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 光學(xué)儀器分辨率 Resolution of optical apparatus,20.2 單縫single-slit的夫瑯和費(fèi)衍射 Fraunhofer diffraction,2020/9/10,Lecture Notes WY,2,20.5 光柵衍射 Grating Diffraction,20.6 光柵光譜 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 ,半波帶,點(diǎn)光源G1和G2(G3和G4), 發(fā)出的光線1和2(3和4), 到P點(diǎn)的光程差是 /2,相鄰的兩個(gè)半波帶上， 1和2,3和4、任何一對(duì) 等分點(diǎn)光源的光,其光程差 總是l/2，結(jié)果光線在P點(diǎn)完全相消.

4、,2020/9/10,Lecture Notes WY,17,當(dāng) 時(shí)，可將縫分為兩個(gè)半波帶,兩個(gè)“半波帶”發(fā)的光在P處干涉相消形成暗紋,2020/9/10,Lecture Notes WY,18,當(dāng) 時(shí)，可將縫分成三個(gè)“半波帶”,P處為明紋中心 (近似),2020/9/10,Lecture Notes WY,19,當(dāng) 時(shí)，可將縫分成四個(gè)“半波帶”, 形成暗紋。,2020/9/10,Lecture Notes WY,20,In general cases：,Dark stripe condition,中央明紋(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,若可分為偶數(shù)個(gè)半波帶，則P點(diǎn)為暗紋（相消完全）,若可分為奇數(shù)個(gè)半波帶， 則P點(diǎn)為亮紋（相消不完全）,a,B,C,半波帶,dark,bright,2020/9/10,Lecture Notes WY,22,dark,3、Diffraction formula for a SS,若在介質(zhì)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)角寬度與線寬度x,其它明紋：,5、characterics of diffraction pattern,中央明紋:,df0,df,f,角寬度,線寬度,角寬度,線寬度,當(dāng)不變時(shí),a越小,條紋寬度越大， 鋪得越開，衍射現(xiàn)象越清楚。 若是白光入射,將出現(xiàn)-衍射光譜,O,2020/9/10,Lecture Notes WY,25,(2) 級(jí)數(shù)K越大;條紋亮度越小.,半波帶 多而窄,B,C,K越大;j 越大； BC越大；半波帶數(shù)目越多、寬度越窄；相消的面積越多.條紋亮度越小。,半波帶 少而寬,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、用波長(zhǎng)6328的光照射，單縫a=0.1mm,透鏡焦距40cm。 求：中央亮紋線寬； 第一級(jí)亮紋的位置；,2020/9/10,Lecture Notes WY,28,Ex2、單縫衍射中, 縫向下平移，條紋_, 向透鏡移近，條紋_; 縫寬變小，條紋間距_。,不動(dòng),不動(dòng),變大,Ex3、單縫衍射中,第3級(jí)暗紋對(duì)應(yīng)的單縫波面可分_個(gè)半波帶。,6,2020/9/10,Lecture Notes WY,29,Ex4、單縫衍射a=0.15mm, f=400mm，屏上兩個(gè)第三級(jí)暗紋相距8mm。求入射光的波長(zhǎng)?,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,望遠(yuǎn)鏡、顯微鏡（圓孔透鏡）中的物鏡相當(dāng)一個(gè)圓孔，成象是一個(gè)圓斑，而不是一個(gè)點(diǎn)。,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：恰能分辨的兩光源的衍射圖象中心的距離，等于中央亮斑的半徑，兩中心角寬為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:通常人眼的瞳孔直徑約為3毫米,問其最小分辨角是多大?遠(yuǎn)處兩根細(xì)絲之間的距離

12、為2毫米,問離開多遠(yuǎn)時(shí)恰能分辯？=5500A,f,2020/9/10,Lecture Notes WY,38,即離開近9m時(shí)尚能分辨，大于這個(gè)距離就無(wú)法分辨了。,2020/9/10,Lecture Notes WY,39, 等寬a、等距a+b 的一組平行狹縫。 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,只開其中一縫，圖樣是以o為中央亮

