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A unique perspective approach based on an analogy method is presented tosolve the ray equation in a model of a continuous inhomogeneous medium, whichhas a spherically symmetric distribution. Basically, in the standardundergraduate physics teaching, the curved ray path caused by refraction in amedium with a continuously varying refractive index has always been arelatively difficult problem to solve. The equation is usually expressed interms of partial differential equations (PDEs), which cannot be solved byanalytical methods. Based on the analogy method, this work proposes thecorrespondence between ray refraction in an established medium model and theinverse-square central force system, succinctly obtaining their relationequations mathematically. We also verify the correctness of the method byqualitative and quantitative analysis. In terms of theoretical validation, weanalyse the relation between Fermat's principle and Hamilton's principle, whichlays a theoretical foundation for the analogy method. In addition, ray paths inthe medium model were also simulated by numerical calculations based on COMSOLMultiphysics, and the results are in perfect agreement with the conclusions.

A Novel Approach for Exploring the Light Traveling Path in the Medium with a Spherically Symmetric Refractive Index