摘要
基于数学分析中求极值方法和导数性质,研究推导得到了一般三棱镜最小偏向角的条件,清楚地说明了偏向角最小时对应的条件与入射角、折射率和棱镜顶角的关系.应用Matlab得到关系曲线,从曲线得到一次导数为0对应的入射角、最小偏向角和二次导数的大小,同时给出了最小入射角对应的偏向角,对应折射率的棱镜最大顶角.应用Visio精准绘出了给定条件下的光线轨迹,从轨迹图中得到偏向角与相关条件的关系.研究结果表明,偏向角最小时对应的入射角与棱镜顶角、折射率有关,为实验或研究中要得到文献定义的偏向角和最小偏向角选择棱镜顶角、折射率参数提供理论依据,解决了教学和学习过程对于最小偏向角条件的理论分析困惑.
Based on the extreme value method and derivative property in mathematical analysis,the conditions for the minimum deflection angle of a general triangular prism are studied and derived,and the relationship between the conditions corresponding to the minimum deflection angle and the incidence angle,refractive index and the top angle of the prism is clearly explained.The relation curve is obtained by using Matlab.The size of the incident angle,the minimum angle of deflection and the second derivative corresponding to the first derivative of 0 are obtained from the curve.At the same time,the angle of deflection corresponding to the minimum incident angle and the maximum vertex angle of the prism corresponding to the refractive index are given.The ray trace under given conditions is accurately drawn by Visio,and the relationship between deflection angle and relevant conditions is obtained from the trace diagram.The research results show that the incident angle corresponding to the minimum deflection angle is related to the top angle and refractive index of the prism,which provides a theoretical basis for selecting the top angle and refractive index parameters of the prism to obtain the deflection angle and the minimum deflection angle defined in the literature in experiments or research,solves the theoretical analysis confusion of the minimum deflection angle condition in the teaching and learning process.
作者
俞轶帆
顾菊观
周天佑
曹炳松
YU Yifan;GU Juguan;ZHOU Tianyou;CAO Bingsong(School of Science,Huzhou University,Huzhou 313000,China)
出处
《高师理科学刊》
2024年第1期56-64,共9页
Journal of Science of Teachers'College and University
基金
国家自然科学基金项目(12047568)。
关键词
一般三棱镜
偏向角
最小偏向角
最小入射角
最大顶角
general prism
deflection angle
minimum deflection angle
minimum incidence angle
maximum vertex angle