УДК: 535.314

Vector and matrix methods of computing the direction of a ray refracted by a system of arbitrarily placed flat refracting surfaces

Ezhova, K.V., Zverev, V.A., Trusov, I.A.

Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Ежова К.В., Зверев В.А., Трусов И.А. Векторный и матричный методы вычисления направления луча, преломленного системой произвольно расположенных плоских преломляющих поверхностей // Оптический журнал. 2014. Т. 81. № 4. С. 26–30.

Ezhova K.V., Zverev V.A., Trusov I.A. Vector and matrix methods of computing the direction of a ray refracted by a system of arbitrarily placed flat refracting surfaces [in Russian] // Opticheskii Zhurnal. 2014. V. 81. № 4. P. 26–30.

For citation (Journal of Optical Technology):

K. V. Ezhova, V. A. Zverev, and I. A. Trusov, "Vector and matrix methods of computing the direction of a ray refracted by a system of arbitrarily placed flat refracting surfaces," Journal of Optical Technology. 81(4), 186-189 (2014). https://doi.org/10.1364/JOT.81.000186

Abstract:

Based on the law of refraction in vector form, an expression is obtained that determines the direction of a ray refracted at two refracting surfaces. As a result of analyzing this expression, represented in matrix form, a form of the expression is proposed that determines the direction of a ray refracted by an arbitrary number of refracting surfaces. The method of mathematical induction is used to prove that the resulting expression is valid for computing the unit vector of a ray refracted by a system of flat, arbitrarily placed refracting surfaces.

Keywords:

law of refraction, matrix form, mathematical induction

OCIS codes: 220.0220, 080.1753

References:

1. M. M. Rusinov, ed., Computational Optics: A Handbook (Mashinostroenie, Leningrad, 1984).
2. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Pergamon Press, Oxford, 1965; Nauka, Moscow, 1970).
3. V. A. Zverev and T. V. Tochilina, Principles of Optical Engineering. A Textbook (SPbGU ITMO, St. Petersburg, 2005).
4. E. Kaspar, “Systèmes de réflexions et de réfractions,” Rev. Opt. Theor. Instrum. 27, No. 1, 15 (1948).
5. I. N. Bronshteı˘n and K. A. Semendyaev, Mathematics Handbook for Engineers and Students of Technical Colleges (Nauka, Moscow, 1986).
6. V. N. Churilovskiı˘, “The pyramidal invariant,” Opt. Mekh. Prom. No. 11, 7 (1932).
7. V. A. Zverev, E. S. Rytova, and I. N. Timoshchuk, “Errors in fabricating and installing reflective prisms,” Opt. Zh. 78, No. 3, 14 (2011) [J. Opt. Technol. 78, 164 (2011)].