| 光线与两种GRIN介质界线的关系式及应用 |
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| 引用本文： | 郭守月,曹春斌,孙兆奇. 光线与两种GRIN介质界线的关系式及应用[J]. 吉林大学学报(理学版), 2009, 47(2): 345-349 |
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| 作者姓名： | 郭守月 曹春斌 孙兆奇 |
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| 作者单位： | 安徽农业大学,理学院,合肥,230036;安徽大学,物理与材料科学学院,合肥,230039 |
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| 基金项目： | 国家自然科学基金,安徽省高等学校自然科学基金 |
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| 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.
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| 关 键 词： | 几何光学 费马原理 变分法 光线方程 |
| 收稿时间： | 2008-06-15 |
Derivation and Applications of Mathematical Expression between Light Ray and Borderline of Two GRIN Mediums |
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| GUO Shou-yue,CAO Chun-bin,SUN Zhao-qi. Derivation and Applications of Mathematical Expression between Light Ray and Borderline of Two GRIN Mediums[J]. Journal of Jilin University: Sci Ed, 2009, 47(2): 345-349 |
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| Authors: | GUO Shou-yue CAO Chun-bin SUN Zhao-qi |
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| Affiliation: | 1. School of Sciences, Anhui Agricultural University, Hefei 230036, China; 2. School of Physics and Material Science, Anhui University, Hefei 230039, China |
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| Abstract: | When propagating light-ray passes through two fixed points in the gradient index(GRIN) mediums and a cuspidal variable-point(at this point the trace 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 differenti... |
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| Keywords: | geometrical optics Fermat principle variational calculus equation of the light rays |
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