大学物理双语课衍射课件

1、Key words And Terms Huygens-Fresnel principle 惠更斯-菲涅耳原理 single-slit diffraction 单缝衍射angle of diffraction 衍射角half-wave zone 半波带circular aperture diffraction 圆孔衍射Airy disk 爱里斑angle of minimum resolution 最小分辨角 grating 光栅grating constant 光栅常数missing order 缺级X-ray diffraction X射线衍射Bragg equation 布拉格方程Hom

2、ework : 31-4, 16, 28, 41, 54, 58, 60 18.1 The phenomenon of diffraction P68118.2 Diffraction by a single slit 31-118.3 Resolution 31-4,518.4 Diffraction in the Double-slit Experiment 31-318.5 Diffraction Grating 31-718.6 X-Ray diffraction 31-10Chapter 18 Diffraction chap. 3118.1 The phenomenon of di

3、ffraction P6811.The phenomenon of diffractionChapter 18 Diffraction chap. 31The waves, as they pass the small obstacle, bent around behind it into the “shadow region” .Small obstacleLarge obstacle2. 惠更斯菲涅耳原理惠更斯原理 在波的传播过程中，波前上的每一点都可看作是发射子波（次波）的波源，在其后的任一时刻，这些子波的包迹就成为新的波阵面。菲涅耳假定 波在传播过程中，从同一波阵面上各点发出的子波，

4、经传播而在空间某点相遇时，产生相干叠加。菲涅耳还指出： 波面是一个等位面，其上各点相位相同。 次波在P点的振幅与距离r成反比。 dA面元所发出的次波的振幅与dA面积成正比。 随dA面元的法线与r之间的夹角增大而减小。数学表达式 波面S上所有面元dA在P点的合振动：式中C为比例系数，K()为倾斜因数, K()K() =0 当 时 1 当 = 0 时Wave front*S衍射屏观察屏a 10 - 3 a衍射屏离光源或接收屏为有限远*S衍射屏观察屏L1L2衍射屏与光源和接收屏为无限远远场衍射近场衍射(2)Fraunhofer diffraction 夫琅禾费衍射(1) Fresnel diffra

5、ction 菲涅耳衍射 3. 衍射的分类:Parallel rays of monochromatic light passing through the narrow slitI18.2 Diffraction by a single slit 31-1（衍射角 ：向上为正，向下为负）We divided the surface of the slit into several equal parts,and the two adjacent part rays have path difference /2 . The intensity of light rays coming from

6、 each parts are equal.angle of diffraction1. Intensity in single-slit diffraction patternslitDark fringeBright fringeCenter bright fringe 中央明纹2 .The positions on which all rays travel with angle aAB/2 /a-( /a)2( /a)-2( /a)sin0.0470.017 1I / I0 0Relative intensity0.0470.017destructiveconstructive3. T

7、he positions of bright and dark bands on the screenI0 x1x2lensscreen f4. angular-width and line-width(1)Center bright fringe xI0 x1x2lensscreenx0 f1Angular-widthLine-width (2)Other fringes Angular-widthLine-widthDiscussion:波长越长，条纹宽度越宽；（2） 缝宽变化对条纹的影响；缝宽越小，条纹宽度越宽当 时，只显出单一的明条纹 单缝的几何光学像几何光学是波动光学在/a 0 时的

8、极限情形(3)单缝衍射的动态变化单缝上移，零级明纹仍在透镜光轴上. 单缝上下移动根据透镜成像原理衍射图不变 . (4)入射光非垂直入射时光程差的计算Monochromatic light falls on a transmission diffraction grating at an angle to the angle P728 31-33（中央明纹向下移动）（中央明纹向上移动） When violet light of wavelength 415nm falls on a single slit, it creates a central diffraction peak that i

9、s 9.2cm wide on the screen that is 2.50m away. How wide (mm) is this slit?Solution:Example Example 焦平面上原来3 级暗纹处，现在明暗情况如何the first order of bright bandAiry diskd：diameter of Airy disk18.3 Resolution 31-4,51. The diffraction of circular aperturesAngular half widthD：diameter of circular opening2. Resol

10、ution 几何光学与波动光学的区别几何光学 : 物点 象点(经透镜)物(物点集合) 象(象点集合)不考虑艾里斑物点 象斑( 经透镜 )波动光学 :物(物点集合) 象(象斑集合)考虑艾里斑The ability that a optical devise can just distinct two points being very close together.可分辨刚可分辨不可分辨 Two images are just resolvable when the center of the diffraction disk of one image is directly over the

