电磁波方程及折射、反射定律的一些思考  

SOME THOUGHTS ON ELECTROMAGNETIC WAVE EQUATIONS AND THE LAWS OF REFECTION AND REFRACTION

作　　者：杨富国[1] 史向华[1] 

机构地区：[1]长沙理工大学物理与电子科学学院,1202班湖南长沙410004

出　　处：《物理与工程》2014年第5期73-75,共3页Physics and Engineering

基　　金："光学"探究式教学和探究性学习模式的研究与实践(湘教通[2010]243号);湖南省教育厅教改项目(sj1005);长沙理工大学教改项目(JG1011z)

摘　　要：本文由电磁波的麦克斯韦方程组出发,介绍导出折射定律和反射定律的一种证明方法.其证明方法,使用了空间微元近似,然后推广至全空间传播的方法,从而简化了麦克斯韦方程组求解的烦琐过程,提出了一种可教学推广的实用性方法.通过使用微元法,求解得到麦克斯韦方程的行波解形式,即得出电磁场是一种行波.由电磁场的向量形式推导空间中电磁波的折射、反射定律,得到折射、反射定律的证明并不需要电磁波的解析形式,在连续函数的情形下是普遍成立的.求解过程中加深对麦克斯韦方程组的理解,体现了电磁过程的深刻物理图像,也为由几何光学向波动光学过渡提供一种思想上的指导.This paper introduces a proof method for the laws of refraction and reflection from the Maxwell equations of electromagnetic wave theory. The spatial element approximation is used in this proof method, and then it is extended to the whole space propagation, which simplifies the tedious process of solving Maxwell equations. Furthermore, we put forward a practical method of teaching promotion. By using the element approximation method, we obtain the traveling wave form solutions of Maxwell equation, which indicates that the electromagnetic field is a kind of traveling wave. Refraction and reflection of electromagnetic wave in space are derived from the electromagnetic field vectors. It is found that the proofs of reflection and refraction do not require analytical form of electromagnetic waves, and the laws are commonly true in continuous function situation. Our work deepens the understanding of Maxwell equations in the process of solution, reflects the profound physical image of the electromagnetic process, and provides an ideological guidance to the wave optics transited from the geometrical optics.

关 键 词：电磁场方程 边界条件 反射定律 折射定律 

分 类 号：O441-4[理学—电磁学] G642[理学—物理]