Abstract

The law of refraction of light rays is derived from Fermat’s principle by means of the Weierstrass-Erdmann corner condition of the calculus of variations. In such a derivation the optical path need only be considered at the point of refraction, and the refraction principle follows from a differential equation rather than from an integral equation or geometric construction for a finite length of path. Likewise, the corner condition taken with Fermat’s principle is a differential equation which requires that an optical path be straight at all points where the velocity is unchanged.

© 1950 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Snell’s Law and the Calculus of Variations

Henry Zatzkis
J. Opt. Soc. Am. 55(1) 59-61 (1965)

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

Hassan A. Elagha
J. Opt. Soc. Am. A 29(12) 2679-2687 (2012)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (2)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (13)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription