Analytical and graphical ray-tracing techniques based on a classical principle for photon refraction.

Area of Science:

• Optics and Photonics
• Classical Mechanics

Background:

• Refraction is governed by Snell's law, but analytical and graphical ray tracing can be complex.
• Previous work derived exact ray-tracing formulas for optical systems.

Purpose of the Study:

• To propose a new classical principle explaining single photon refraction.
• To simplify analytical and graphical ray tracing methods.
• To unify meridional and skew ray-tracing formulas for systems of spherical surfaces.

Main Methods:

• Derivation of a linear form of Snell's law from a new classical principle.
• Rewriting existing exact ray-tracing formulas using the linear form of Snell's law.
• Generalization of meridional exact formula for systems of spherical surfaces.
• Development of a new ray-tracing procedure for skew rays.
• Introduction of a new graphical ray-tracing technique.

Main Results:

• A new classical principle explaining photon refraction and leading to a linear Snell's law.
• Unified mathematical forms for meridional ray-tracing formulas.
• Generalization of thick lens formula to systems of spherical surfaces.
• Exact formulas for ball lens and its longitudinal spherical aberration.
• A new ray-tracing procedure for skew rays in complex systems.
• A simpler graphical ray-tracing technique.

Conclusions:

• The proposed linear form of Snell's law simplifies optical analysis and ray tracing.
• The new principle provides a unified framework for various ray-tracing formulas.
• The developed methods offer efficient tools for designing and analyzing optical systems.