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.

© 2014 Optical Society of America

Determination of unit normal vectors of aspherical surfaces given unit directional vectors of incoming and outgoing rays

Psang Dain Lin and Chung-Yu Tsai
J. Opt. Soc. Am. A 29(2) 174-178 (2012)

Design of optical systems using derivatives of rays: derivatives of variable vector of spherical boundary surfaces with respect to system variable vector

Psang Dain Lin
Appl. Opt. 52(30) 7271-7287 (2013)

Analysis of optical elements with flat boundary surfaces

Te-Tan Liao and Psang Dain Lin
Appl. Opt. 42(7) 1191-1202 (2003)

First-order derivative matrix of a ray: a simple and flexible alternative computation method

Psang Dain Lin
Opt. Express 27(24) 35402-35417 (2019)

Ray-tracing method for creeping waves on arbitrarily shaped nonuniform rational B-splines surfaces

Xi Chen, Si-Yuan He, Ding-Feng Yu, Hong-Cheng Yin, Wei-Dong Hu, and Guo-Qiang Zhu
J. Opt. Soc. Am. A 30(4) 663-670 (2013)