基于费马原理的光学元件成像规律探究  

Exploration of Imaging Law of Special Optical Element Based on Fermat Principle

作　　者：张思宇 王伟[1] ZHANG Siyu;WANG Wei(School of Physics,Northeast Normal University,Changchun 130024,China;The Affiliated High School of Shanxi University,Taiyuan 030000,China)

机构地区：[1]东北师范大学物理学院,长春130024 [2]山西大学附属中学,太原030000

出　　处：《实验科学与技术》2022年第6期141-146,共6页Experiment Science and Technology

基　　金：吉林省高校“金课”建设项目(省级A类)。

摘　　要：运用费马原理推导出同光轴平行光束经反射和折射后完美汇聚在一点时,反射和折射界面需满足的条件。通过旋转抛物面反射、旋转椭球面折射与球面反射和球面折射的对比,得到近轴光线条件下光学元件的成像规律,并使用ZEMAX软件进行了模拟,得到了上述各光学元件的模拟光路图。运用费马原理推导出了主轴外物点在非近轴近似条件下,球面反射、球面折射、厚透镜的物像方程。该方程表明:只有近轴物在近轴光线条件下,才能得到唯一确定的像点,即近轴近似是理想成像充要条件的结论。Fermat’s principle is applied to derive the condition for the interface of reflection and refraction to enable the perfect convergence of parallel beams at a single point.An imaging law of each optical elements with paraxial light is obtained by examining the light propagation through the rotating parabolic surface,ellipsoid surface,spherical surface and the spherical lens.With the ZEMAX software,we simulate the light propagation and obtain optical path diagram for the aforementioned optical elements.Furthermore,we deduce an object image equation for the spherical surface,spherical surface and thick lens under the condition of nonparaxial approximation by applying Fermat’s principle.Namely,a unique image point can be observed only for paraxial objects in paraxial light,and the paraxial approximation is the necessary and sufficient condition for ideal imaging.

关 键 词：费马原理 非近轴近似 主轴外物点 理想成像 

分 类 号：G633.7[文化科学—教育学]