大学物理 ›› 2017, Vol. 36 ›› Issue (5): 19-23.doi: 10.16854 /j.cnki.1000-0712.2017.05.006

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几何光学教学中关于变折射率材料问题的计算实例

何健   

  1. 绵阳师范学院数理学院,四川绵阳621000
  • 收稿日期:2016-04-15 修回日期:2016-09-30 出版日期:2017-05-20 发布日期:2017-05-20
  • 作者简介:何健( 1980—) ,男,四川自贡人,绵阳师范学院数理学院讲师,硕士,主要从事物理教学科研工作,研究方向为光学、大学物理教学论.
  • 基金资助:
    绵阳师范学院2016 年科研启动课题( QD2016A002) 资助

Calculation example of the problem with variable refractive index materials in geometrical optics teaching

HE Jian   

  1. school of Mathematics and Physics; Mianyang Normal University; Mianyang,Sichuan 621000,China
  • Received:2016-04-15 Revised:2016-09-30 Online:2017-05-20 Published:2017-05-20

摘要: 针对大学光学课程中所讨论的成像问题均为“近轴近似”这一情形,指出为增强教学效果、提升学生对所学理论在 实践上的信心,需对非近轴近似的一般化情形给予一定讨论; 明确了直接从费马原理反解折射率变化规律的不可行性,采用近似办法,将变折射率的泛函问题转化为关于斜率的一维函数问题,利用欧拉方程进行分析,通过数值计算得出适合于材料 制作的一组参考参数.

关键词: 变折射率, 近轴条件, 费马原理, 变分法

Abstract: The problem of imaging discussed in the course of optics customarily is under the conditions of “paraxial approximation”. In order to enhance the effectiveness of teaching and their confidence of the theory in practice,we need to give some discussion on non-paraxial approximation of the general situation. It makes clear that directly inverse solution for the change regulation of the refractive index from Fermat’s principle is not a feasible solution. The approximate method will let the refractive index’s functional problem change as the slope of one-dimensional function problem. By using the Euler equation and numerical calculation,we obtain a set of reference parameters for material made.

Key words: variable refractive index, near axis condition, Fermat principle, variational method