Skip to main content

Ray Tracing Gradient Index Lenses

  • Conference paper
Book cover Scientific Visualization of Physical Phenomena

Abstract

The trajectories of light rays are studied in media in which the refractive index varies with position. These are known as gradient index media, and the equation of motion of light rays through such media can be written in the same form as Newton’s law of motion for a particle moving in a conservative force field. We present ray traced images of two families of gradient index lenses: Luneberg Lenses and gradient index rod lenses. The equation of motion of light rays through the lenses are either solved exactly, or solved accurately by numerical means. Ray tracing is an important tool for visualizing the optical properties of such lenses and other gradient index media.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Berger M, Trout T, Levit N (1990) Ray Tracing Mirages. IEEE Comp. Graph, and Appi., May, 1990 36–41

    Google Scholar 

  • Born M, Wolf E (1980) Principles of Optics, 6th ed. Pergamon, Oxford, pp 101–132

    Google Scholar 

  • Evans J (1990) Simple forms for equations of rays in gradient-index lenses. Am. J. Phys., 58: 773–778

    Article  Google Scholar 

  • Evans J, Rosenquist M (1985) F = ma optics. Am. J. Phys., 54: 876–883

    Article  Google Scholar 

  • Getto P H, Breen D (1990) An Object Oriented Architecture for Computer Animation System. Visual Computer 6: 79–92.

    Article  Google Scholar 

  • Halliday D, Resnick R (1978), Physics 4th ed., ( John Wiley & Sons, New York ), pp. 972–973.

    Google Scholar 

  • Luneberg R P (1944) Mathematical Theory of Optics. Brown University mimeographed notes, University of California, Berkely, CA, 1964

    Google Scholar 

  • Melles Griot (1988) Optics Guide 4, Melles Griot, Irvine, California

    Google Scholar 

  • Misner C W, Thorne K S, Wheeler J A, Gravitation. Freeman, San Francisco Musgrave F K (1990) A Note on Ray Tracing Mirages. IEEE Comp. Graph, and Appl., November, 1990: 10–12

    Google Scholar 

  • Press W H, Flannery B P, Teukolsky S A, Vettering W T (1988) Numerical Recipes in C: the art of scientific computation. Cambridge University Press, Cambridge

    Google Scholar 

  • Walker J (1975) The Flying Circus of Physics With Answers. John Wiley & Sons, New York, p 120

    Google Scholar 

  • Watt A (1989) Fundamentals of Three Dimensional Computer Graphics. Addison-Wesley, New York, pp 166

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Tokyo

About this paper

Cite this paper

Suffern, K.G., Getto, P.H. (1991). Ray Tracing Gradient Index Lenses. In: Patrikalakis, N.M. (eds) Scientific Visualization of Physical Phenomena. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68159-5_18

Download citation

  • DOI: https://doi.org/10.1007/978-4-431-68159-5_18

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68161-8

  • Online ISBN: 978-4-431-68159-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics