light interference

1. light interference 1) Young’s Double slit experiment The positions of bright fringes: K = 0，1，2，... The positions of dark fringes: K = 1，2，... The distance between adjacent bright/dark fringes:

2. 2) Interference of equal inclination The conditions of bright fringes: The conditions of dark fringes: For one incident angle, if the reflected lights form bright fringe then the transmitted lights for dark fringe.

3. 3) Interference of equal thickness a) Interference in a wedge-shaped film Bright fringe

4. The thickness of film for the bright fringes: The thickness of film for the dark fringes:

5. The thickness difference of the film between two adjacent bright/dark fringes: The difference on the surface between two adjacent bright/dark fringes:

6. b) Newton’s rings The radii of bright fringes in Newton’s rings: The radii of dark fringes in Newton’s rings:

7. 1 2 2ˊ 1ˊ 4) Michelson Interferometer The relationship between the distance of mirror M1Δdand the number of moved fringes m:

8. §3-4 light diffraction 1) Classification of light diffraction A. Fraunhofer Single Slit Diffraction Diffraction of parallel lights

9. B. FresnelSingle Slit Diffraction

10. 2) Comparison of diffraction & interference Yellow light Intensity distribution Pattern of diffraction Pattern of interference

11. white light Pattern of diffraction Pattern of interference

12. 3) Fraunhofer Single Slit Diffraction A. Experimental set-up B. results

13. C. Discussion Fresnel-zone half band Method 菲涅耳“半波带法” The width of the slit is a. Assume light A, A1, A2, A3 and B pass through the slit. The optical difference between light A and light B is: Divided BC with λ/2. Draw lines from the divided points parallel with AC. Divided the wave surface in the slit into several half bands.

14. The number of the half bands in the slit: It depends on the diffraction angle θ.

15. The phase difference of two adjacent half bands is: π The superposition of these two half bands results in destructive interference. For a given diffraction angle θ, if the wave surface is divided into even half bands, the corresponding point on the viewing screen is the center of dark fringe.

16. D. Conditions of bright/dark fringes in light diffraction 1) Condition of dark fringes: 2) Condition of bright fringes: 3)When θ=0, Middle bright fringe Θis variable.

17. E. location of bright/dark fringes in light diffraction x I The distance between k fringe and the O axis is: Small angle approximation f: focal length of the lens

18. 1) If the fringe is dark: x I

19. 2) If the fringe is bright: x I

20. F. The width of middle bright fringe The width of the middle bright fringe equals the location difference between k=1 and k=-1 dark fringes. The location of k=1 dark fringe: L0 in this figure The width of middle bright fringe:

21. If all the fringes located in the middle of the viewing screen, no diffraction is observed. The light travels in straight line. The width of middle bright fringe: For a given lens and used light wavelength, the smaller the slit, the more obvious the diffraction is.

22. Example 3-1 In Fraunhofer single slit diffraction, the width of the slit a=100λ, the focal length of the lens f=40 cm. Find: the width of middle and k=1 bright fringes. Solution: The width of middle bright fringe is: The width of k=1 bright fringe is the location difference between k=2 and k=1 dark fringes:

23. Example 3-2 In Fraunhofer single slit diffraction, the wave surface in the slit corresponding to k=3 dark fringe can be divided into half bands. If the width of the slit decreases into its half, the k=3 dark fringe will turn to be fringe. bright

24. 4) Circle Aperture Fraunhofer Diffraction A. Experimental set-up 爱里斑 Ariy Spot  — half angle of Ariy spot

25. B. Discuss )θ The first dark fringe: D: The diameter of the circle aperture Θ: the half angle of Ariy spot Θis very small.

26. 5) Resolution of optical systems S1 S1  ( (  S2 S2 Slit Slit Once you are able to see two separate headlights, you describe the light sources as being resolved. A. Resolution of single slit The diffraction pattern is distinguished. The two light sources are resolved. The diffraction pattern overlapped. The two light sources are not well resolved.

27. Rayleigh’s criterion 瑞利判据 When the central maximum of the diffraction pattern of one source falls on the first minimum of the diffraction pattern of another source, the sources are said to be just resolved. The limiting condition of resolution is known as Rayleigh’s criterion. 点物 S1 的衍射中心的最大恰好与另一个点物 S2 的第一衍射的极小相重合时，恰可分辨两物点。

28. For the single slit, the first minimum diffraction (dark fringe) satisfies the following relationship: S1 (  S2 Slit That is: Therefore, the limiting angle of resolution for a slit with width a is:

29. B. Resolution of circle aperture S1 S2 S1 S2 100% 73.6% S1 S2 resolved Just resolved Can not resolved

30. The limiting angle of resolution for a circle aperture with diameter D is: Compare with limiting angle of single slit

31. 6) Resolving power 分辨本领 Increasing D or decreasing λcan enhance the resolving power.

32. §3-5 the diffraction grating Planar grating concave grating

33. 1) Kinds and construction of grating 透 射 光 栅 反射光栅 刻痕处不透光 Transmission grating Reflection grating

34. 2) Grating constant 光栅常数 a: width of transmission part b: width of reflection part For example, a grating ruled with 5000 lines/cm has a grating constant / slit spacing of

35. 3) The function of diffraction grating Single slit diffraction Decreasing the width of the slit a can enhance the resolution of the diffraction, but it will decrease the energy of middle fringe, which will make the diffraction fringe unclear. Grating: many many narrow slits

36. 4) Schematic diagram of diffraction grating  A E  F G O  a P f b

37. 5) Intensity distribution in diffraction grating I u v u: intensity distribution of diffraction grating v: intensity distribution of single slit diffraction

38. Diffraction grating: the superposition of many single slit-diffraction 光栅是单缝衍射和多缝干涉的共同作用效果，是多个单缝衍射叠加（干涉）的结构