“几何光学”教学中物象关系的讨论及符号法则建立再分析

Reanalysis on the Relationship between Objects and Images and Establishment of Signs Convention in the Teaching Process of Geometrical Optics

本文分析了目前各高校物理类专业光学课程中对于几何光学符号法则部分在教材编排及教学过程中存在的一些缺陷,如:"物象虚实"界定的不严谨、成像公式建立过程中的逻辑缺陷等,指明了几何光学中的"物象虚实"概念与日常习惯表达的差异并分析了由此导致的一系列问题(虚实判定的错误、符号运算的混乱等),给出了"物象虚实"关系的判定法则——因果关系、空间关系;通过对反射及逆向问题的剖析建立起实正虚负法则到新笛卡尔法则的过渡,强调了新笛卡尔符号法则的灵魂是"坐标",基于该法则下成像公式的数学实质是一对共轭坐标点的约束关系,最后对教材编排及教学过程设计给出了相关建议.

This paper analyses some defects in the text and teaching process about the geometrical optics symbol laws in the physics course of universities and colleges, such as no strict differences between the concept of “object,image,virtual and real” and the differences between this concept’s daily expression andthe aspect of geometrical optic. The series problems caused by such problems are analyzed, such as judgement faults on virtual and real, chaos on symbol operation, etc. And then the judgement principles are proposed: causal relationship and spatial relationship. Through the analysis of reflection and inverse problems, the paper establishes the transition from the real positive and imaginary negative law to the signs convention of newCartesian, and emphasizes that the soul of the new Cartesian signsconvention is "coordinates", the mathematical essence of the imaging formula based on this rule is the constraint relation of a pair of conjugate coordinate points. Finally, some suggestions are given for the arrangement of course text and the design of teaching process.