本文基于数理方程的分离变量法，由Maxwell方程组和介质分界面衔接条件导出了菲涅尔公式. 并利用反 (透) 射率的模值和辐角随相对折射率和入射角的等值线图，系统讨论了反射波产生半波损失的条件和薄膜干涉问题中产生额外光程差的条件. 体现了光学课程与数学物理方法课程的紧密联系，有助于激发学生综合利用所学知识的兴趣.

In this paper, based on the separation of variables method from mathematical physics equations, we derive the Fresnel equations from Maxwell’s equations and the boundary conditions at dielectric interfaces. Then using contour plots of the reflection (transmission) coefficient’s modulus and argument vs. relative index of refraction and incident angle, we systematically analyze the conditions for half-wave loss in reflected waves and additional optical path differences in thin-film interference problems. This work underscores the intrinsic link between optics and methods of mathematical physics, serving to stimulate students’ interest in comprehensively applying their knowledge.