11、first minimum in the diffraction pattern of the other.P711 Rayleigh criterion P710resolvableresolvable not resolvable Angle of minimum resolution Resolution of optical deviseResolving power (RP)It is not possible to resolve detail of objects smaller than the wavelength of the radiation being used.P7

12、12Hubble space telescope哈勃望远镜基本信息 长：13.2米 宽：4.2米 重：11吨 主镜口径：2.4米 副镜口径：0.3米 轨道：612公里，相对赤道倾斜28.5度 轨道周期：97分钟 轨道速度：28,000公里/小时 成本：22亿美元（发射） 寿命：约20年 眼睛的最小分辨角为设人离车的距离为 d 时，恰能分辨这两盏灯。取在迎面驶来的汽车上，两盏前灯相距120 cm ，设夜间人眼瞳孔直径为5.0 mm ，入射光波为 550 nm。例人在离汽车多远的地方，眼睛恰能分辨这是两盏灯？求解s =120 cmd由题意有观察者 It is said that a camera

13、in a spy-satellite can distinguish clearly the number of cars license.To distinguish the distance of 5cm between numbers on a license from the height of 160km, what should the diameter of camera be? (要识别牌照上的字划间的距离为5cm.在160km高空的照相机的孔径需要大)? ( assume = 500nm)Solution:Example I00I18.4 Diffraction in the

14、 Double-slit Experiment 31-3Intensity of the Double-slit Experiment constructivedestructivead flensI设双缝的每个缝宽均为a，在夫琅禾费衍射下，每个缝的衍射图样位置是相重叠的。双缝干涉单缝衍射双缝衍射（2）在 时，双缝衍射的强度分布情况变为理想的杨氏干涉的强度分布情况 结论：（1）双缝衍射的强度曲线是单缝衍射强度对双缝干涉强度进行调制的结果DestructiveDouble-slit interferenceOne-slit diffractionConstructiveDouble-slit i

15、nterference强度为零的衍射光相干，相长干涉的强度仍为零缺级Missing order： p, q为互质整数比时，缺 np 级缺第 3 ， 6、9、12 级1.GratingTypes: b+aReflection gratingb+aTransmission gratinga 透光部分的宽度d=a + b 光栅常数b 不透光部分的宽度 Grating constant18.5 Diffraction Grating 31-7a number of equally spaced parallel slits (104 -105 lines per cm)2. Grating equat

16、ionGrating equation Grating diffraction= diffraction of every slit+ interferenceQ点为主极大时Bright fringe,明纹，主极大oscreenLens（a+b）sina+bQNEQEQDark fringe：N个缝在Q点的N个振幅的矢量合为零Combine (1)、(2)暗纹间距=(主明纹间距/N) 相邻主明纹间有 N1 个暗纹和 N2 个次明纹。ENE3E2E1如 N = 4,有三个极小1234 /241 1234 3 /2IN2I0单sin048-4-8( /d)单缝衍射 轮廓线光栅衍射光强曲线N = 4

17、a+b= 4a3. Discussion:(2) missing orders 缺级(1) The maximum order 最高级次 p,q为互质整数比时，缺 np 级Number of bright lines=2mmax+1 the greater of number of slits, the narrower and brighter the bright bands(a) 1 slit (f) 20 slits(e) 6 slits(c) 3 slits(b) 2 slits(d) 5 slits (P715 Example 31-7) Diffraction grating:

18、lines. Calculate the first- and second-order angles for light of wavelength 400 nm and 700nm if the grating contains10000 lines/cm.Solution:fSo In first order, the angles areIn second orderSo Example 600-nm monochromatic light falls on a diffraction grating normally, and the first order bright band

19、is observed at a angle . If a=b , determine how many orders can be seen on the screen.Solution:Missing orders:So, orders can be seen on the screenExample = 0.5 m 的单色光垂直入射到光栅上，测得第3级主极大的衍射角为30o，且第4级为缺级。求：（1）光栅常数d；（2）透光缝最小宽度a；（3） 对上述 a、d 屏幕上可能出现的谱线数目。d =3 m （2）缺4级a =0.75 m （3）m = 0， 1， 2， 3， 59条！Example:例 用每毫米有500条栅纹的衍射光栅观察钠光谱线问：1、光线垂直入射； 2、光线以30度角入射时，最多能看到第几级条纹？解：1、最多条纹数由决定2、fABC第三级条纹第五级条纹White bight strikes a grating, there will be a color spectrum.4. Diffraction spectrum m=1 m=2 m=3 例 用白光垂直照射在每厘米有6500条刻痕的平面光栅上，求第三级光谱的张角.解红光紫光 不可见第三级光谱的张角第三级光谱所能出现的最大波长绿光 In 1885, Roentgen d