光线与两种GRIN介质界线的关系式及应用  

Derivation and Applications of Mathematical Expression between Light Ray and Borderline of Two GRIN Mediums

作　　者：郭守月[1] 曹春斌[1] 孙兆奇[2] 

机构地区：[1]安徽农业大学理学院,合肥230036 [2]安徽大学物理与材料科学学院,合肥230039

出　　处：《吉林大学学报（理学版）》2009年第2期345-349,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:50872001);安徽省高校自然科学研究项目基金(批准号:KJ2008B09ZCKJ2008B015)

摘　　要：当光线通过梯度折射率(GRIN)介质中两个固定点和两个GRIN介质界线上的可动尖点(光线轨迹方程的不可微点)时,由费马原理和变分法运算推得传输光线的轨迹方程与两种不同GRIN介质的界线方程应满足的微分关系式.通过应用示例可见,此微分关系式包含了几何光学的3个实验定律和球面镜成像公式等,而且是光线方程的另一种表达形式.When propagating light-ray passes through and a cuspidal variable-point （at this point the trace two fixed points in the gradient index （GRIN） mediums equation of propagating light-ray is non-differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light-ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat＇ s principle and calculus of variation. Some applied examples show that the differential relationship not only contains fundamental content in geometrical optics, such as the three laws of geometrical optics, imaging formula of single spheric face, but is another form of differential equation of the light ray.

关 键 词：几何光学 费马原理 变分法 光线方程 

分 类 号：O435.1[机械工程—光学工程]