malacara, Handbook of Optical Design(Marcel Dekker, 2004).
  6. W. J. Smith, “Optical computation,” in Modern Optical Engineering (McGraw-Hill, 1990), pp. 308–404.
  7. J. E. Harvey, “Exact ray trace procedure,” http://ebookbrowse.com/3-5-exact-ray-trace-procedure-pdf-d354859582 .

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