大學(xué)物理雙語奧本漢姆ChapOpticDif

1、Chapter 31 Diffraction and Polarization 1. Diffraction of Light 2. Diffraction Gratings 3. X-Ray Diffraction 4. Polarized Light When the slip wider, light travels in straight line. 31-1. Diffraction of Light (P703) 1. Diffraction (衍射衍射) by a single slit screen shadow screen When the slip gets narrow

2、, the light produce a diffraction pattern on the screen. When monochromatic (單色) light from a distant source passes through a narrow slit or obstacle produces a diffraction pattern (光能繞過障礙物的邊緣傳播形成 具有明暗相間的衍射圖樣) ) is called diffraction of light (P703)(P703). Condition of diffraction: the width of slit

3、 (dimension of barrier) is similar to the wavelength a 波傳到的任何一點都是子波的波源，各次級子波 在空間某點的相干疊加，就決定了該點波的強度。 Hugens-Fresnels principle Recalling: The method discussing location of diffraction pattern for a single-slit diffraction is called fresnel half-wave-zone method (半波帶半波帶). 2. Locating the diffraction b

4、ands (P704) * S f f a L L A B slit a E O P sin max a Path difference of AP (b) Between center and first minimum; (c) The first minimum; (d) Near secondary maximum. See Fig.31-8 in P706 )sin( 2 l l x 當(dāng)當(dāng) 增加增加,半波帶數(shù)增加半波帶數(shù)增加, ,未被抵消的未被抵消的 半波帶面積減少半波帶面積減少, ,所以光強所以光強I I 變小變小. . i.e. , I 31-2. Diffraction by

5、a Circular Aperture Diffraction pattern of a circular aperture (P710): Basic arrangement of experiment S * d l l L 1 f Based on theoretical calculation, the first minimum of diffraction pattern of a circular aperture of diameter d (radius r) locates (第一第一 級暗環(huán)的衍射角滿足級暗環(huán)的衍射角滿足): rd l ll l 61. 022. 1sin

6、 1 dr l ll l 22. 161. 0sin 11 Angular-radius of central maximum (艾里斑艾里斑): If d l l, diffraction cant be seen 僅當(dāng)通光孔徑足夠大時僅當(dāng)通光孔徑足夠大時, ,艾里斑才可能很小艾里斑才可能很小. . 占入射光總 光強的84% d d l l AiryAiry spot getting small The angular separation of the two point sources is such that the central maximum of the diffraction

7、 pattern of one source is centered on the first minimum of the diffraction pattern of the other a condition called Rayleighs criterion for resolvability. 瑞利判據(jù)瑞利判據(jù)：如果一個點光源的衍射圖像的中央最亮處剛好與另一個點光源的衍射圖像：如果一個點光源的衍射圖像的中央最亮處剛好與另一個點光源的衍射圖像 第一個最暗處相重合第一個最暗處相重合, 認為這兩個點光源恰好能為這一光學(xué)儀器所分辨。認為這兩個點光源恰好能為這一光學(xué)儀器所分辨。 Resolv

8、ability( (分辨分辨) ) only the intensities are affected. 31-4. Diffraction Gratings ( (衍射光柵衍射光柵)()(P713) One of the most useful tools in the study of light and of objects that emit and absorb light is the diffraction grating. a b P O 1. Characteristic parameters (1) The width of a slit: a (2) Separation

9、 between slits: d It is also called grating spacing 光柵常數(shù)光柵常數(shù): d=a+b (10-4 10-6m) 2. The diffraction pattern of gratings Diffraction-pattern of gratings is the superposition of single-slit diffraction and N-slit interference. . If N rulings occupy a total width w, then d = w/N (3) For grating, the sl

10、its on it are often called rulings (劃線劃線) or lines. 光柵公式 (i) If the path length difference between adjacent rays is an integer number of wavelengths, i.e. l l mdba sinsin)( (m=0,1,2,) principal maxima The important difference between a double-slit and multiple-slit diffraction pattern is that bright

11、 maxima are much sharper (b) using a polarizer which is adjusted to absorb most of the polarized light reflected from the waters surface, and any fish to be seen more readily. P Brewster Brewster 或或 起偏角起偏角 i0 0 + +r0 0 = 90 = 90 from 020201 cossinsininrnin Brewsters law We have 21 1 2 0 tann n n i T

12、he amount of polazization in the reflected beam depends on the angle, varying from no polazization at normal incident to 100 percent polazization at an angle known as the polarizing angle, P. Solution: 56 B i 50. 1tan B i 50. 1 21 n The index of refraction of glass to the air (玻璃對玻璃對 空氣空氣) is . Find

13、 the angle of Brewsters. Example: Conclusion: 0sin a opposite to the condition of interference pattern l l l l sin i.e.a bright, 3 , 2 , 1 2 )12( dark, 3 , 2 , 1 sin mm mm al l l l Angular-width(角寬度角寬度): a l l 22 10 tansin For central bright fringe: Linear-width: a ffx l l 2ant2 10 whena 0 x 1:半角寬度

14、0 2 1 x a f x l l half of the central width. 其他明紋寬度為中央明紋寬度的一半其他明紋寬度為中央明紋寬度的一半 tansinaa For 1-order dark fringe, l l f x a 1 a f x l l 1 Similarly, for 2-order dark fringe, a f x l l2 2 Position of 1th dark fringe一級暗紋坐標(biāo)一級暗紋坐標(biāo) Position of 2th dark fringe Width of each order of bright fringes: 3. Inten

15、sity in single-slit diffraction (P705) (a) The central maximum; (b) Between center and first minimum; (c) The first minimum; (d) Near secondary maximum. See Fig.31-8 in P706 )sin( 2 l l x 當(dāng)當(dāng) 增加增加,半波帶數(shù)增加半波帶數(shù)增加, ,未被抵消的未被抵消的 半波帶面積減少半波帶面積減少, ,所以光強所以光強I I 變小變小. . i.e. , I The angular separation of the tw

16、o point sources is such that the central maximum of the diffraction pattern of one source is centered on the first minimum of the diffraction pattern of the other a condition called Rayleighs criterion for resolvability. 瑞利判據(jù)瑞利判據(jù)：如果一個點光源的衍射圖像的中央最亮處剛好與另一個點光源的衍射圖像：如果一個點光源的衍射圖像的中央最亮處剛好與另一個點光源的衍射圖像 第一個最

17、暗處相重合第一個最暗處相重合, 認為這兩個點光源恰好能為這一光學(xué)儀器所分辨。認為這兩個點光源恰好能為這一光學(xué)儀器所分辨。 Resolvability( (分辨分辨) )& Rayleighs criterion( (判據(jù)判據(jù)) )(P710): It can be seen from the text given in page 710 that d d l l Increasing Increasing R R The condition of two objects are barely resolved by this criterion of an angle separation R (最小分辨角最小分辨角 ): d R l l 22. 1 arcsin For small angle, d R l l 22. 1 (Rayleighs criterion) l l 22. 1 1d R R Resolvability(分辨本領(lǐng)): s 1 d * * s 2 R R 2. Partially polarized light (部分部分偏振光偏振光) Its field oscillations are neither completely random nor parallel to a single axis (the e