摘要雨后的天空中经常会出现色彩鲜艳的彩虹，它的形成曾使人们感到困扰。从遥远的殷商时代开始，我国就出现了虹的象形文字，之后的各个朝代，都有对彩虹的描述，包括彩虹的产生、彩虹的位置以及人造彩虹的出现。西方对于彩虹的研究从亚里士多德开始，历经费马、笛卡尔、牛顿等人，通过理论的研究以及实验的探索大致上解决了有关彩虹的一些问题，包括彩虹产生的机理以及彩虹的颜色。随着时代的发展，人们对于彩虹的认识也越来越深刻，彩虹对于人们来说也不再神秘。本文将站在前人研究的基础上，从数学物理的角度出发，通过几何光学，包括费马原理、光的反射定律、光的折射定律以及最小偏向角来研究彩虹的形成，包括彩虹在天空出现的位置及其形状、色彩的分布、副虹的存在以及亚历山大暗带的形成。关键词：几何光学：偏向角：彩虹ABSTRACTAfter raining,there are colorful rainbow in the sky,its formation has made peoplefeel troubled.From distant Shang Dynasty,our country appeared rainbowpictographs.After various dynasties,there are descriptions of the rainbow,including thegeneration of rainbow,rainbow location and the appearance of the artificialrainbow .For the Western study of the rainbow from Aristotle,after Fermat,Descartes,Newton et al.They through the theoretical research and experimental exploration,it hassolved some problems about the rainbow,including the mechanism of the rainbow andthe color of the rainbow.With the society development,people are more and moreprofound understanding of the rainbow,the rainbow for people is no longermysterious.This article will stand on the basis of previous studies,by the perspective ofmathematical physics,by geometrical optics,including Fermat principle,reflection law,refraction law and minimum deviation angle to study the form of the rainbow,includingthe position,the shape,the color of the rainbow,and the deputy rainbow,as well as thedark band of Alexander.Key words:geometrical optics:minimum deviation angle:rainbow目录ABSTRACT...第1章绪论11.1问题的提出.1.2前人的观察及研究…1.3本文的主要内容2第2章彩虹的几何光学原理32.1笛卡尔光线…32.2费马原理32.3光的反射定律2.4光的折射定律2.5最小偏向角第3章彩虹的形成3.1彩虹形成的条件3.2彩虹的位置3.3彩虹的形状133.4彩虹的颜色.153.5副虹的形成3.6亚历山大暗带..17结论与展望..19