论文标题
一种新型的方法，用于探索具有球形对称折射率的介质中的光线行进路径
A Novel Approach for Exploring the Light Traveling Path in the Medium with a Spherically Symmetric Refractive Index
论文作者
论文摘要
提出了一种基于类比方法的独特透视方法，以在连续不均匀介质的模型中求解射线方程，该介质具有球形对称分布。基本上，在标准的本科物理学教学中，在具有持续变化的折射率的培养基中折射引起的弯曲射线路径一直是一个相对困难的问题。该方程通常用部分微分方程（PDE）表示，该方程无法通过分析方法来解决。基于类比方法，这项工作提出了在已建立的培养基模型中的射线折射与逆方中央力系统中的对应关系，从数学上简洁地获得了其关系方程。我们还通过定性和定量分析来验证该方法的正确性。就理论验证而言，我们分析了费马特原理与汉密尔顿原理之间的关系，汉密尔顿的原理为类比方法奠定了理论基础。此外，还通过基于COMSOL多物理学的数值计算来模拟中介质中的射线路径，结果与结论完全一致。
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.
