大学物理双语奥本汉姆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 (单色) light from a distant source passes through a narrow slit or obstacle produces a diffraction pattern (光能绕过障碍物的边缘传播形成 具有明暗相间的衍射图样) ) is called diffraction of light (P703)(P703). Condition of diffraction: the width of slit

3、 (dimension of barrier) is similar to the wavelength a 波传到的任何一点都是子波的波源，各次级子波 在空间某点的相干叠加，就决定了该点波的强度。 Hugens-Fresnels principle Recalling: The method discussing location of diffraction pattern for a single-slit diffraction is called fresnel half-wave-zone method (半波带半波带). 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 当当 增加增加,半波带数增加半波带数增加, ,未被抵消的未被抵消的 半波带面积减少半波带面积减少, ,所以光强所以光强I I 变小变小. . 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 级暗环的衍射角满足级暗环的衍射角满足): 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 仅当通光孔径足够大时仅当通光孔径足够大时, ,艾里斑才可能很小艾里斑才可能很小. . 占入射光总 光强的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. 瑞利判据瑞利判据：如果一个点光源的衍射图像的中央最亮处刚好与另一个点光源的衍射图像：如果一个点光源的衍射图像的中央最亮处刚好与另一个点光源的衍射图像 第一个最暗处相重合第一个最暗处相重合, 认为这两个点光源恰好能为这一光学仪器所分辨。认为这两个点光源恰好能为这一光学仪器所分辨。 Resolv

8、ability( (分辨分辨) ) only the intensities are affected. 31-4. Diffraction Gratings ( (衍射光栅衍射光栅)()(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 光栅常数光栅常数: 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 (划线划线) or lines. 光栅公式 (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 (玻璃对玻璃对 空气空气) 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(角宽度角宽度): a l l 22 10 tansin For central bright fringe: Linear-width: a ffx l l 2ant2 10 whena 0 x 1:半角宽度

14、0 2 1 x a f x l l half of the central width. 其他明纹宽度为中央明纹宽度的一半其他明纹宽度为中央明纹宽度的一半 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一级暗纹坐标一级暗纹坐标 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 当当 增加增加,半波带数增加半波带数增加, ,未被抵消的未被抵消的 半波带面积减少半波带面积减少, ,所以光强所以光强I I 变小变小. . 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. 瑞利判据瑞利判据：如果一个点光源的衍射图像的中央最亮处刚好与另一个点光源的衍射图像：如果一个点光源的衍射图像的中央最亮处刚好与另一个点光源的衍射图像 第一个最

17、暗处相重合第一个最暗处相重合, 认为这两个点光源恰好能为这一光学仪器所分辨。认为这两个点光源恰好能为这一光学仪器所分辨。 Resolvability( (分辨分辨) )& Rayleighs criterion( (判据判据) )(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(分辨本领): 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