Chapter-20-光的衍射Diffraction-of-Light.ppt

1、2020/9/10,Lecture Notes WY,1,Chapter 20 光的衍射Diffraction of Light,20.1 光的衍射和惠-菲原理 HuygensFresnel principle,20.3 光学仪器分辨率 Resolution of optical apparatus,20.2 单缝single-slit的夫琅和费衍射 Fraunhofer diffraction,2020/9/10,Lecture Notes WY,2,20.5 光栅衍射 Grating Diffraction,20.6 光栅光谱 Grating Spectrum,20.7 X-ray衍射 X

2、-ray diffraction,2020/9/10,Lecture Notes WY,3,1、Diffraction phenomenon,20.1 Diffraction PhenomenaHuygens-Fresnel principle,The idea of Huygenssecondary waves,2020/9/10,Lecture Notes WY,4,The future position of a wavefront maybe derived from a past position by considering every point of the wavefront

3、 to be a source of secondary waves.,2020/9/10,Lecture Notes WY,5,The diffraction effects depends on the scale of the obstacle or aperture compared with the wavelength. Distinguish of interference ,半波带,点光源G1和G2(G3和G4), 发出的光线1和2(3和4), 到P点的光程差是 /2,相邻的两个半波带上， 1和2,3和4、任何一对 等分点光源的光,其光程差 总是l/2，结果光线在P点完全相消.

4、,2020/9/10,Lecture Notes WY,17,当 时，可将缝分为两个半波带,两个“半波带”发的光在P处干涉相消形成暗纹,2020/9/10,Lecture Notes WY,18,当 时，可将缝分成三个“半波带”,P处为明纹中心 (近似),2020/9/10,Lecture Notes WY,19,当 时，可将缝分成四个“半波带”, 形成暗纹。,2020/9/10,Lecture Notes WY,20,In general cases：,Dark stripe condition,中央明纹(中心),a sin k ，(k=1,2,),Bright stripe (中心) co

5、ndition,a sin 0,2020/9/10,Lecture Notes WY,21,若可分为偶数个半波带，则P点为暗纹（相消完全）,若可分为奇数个半波带， 则P点为亮纹（相消不完全）,a,B,C,半波带,dark,bright,2020/9/10,Lecture Notes WY,22,dark,3、Diffraction formula for a SS,若在介质n中？,若以q斜入射：,bright,d,2020/9/10,Lecture Notes WY,23,若j很小，,4、stripe position and the focus,2020/9/10,Lecture Notes

6、 WY,24,(1)角宽度与线宽度x,其它明纹：,5、characterics of diffraction pattern,中央明纹:,df0,df,f,角宽度,线宽度,角宽度,线宽度,当不变时,a越小,条纹宽度越大， 铺得越开，衍射现象越清楚。 若是白光入射,将出现-衍射光谱,O,2020/9/10,Lecture Notes WY,25,(2) 级数K越大;条纹亮度越小.,半波带 多而窄,B,C,K越大;j 越大； BC越大；半波带数目越多、宽度越窄；相消的面积越多.条纹亮度越小。,半波带 少而宽,B,j,C,j,2020/9/10,Lecture Notes WY,26,Ex. Hel

7、ium-neon laser light of wavelength 633 nm passes through a single slit of width 0.10mm. The diffraction pattern is observed on a screen 3m away-far enough so that the conditions for Fraunhofer diffraction apply. What is the distant between the two minima on either side of the central maximum? Soluti

8、on:,2020/9/10,Lecture Notes WY,27,Ex1、用波长6328的光照射，单缝a=0.1mm,透镜焦距40cm。 求：中央亮纹线宽； 第一级亮纹的位置；,2020/9/10,Lecture Notes WY,28,Ex2、单缝衍射中, 缝向下平移，条纹_, 向透镜移近，条纹_; 缝宽变小，条纹间距_。,不动,不动,变大,Ex3、单缝衍射中,第3级暗纹对应的单缝波面可分_个半波带。,6,2020/9/10,Lecture Notes WY,29,Ex4、单缝衍射a=0.15mm, f=400mm，屏上两个第三级暗纹相距8mm。求入射光的波长?,2020/9/10,Lec

9、ture Notes WY,30,S,中央亮斑 -Airy disk,2、Fraunhofer diffraction pattern,2020/9/10,Lecture Notes WY,31,Fraunhofer diffraction of a circular aperture,intensity：the bright central area nearly containing 84% of total intensity of the light。,Airy disk George Airy 1830s,2020/9/10,Lecture Notes WY,32,D,If , th

10、e diffraction effects can be neglected.,The first minimum angle of Airy disk：,2020/9/10,Lecture Notes WY,33,望远镜、显微镜（圆孔透镜）中的物镜相当一个圆孔，成象是一个圆斑，而不是一个点。,20.3 Resolution of an optical aperture (lens),D,S1,2020/9/10,Lecture Notes WY,34,1、The Rayleith criterion,2020/9/10,Lecture Notes WY,35,2、The minimum re

