力学与光学，是两门古老而又极具生命力的学科，两者在基本概念、物理规律和过渡关系等许多方面都存在着相似性和对应关系。对其对应关系的研究，对整个物理学的发展都有着重要的意义。在学习中找出力学与光学的对应关系，将有助于提高我们学习物理的兴趣，培养我们的思考习惯和类比归纳的能力。本文首先阐述了光学和力学的相似性。然后分别采用牛顿力学和分析力学的方法分析求解了悬链问题，得到了悬链线方程，又求得了线性变折射率模拟的海市蜃楼的光线轨迹的方程，最后对比了二者之间的相似性和对应关系。发现悬链的形状和线性变折射率模型下的光线轨迹都是双曲余弦，并得到了一些物理量和物理规律之间的对应关系。

mechanics and optics, are two science of great history and vitality, both of which exist in many respects.The basic concepts, physical laws and transitional relations of potics and mechanics are connecting with each other.Correlation between mechanical and optical research, casts great significance to the development of the entire physics. Trying to find corresponding relationship of mechanics and optics, will help to improve our interest in learning physics, cultivate our ability of thinking habits and inductive analogy.This article firstly expounds the similarity of optical and mechanical. Then Newtonian mechanics, and Analytical Mechanics were used to solve the problem of catenary and got the catenary equation,and obtain the equation becomes linear refractive index of the light trajectory simulating mirage, and finally compare the similarities between the two.Found that the shape of the catenary and linear variable refractive index model of light trails are hyperbolic cosine, and obtained some parameters and the corresponding relation between the physical laws.