双凸对称理想薄透镜傍轴物像公式的系统误差分析  

Systematic Error Analysis of Paraxial Object Image Formula for Biconvex Symmetric Ideal Thin Lens

作　　者：邵云 Shao Yun(School of Electronic Engineering,Nanjing Xiaozhuang University,Nanjing 211171,Jiangsu,China)

机构地区：[1]南京晓庄学院电子工程学院,江苏南京211171

出　　处：《激光与光电子学进展》2022年第13期227-232,共6页Laser & Optoelectronics Progress

基　　金：江苏省教育科学“十三五”规划课题(D/2020/01/55)。

摘　　要：首先指出凸透镜的实际厚度是一个不容被忽视的问题,然后逐步推导出空气中双凸对称厚透镜在傍轴情形下的物像关系及焦距,通过举例和作图,揭示出厚、薄两种凸透镜理论在焦距和像距上的具体差异,并分析出其中的一些规律性。通过取近似,推导出较薄凸透镜焦距及理想薄凸透镜焦距误差的近似表达式,指出后者与焦距近似无关。此外还推得“物焦比”大于2时较薄凸透镜像距和理想薄凸透镜像距的近似表达式,发现其间误差也与焦距无关,而仅与透镜的厚度、折射率及“物焦比”有关。最后指出,取“物焦比”大于2的原因在于物距处在2倍焦距以内时不便于取近似,而将凸透镜分为厚凸透镜、理想薄凸透镜、较薄凸透镜这3种类别的原因则在于严格区分。This study demonstrates that the actual thickness of a convex lens is a problem that cannot be ignored,then gradually deduces the object image relationship and focal length of a biconvex symmetric thick lens in the paraxial case in air.The specific differences in focal length and image distance between thick and thin convex lens theories are revealed through examples and drawings,and some of the rules are analyzed.The approximate expression of the focal length of a thin convex lens and the approximate expression of the focal length error of an ideal thin convex lens are derived using approximation,and the latter is almost independent of the focal length.This study also derives that the approximate expressions of image distances of a thin convex lens and ideal thin convex lens on the condition of“the ratio of object distance to focal length”is greater than 2,and the error between them has nothing to do with the focal length,but only with the thickness,refractive index and“the ratio of object distance to focal length”of the lens.At the end of the study,the reason for setting“the ratio of object distance to focal length”greater than 2 is that it is difficult to take approximation when the object distance is within 2 times the focal length,and the reason for dividing the convex lens into the thick convex lens,ideal thin convex lens,and thin convex lens lies in strict distinction.

关 键 词：几何光学 双凸对称厚透镜 理想薄凸透镜 较薄凸透镜 误差 

分 类 号：O435.1[机械工程—光学工程]