13、紋的單縫衍射圖。,k級(jí)主極大 P,多縫同時(shí)開放,各縫光束相干疊加。,o,j,零級(jí)主極大,2020/9/10,Lecture Notes WY,41,圖22.13,o,I,(1)明紋亮而窄;d越大越細(xì)亮。,(2)亮紋之間有很寬的暗區(qū),由若干弱明紋 和若干暗紋組成。,衍射光柵圖樣,在單縫衍射圖樣的輪廓下， 呈現(xiàn)出更精細(xì)的明暗結(jié)構(gòu)。,2020/9/10,Lecture Notes WY,42,3、difference of light path,相鄰狹縫的光束到達(dá)觀測(cè)點(diǎn)時(shí)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點(diǎn)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,(主極大位置),2020/9/10,Lecture Notes WY,45,5. Missing orders effects,B,D,單縫衍射極小,多縫干涉極大,D,這些級(jí)數(shù)的暗紋稱為缺級(jí)條紋。 例：if d/a=2，則缺k=2,4,諸主極大,（主極大消失 見書中277頁(yè)圖18(c)所示）,2020/9/10,Lecture Notes WY,46,但當(dāng)m=Nk 時(shí),設(shè)狹縫數(shù)目為N 若ND

15、j =m2 m=1,2,3 則P為暗紋，即:,所以兩主極大之間共有N-1個(gè)暗紋。,-主極大,-暗,*6.主極大間隔,2020/9/10,Lecture Notes WY,47,7.Several special characters of grating diffraction：,A、單縫衍射中央亮斑,o,I,有主極大條數(shù)為：,k=2d/a,2020/9/10,Lecture Notes WY,48,第三級(jí)光譜,C、入射白光4000A0-7600A0：,B、最多能看到幾級(jí)： 把j=900代入光柵公式求k,2020/9/10,Lecture Notes WY,49,注意光柵幾點(diǎn),D、非垂直入射,

16、入射角q,光程差,光柵公式,P,o,j,d=dsinq+dsinj,2020/9/10,Lecture Notes WY,50,E、雙縫衍射光柵 -與楊氏雙縫干涉的區(qū)別,例.,2020/9/10,Lecture Notes WY,51,Ex.6: 一雙縫, 縫距d=0.40mm,兩縫寬 度都是a=0.08mm,入射平行光 =4800A0，在縫后透鏡焦距f=2.0m . 求: (1) 在透鏡焦平面的屏上, 雙縫干涉條 紋的間距Dx (2) 在單縫衍射中央亮紋范圍內(nèi)的雙縫 干涉亮紋的數(shù)目和相應(yīng)的級(jí)數(shù)。,光柵常數(shù)d,2020/9/10,Lecture Notes WY,52,(1)干涉條紋間距Dx,

17、等間距,2020/9/10,Lecture Notes WY,53,Ex.7:用500條縫/mm的光柵觀察鈉光譜,縫寬0.001mm,=5893A0,最多能看到幾條譜線?,Sol:,得k =3.4,考慮到,所以,可看到,等5條譜線。,d=1mm/500=0.002mm,缺級(jí),2020/9/10,Lecture Notes WY,54,Ex.8: 上例中，若光波以300入射到光柵上,能看到的光譜線的最高級(jí)數(shù)是多少? 最多能看到幾條譜線?,k=5.1 最高級(jí)為5。,考慮到缺級(jí), 所以能看到,等7條譜線。,d=dsin30o+dsinj,2020/9/10,Lecture Notes WY,55,2

18、0.7 XRay Diffraction,M.K.Rntgen,倫琴,德國(guó)物理學(xué)家,(1845-1923),1895年 倫琴(Roentgen)發(fā)現(xiàn)x-ray,2020/9/10,Lecture Notes WY,56,倫琴夫人的手 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.,波長(zhǎng)與晶格常數(shù)(16）d0相當(dāng),wavelength：10 0.01 （angstrom）,2020/9/10,Lectu

19、re Notes WY,59,勞厄(Laue)相1912: 連續(xù)X光譜照射，不確定波長(zhǎng)，每個(gè)晶面系都有滿足的波長(zhǎng)及主極強(qiáng)方向。,德拜 (Debye)相: 單色X射線，多晶粉末，即給定波長(zhǎng)，不限定晶體取向。,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