2022/12/05 by Shengyang Zhuang, Zhuang, Shengyang, Jiaqi Yin +3
Engineering · Physics and Astronomy · #Advanced Fiber Optic Sensors #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Optics (physics.optics) #Photonic and Optical Devices
paper · pdf · doi:10.48550/arxiv.2212.02642
openalex publication_date 2022/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A unique perspective approach based on an analogy method is presented to solve the ray equation in a model of a continuous inhomogeneous medium, which has a spherically symmetric distribution. Basically, in the standard undergraduate physics teaching, the curved ray path caused by refraction in a medium with a continuously varying refractive index has always been a relatively difficult problem to solve. The equation is usually expressed in terms of partial differential equations (PDEs), which cannot be solved by analytical methods. Based on the analogy method, this work proposes the correspondence between ray refraction in an established medium model and the inverse-square central force system, succinctly obtaining their relation equations mathematically. We also verify the correctness of the method by qualitative and quantitative analysis. In terms of theoretical validation, we analyse the relation between Fermat's principle and Hamilton's principle, which lays a theoretical foundation for the analogy method. In addition, ray paths in the medium model were also simulated by numerical calculations based on COMSOL Multiphysics, and the results are in perfect agreement with the conclusions.