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1、Geometrical Optics几何光学,*Basing on the three basic law*Basic theories of designing of optical instruments,1 Propagation of Light using Geometry,几何光学三定律 1.光的直线传播 Rectilinear propagation of light 2.反射定律 The Law of Reflection 3.折射定律 The Law of Refraction全反射 Total Internal Reflection棱镜和色散 Prism and Dispe
2、rsion光路可逆性 Optical Reversibility,Note:These three laws are valid when the wavelength of the light is much smaller than the dimensions of the relevant components of the optical system,that is,wavelength0,几何光学三定律,物体的影子,小孔成像,海市蜃楼,P100 in Optics,More hot,lower the index of refraction of the air,A ray wo
3、uld pass through more of the less dense air than if it had traveled straight.To take a route that minimized the OPL(optical path length),非均匀介质,当n1n2时，将发生全反射.,全反射 Total Internal reflection,Fiber,Fingerprint sensors,全反射临界角,min 是对应于顶角 时的最小偏向角 minimum deviation angle.棱镜主要用途：全反射棱镜测定棱镜材料的折射率n棱镜还是一种色散元件，主要
4、应用于分光。即利用棱镜对不同的波长的光有不同的折射率性质来分析光谱。光谱仪 望远镜,棱镜和色散 Prism and Dispersion,i1,i2,色散 Dispersion：n随的变化而变的现象。正常色散：棱镜的折射率n随波长的减小而增加，有经验公式：n=A+B/2+C/4A+B/2(变化范围不大时)白光：具有和太阳连续光谱相似的多色混合光。,研究光谱的重要仪器棱镜光谱仪,光的可逆性 Reversibility principle of light,光的可逆性原理：当光线的方向反转时，它将逆着同一路径传播。,2 Huygenss Principle惠更斯原理,波的几何描述惠更斯原理的表述对
5、反射和折射定律的解释惠更斯原理的局限,The Description of The WaveThe wave can be seen as the propagation of the period permutation spherical wave plane wave,波面为（以振源为中心的）球面的波称为球面波。在离振源很远的地方，波面趋于一个平面，这种波称为平面波。,波线,波线,波面（等相位面）,波面,each point on the leading surface of a wave disturbance may be regarded as a secondary source
6、 of spherical waves,which themselves progress with the speed of light in the medium and whose envelope at later times constitutes the new wavefront.The explanations of rectilinear propagation law,reflection and refraction laws by Huygens Principle(p16-19)Shortage of Huygens principle,Huygenss Princi
7、ple,The explanations of reflection and refraction laws by Huygens Principle(p16-19),每条光线到达分界面上时，都同时发射两个次波：反射次波和折射次波当光线n到达Bn点时，A1点发出的反射次波波面和透射次波波面分别是以V1tn V2tn半径的半球面。,按惠更斯原理：某一时刻总扰动的波面是这些次波面的包络面反射次波和透射次波总扰动的波面是这些次波的波面的包络面，且包络面是通过Bn点的平面。设反射波总扰动的波面与各次波面相切于C1C2C3Cn透射波总扰动的波面与各次波面相切于D1D2D3Dn连接次波源与切点，即得总扰动
8、的波线即反射光线A1C1 B2C2透射光线A1D1 B2D2（折射光线）,由此可见，一种媒质的绝对折射率为v：该种媒质中的光速，n的物理意义：光在两种媒质中传播速度之比。从 知，光在光密媒质中传播速度小，这与实验相符。,折射定律：在A1AnBn,A1BnD1中,(常数),反射定律：,令,由惠更斯原理知，波面AB上每个面元都是一个次波中心，t时刻AB部分每一点发出的次波面是以vt为半径的球面，这些次波面的包络面为CD，可见CD也是以Q为中心的球面的一部分。按惠更斯说法，只有各次波面的包络面CD上发生可察觉的总扰动，即包络面两侧C和D之外的扰动是可以忽略不计的。所以QAC和QBD就是透过孔隙的边缘
9、线，它们都是直线。惠更斯这样说明了波的直进性。以上解释并不令人十分满意，因为CD两侧之外还有次波存在着，为什么次波在这些地方不发生作用呢？,The explanation of rectilinear propagation law,D,C,Disregarding the effectiveness of the overlapping wavelets,Huygens avoided the possibility of diffraction of the light into the region of geometric shadow.Huygens also ignored the
10、 wavefront formed by the back half of the wavelets,since these wavefronts implied a light disturbance traveling in the opposite direction.,diffraction of water wave：,wavelength0,几何光学是短波的极限情形,Shortage of Huygens principle,3 Fermats Principle,光程 Optical length费马原理 Fermats Principle对几何三定律的解释,Optical le
11、ngth L=nl,and it can be regarded as the length of light traveling in the vacuum in the same time,Optical length,光程：将在介质中行走的路径折算成相同时间内在真空中行走的路程,Description of Fermats principleIt means the path of light between two points should be minimum,maximum or stationary,费马用光程的概念把几何光学三定律归结为一个统一的原理费马原理,Fermats
12、Principle:A light ray in going from point A to point B must traverse an optical path length that is stationary with respect to variations of that path.,光程一阶变分为零的四种情况横轴：不同的光线路径 纵轴：光程,The actual path taken by a light ray in its propagation between two given points in an optical system is such as to ma
13、ke its optical path equal,in the first approximation,to other paths closely adjacent to the actual one.,直线QMP最短，从而路径QMP的长度最短。根据费马原理，QMP是光线的实际路径。由对称性不难看出i=i。,Explaining the three laws of geometrical optics,The Law of Reflection,The Law of Refraction,既然几何光学三定律可以归结为费马原理,那么费马原理就可以代替三定律而作为几何光学的理论基础.以下我们在讨论光线追迹问题或者说成象问题时可以采用费马原理结合几何学的知识来解决.光学仪器中很大一部分是成像的的仪器，如显微镜，望远镜，投影仪和照相机等皆是。成像是几何光学要研究的中心问题之一。下面介绍一些成像的基本概念。,