11、solution angle ,Definition：恰能分辨的两光源的衍射图象中心的距离，等于中央亮斑的半径，两中心角宽为1.22l/D,2020/9/10,Lecture Notes WY,36,3 、Resolution 1/D,reciprocal value of RA,It is proportional to diameter D of the lens and a reverse ratio of wavelength,2020/9/10,Lecture Notes WY,37,D,S1,S2,Ex.5:通常人眼的瞳孔直径约为3毫米,问其最小分辨角是多大?远处两根细丝之间的距离

12、为2毫米,问离开多远时恰能分辩？=5500A,f,2020/9/10,Lecture Notes WY,38,即离开近9m时尚能分辨，大于这个距离就无法分辨了。,2020/9/10,Lecture Notes WY,39, 等宽a、等距a+b 的一组平行狭缝。 A large number of slits,1.Definition,Grating constant: d=a+b,20.5 The diffraction grating,2020/9/10,Lecture Notes WY,40,2、Diffraction pattern of grating,只开其中一缝，图样是以o为中央亮

13、纹的单缝衍射图。,k级主极大 P,多缝同时开放,各缝光束相干叠加。,o,j,零级主极大,2020/9/10,Lecture Notes WY,41,图22.13,o,I,(1)明纹亮而窄;d越大越细亮。,(2)亮纹之间有很宽的暗区,由若干弱明纹 和若干暗纹组成。,衍射光栅图样,在单缝衍射图样的轮廓下， 呈现出更精细的明暗结构。,2020/9/10,Lecture Notes WY,42,3、difference of light path,相邻狭缝的光束到达观测点时的光程差相等,j,d=dsinj equidistant,4,1,2,3,2020/9/10,Lecture Notes WY,4

14、3,相位差相等 :,4,1,2,3,P点合振幅,2落后1Dj，,3落后2Dj,2020/9/10,Lecture Notes WY,44,If Dj =2kp,thus,4.Grating formula,(主极大位置),2020/9/10,Lecture Notes WY,45,5. Missing orders effects,B,D,单缝衍射极小,多缝干涉极大,D,这些级数的暗纹称为缺级条纹。 例：if d/a=2，则缺k=2,4,诸主极大,（主极大消失 见书中277页图18(c)所示）,2020/9/10,Lecture Notes WY,46,但当m=Nk 时,设狭缝数目为N 若ND

15、j =m2 m=1,2,3 则P为暗纹，即:,所以两主极大之间共有N-1个暗纹。,-主极大,-暗,*6.主极大间隔,2020/9/10,Lecture Notes WY,47,7.Several special characters of grating diffraction：,A、单缝衍射中央亮斑,o,I,有主极大条数为：,k=2d/a,2020/9/10,Lecture Notes WY,48,第三级光谱,C、入射白光4000A0-7600A0：,B、最多能看到几级： 把j=900代入光栅公式求k,2020/9/10,Lecture Notes WY,49,注意光栅几点,D、非垂直入射,

16、入射角q,光程差,光栅公式,P,o,j,d=dsinq+dsinj,2020/9/10,Lecture Notes WY,50,E、双缝衍射光栅 -与杨氏双缝干涉的区别,例.,2020/9/10,Lecture Notes WY,51,Ex.6: 一双缝, 缝距d=0.40mm,两缝宽 度都是a=0.08mm,入射平行光 =4800A0，在缝后透镜焦距f=2.0m . 求: (1) 在透镜焦平面的屏上, 双缝干涉条 纹的间距Dx (2) 在单缝衍射中央亮纹范围内的双缝 干涉亮纹的数目和相应的级数。,光栅常数d,2020/9/10,Lecture Notes WY,52,(1)干涉条纹间距Dx,

17、等间距,2020/9/10,Lecture Notes WY,53,Ex.7:用500条缝/mm的光栅观察钠光谱,缝宽0.001mm,=5893A0,最多能看到几条谱线?,Sol:,得k =3.4,考虑到,所以,可看到,等5条谱线。,d=1mm/500=0.002mm,缺级,2020/9/10,Lecture Notes WY,54,Ex.8: 上例中，若光波以300入射到光栅上,能看到的光谱线的最高级数是多少? 最多能看到几条谱线?,k=5.1 最高级为5。,考虑到缺级, 所以能看到,等7条谱线。,d=dsin30o+dsinj,2020/9/10,Lecture Notes WY,55,2

18、0.7 XRay Diffraction,M.K.Rntgen,伦琴,德国物理学家,(1845-1923),1895年 伦琴(Roentgen)发现x-ray,2020/9/10,Lecture Notes WY,56,伦琴夫人的手 X照片,2020/9/10,Lecture Notes WY,57,2020/9/10,Lecture Notes WY,58,1、X-Ray is an electromagnetic wave with small wavelength.,波长与晶格常数(16）d0相当,wavelength：10 0.01 （angstrom）,2020/9/10,Lectu

19、re Notes WY,59,劳厄(Laue)相1912: 连续X光谱照射，不确定波长，每个晶面系都有满足的波长及主极强方向。,德拜 (Debye)相: 单色X射线，多晶粉末，即给定波长，不限定晶体取向。,2、 X-ray diffraction pattern,2020/9/10,Lecture Notes WY,60,2020/9/10,Lecture Notes WY,61,Peter Debye,Peter Joseph William Debye,2020/9/10,Lecture Notes WY,62,Petrus Josephus Wilhelmus Debije (March 24,1884-November