大學(xué)物理雙語課衍射課件

1、Key words And Terms Huygens-Fresnel principle 惠更斯-菲涅耳原理 single-slit diffraction 單縫衍射angle of diffraction 衍射角half-wave zone 半波帶circular aperture diffraction 圓孔衍射Airy disk 愛里斑angle of minimum resolution 最小分辨角 grating 光柵grating constant 光柵常數(shù)missing order 缺級(jí)X-ray diffraction X射線衍射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 在波的傳播過程中，波前上的每一點(diǎn)都可看作是發(fā)射子波（次波）的波源，在其后的任一時(shí)刻，這些子波的包跡就成為新的波陣面。菲涅耳假定 波在傳播過程中，從同一波陣面上各點(diǎn)發(fā)出的子波，

4、經(jīng)傳播而在空間某點(diǎn)相遇時(shí)，產(chǎn)生相干疊加。菲涅耳還指出： 波面是一個(gè)等位面，其上各點(diǎn)相位相同。 次波在P點(diǎn)的振幅與距離r成反比。 dA面元所發(fā)出的次波的振幅與dA面積成正比。 隨dA面元的法線與r之間的夾角增大而減小。數(shù)學(xué)表達(dá)式 波面S上所有面元dA在P點(diǎn)的合振動(dòng)：式中C為比例系數(shù)，K()為傾斜因數(shù), K()K() =0 當(dāng) 時(shí) 1 當(dāng) = 0 時(shí)Wave front*S衍射屏觀察屏a 10 - 3 a衍射屏離光源或接收屏為有限遠(yuǎn)*S衍射屏觀察屏L1L2衍射屏與光源和接收屏為無限遠(yuǎn)遠(yuǎn)場(chǎng)衍射近場(chǎng)衍射(2)Fraunhofer diffraction 夫瑯禾費(fèi)衍射(1) Fresnel diffra

5、ction 菲涅耳衍射 3. 衍射的分類:Parallel rays of monochromatic light passing through the narrow slitI18.2 Diffraction by a single slit 31-1（衍射角 ：向上為正，向下為負(fù)）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 中央明紋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:波長(zhǎng)越長(zhǎng)，條紋寬度越寬；（2） 縫寬變化對(duì)條紋的影響；縫寬越小，條紋寬度越寬當(dāng) 時(shí)，只顯出單一的明條紋 單縫的幾何光學(xué)像幾何光學(xué)是波動(dòng)光學(xué)在/a 0 時(shí)的

8、極限情形(3)單縫衍射的動(dòng)態(tài)變化單縫上移，零級(jí)明紋仍在透鏡光軸上. 單縫上下移動(dòng)根據(jù)透鏡成像原理衍射圖不變 . (4)入射光非垂直入射時(shí)光程差的計(jì)算Monochromatic light falls on a transmission diffraction grating at an angle to the angle P728 31-33（中央明紋向下移動(dòng)）（中央明紋向上移動(dòng)） 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 焦平面上原來3 級(jí)暗紋處，現(xiàn)在明暗情況如何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 幾何光學(xué)與波動(dòng)光學(xué)的區(qū)別幾何光學(xué) : 物點(diǎn) 象點(diǎn)(經(jīng)透鏡)物(物點(diǎn)集合) 象(象點(diǎn)集合)不考慮艾里斑物點(diǎn) 象斑( 經(jīng)透鏡 )波動(dòng)光學(xué) :物(物點(diǎn)集合) 象(象斑集合)考慮艾里斑The ability that a optical devise can just distinct two points being very close together.可分辨剛可分辨不可分辨 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哈勃望遠(yuǎn)鏡基本信息 長(zhǎng)：13.2米 寬：4.2米 重：11噸 主鏡口徑：2.4米 副鏡口徑：0.3米 軌道：612公里，相對(duì)赤道傾斜28.5度 軌道周期：97分鐘 軌道速度：28,000公里/小時(shí) 成本：22億美元（發(fā)射） 壽命：約20年 眼睛的最小分辨角為設(shè)人離車的距離為 d 時(shí)，恰能分辨這兩盞燈。取在迎面駛來的汽車上，兩盞前燈相距120 cm ，設(shè)夜間人眼瞳孔直徑為5.0 mm ，入射光波為 550 nm。例人在離汽車多遠(yuǎn)的地方，眼睛恰能分辨這是兩盞燈？求解s =120 cmd由題意有觀察者 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? (要識(shí)別牌照上的字劃間的距離為5cm.在160km高空的照相機(jī)的孔徑需要大)? ( assume = 500nm)Solution:Example I00I18.4 Diffraction in the

14、 Double-slit Experiment 31-3Intensity of the Double-slit Experiment constructivedestructivead flensI設(shè)雙縫的每個(gè)縫寬均為a，在夫瑯禾費(fèi)衍射下，每個(gè)縫的衍射圖樣位置是相重疊的。雙縫干涉單縫衍射雙縫衍射（2）在 時(shí)，雙縫衍射的強(qiáng)度分布情況變?yōu)槔硐氲臈钍细缮娴膹?qiáng)度分布情況 結(jié)論：（1）雙縫衍射的強(qiáng)度曲線是單縫衍射強(qiáng)度對(duì)雙縫干涉強(qiáng)度進(jìn)行調(diào)制的結(jié)果DestructiveDouble-slit interferenceOne-slit diffractionConstructiveDouble-slit i

15、nterference強(qiáng)度為零的衍射光相干，相長(zhǎng)干涉的強(qiáng)度仍為零缺級(jí)Missing order： p, q為互質(zhì)整數(shù)比時(shí)，缺 np 級(jí)缺第 3 ， 6、9、12 級(jí)1.GratingTypes: b+aReflection gratingb+aTransmission gratinga 透光部分的寬度d=a + b 光柵常數(shù)b 不透光部分的寬度 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點(diǎn)為主極大時(shí)Bright fringe,明紋，主極大oscreenLens（a+b）sina+bQNEQEQDark fringe：N個(gè)縫在Q點(diǎn)的N個(gè)振幅的矢量合為零Combine (1)、(2)暗紋間距=(主明紋間距/N) 相鄰主明紋間有 N1 個(gè)暗紋和 N2 個(gè)次明紋。ENE3E2E1如 N = 4,有三個(gè)極小1234 /241 1234 3 /2IN2I0單sin048-4-8( /d)單縫衍射 輪廓線光柵衍射光強(qiáng)曲線N = 4

17、a+b= 4a3. Discussion:(2) missing orders 缺級(jí)(1) The maximum order 最高級(jí)次 p,q為互質(zhì)整數(shù)比時(shí)，缺 np 級(jí)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 的單色光垂直入射到光柵上，測(cè)得第3級(jí)主極大的衍射角為30o，且第4級(jí)為缺級(jí)。求：（1）光柵常數(shù)d；（2）透光縫最小寬度a；（3） 對(duì)上述 a、d 屏幕上可能出現(xiàn)的譜線數(shù)目。d =3 m （2）缺4級(jí)a =0.75 m （3）m = 0， 1， 2， 3， 59條！Example:例 用每毫米有500條柵紋的衍射光柵觀察鈉光譜線問：1、光線垂直入射； 2、光線以30度角入射時(shí)，最多能看到第幾級(jí)條紋？解：1、最多條紋數(shù)由決定2、fABC第三級(jí)條紋第五級(jí)條紋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條刻痕的平面光柵上，求第三級(jí)光譜的張角.解紅光紫光 不可見第三級(jí)光譜的張角第三級(jí)光譜所能出現(xiàn)的最大波長(zhǎng)綠光 In 1885, Roentgen d