Abstract

In this work, a new classical principle that can explain the refraction of a single photon path at the boundary between two different media is proposed. This principle leads to the two well-known laws of refraction and also to a simple linear form of Snell’s law. This linear form not only played a vital role in simplifying the mathematics of analytical ray tracing, but also led to a unified common form for the meridional ray-tracing formulas. Also, it works as a basic rule for a new graphical ray-tracing technique. In a previous work [J. Opt. Soc. Am. A. 34, 335 (2017) [CrossRef]  ], new exact ray-tracing formulas were derived. All of these formulas are rewritten, in the current work, in terms of that linear form of Snell’s law that revealed their common mathematical form. The meridional exact formula of a thick lens is generalized to include a whole system of spherical surfaces. From the latter, all the other exact ray-tracing formulas can be easily derived. As an application, a single exact meridional formula for a ball lens and a formula for its longitudinal spherical aberration are derived. Also, we present a new ray-tracing procedure for skew rays propagating through a system of spherical surfaces that can be centered, decentered, and/or tilted without the need to determine the point of incidence or the normal to the surface. Finally, and also based on that linear form of Snell’s law, a new graphical ray-tracing technique that is simpler than the classical one is presented.

© 2017 Optical Society of America

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