1. Fundamental Physics II PETROVIETNAM UNIVERSITY FACULTY OF FUNDAMENTAL SCIENCES Vungtau, 2013 Pham Hong Quang E-mail: quangph@pvu.edu.vn

2. Chapter 7 Pham Hong Quang Fundamental of Drilling and Production 2 Diffraction

3. 7.1 Diffraction is a wave effect Pham Hong Quang Fundamental of Drilling and Production 3 In his 1704 treatise on the theory of optical phenomena (Opticks), Sir Isaac Newton wrote that "light is never known to follow crooked passages nor to bend into the shadow". He explained this observation by describing how particles of light always travel in straight lines, and how objects positioned within the path of light particles would cast a shadow because the particles could not spread out behind the object.

4. 7.1 Diffraction is a wave effect Pham Hong Quang Fundamental of Drilling and Production 4 On a much smaller scale, when light waves pass near a barrier, they tend to bend around that barrier and spread at an angles. This phenomenon is known as diffraction of the light, and occurs when a light wave passes very close to the edge of an object or through a tiny opening, such as a slit or aperture.

5. 7.1 Diffraction is a wave effect Pham Hong Quang Fundamental of Drilling and Production 5 Diffraction is a wave effect Interference pattern of light and dark bands around the edge of the object. Diffraction is often explained in terms of the Huygens principle, which states that each point on a wavefront can be considered as a source of a new wave.

6. 7.1 Diffraction is a wave effect Pham Hong Quang Fundamental of Drilling and Production 6 All points on a wavefront serve as point sources of spherical secondary wavelets. After a time t, the new position of the wavefront will be that of a surface tangent to these secondary wavefronts

7. 7.1 Diffraction is a wave effect Pham Hong Quang Fundamental of Drilling and Production 7 Using Fresnel's theory, a bright spot should appear behind a circular obstruction,

8. 7.2 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 8 D >> a, rays are parallel Divide the screen into two zones of width a/2 Find the first minima above the midpoint by pairing up rays from the top point of the top zone and the top point of the bottom zone Rays are in phase at the slit but must be out of phase by by λ /2 at screen The path length difference = a/2 sin θ Locate the First Minima

9. 7.2 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 9 Repeat for other pairs of rays in the upper zone and lower zone: the first dark fringe occurs when: a/2 sin θ = λ /2 a sin θ =λ first minima If we narrow the slit the angle must get bigger what happens when a = λ ?

10. 7.2 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 10 Repeat the process for paired rays (4) from corresponding points from each of the zones Rays are in phase at the slit but must be out of phase by by λ/2 at screen Subsequent Minima

11. 7.1 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 11 Intensity in Single-Slit Diffraction Pattern Light passing through a single slit can be divided into a series of narrower strips; each contributes the same amplitude to the total intensity on the screen, but the phases differ due to the differing path lengths:

12. 7.1 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 12 Slit of width D divided into N strips of width Δy. Each strip is a wave with intensity of I 0 /N. Path difference between two adjacent strips is and the corresponding phase angle difference is. The intensity of the diffraction is, by superposition, the vector sum of the N strips of light with N approaching infinity.

13. 7.1 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 13

14. 7.1 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 14 Phasor diagrams give us the intensity as a function of angle.

15. 7.1 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 15

16. 7.1 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 16

17. 7.1 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 17 Finally, we have the phase difference and the intensity as a function of angle:.

18. 7.2 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 18

19. 7.1 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 19

20. 7.2 Diffraction by a Single Slit Pham Hong Quang Fundamental of Drilling and Production 20

21. 7.3 Diffraction in the Double-Slit Experiment Pham Hong Quang Fundamental of Drilling and Production 21 Diffraction plus interference

22. 7.3 Diffraction in the Double-Slit Experiment Pham Hong Quang Fundamental of Drilling and Production 22

23. 7.4 Diffraction Gratings Pham Hong Quang Fundamental of Drilling and Production 23 Like the double slit arrangement but with a much greater number of slits (rulings), sometimes as many as several 1000 per millimeter Light passed through the grating forms narrow interference fringes that can be analyzed to determine the wavelength

24. 7.4 Diffraction Gratings Pham Hong Quang Fundamental of Drilling and Production 24 Here is the diffraction pattern for five slits:

25. 7.4 Diffraction Gratings Pham Hong Quang Fundamental of Drilling and Production 25 Position of maxima, where all waves interfere constructively are found with a familiar procedure: So the angle to a particular line depends on the wavelength being used

26. 7.4 Diffraction Gratings Pham Hong Quang Fundamental of Drilling and Production 26 Dispersion In order to distinguish different wavelengths that are close to each other a diffraction grating must spread out the lines associated with each wavelength. Dispersion is the term used to quantify this and is defined as

27. 7.4 Diffraction Gratings Pham Hong Quang Fundamental of Drilling and Production 27 Δθ is the angular separation between two lines that differ by Δλ. The larger D the larger the angular separation between lines of different λ. It can be shown that and D gets larger for higher order (m) and smaller grating spacing (d)

28. 7.4 Diffraction Gratings Pham Hong Quang Fundamental of Drilling and Production 28 Resolving Power To make lines that whose wavelengths are close together (to resolve them) the line should be as narrow as possible The resolving power is defined by where λ avg is the average of the two wavelengths studied and Δλ is the difference between them. Large R allows two close emission lines to be resolved. It can be shown that To get a high resolving power we should use as many rulings

29. 7.4 Diffraction Gratings Pham Hong Quang Fundamental of Drilling and Production 29 Three gratings illuminated with light of λ=589 nm, m = 1GratingNd(nm)θ D( o /μm) R A10000254013.423.210000 B20000254013.423.220000 C10000136025.546.310000

30. 7.5 Limits of Resolution; Circular Apertures Pham Hong Quang Fundamental of Drilling and Production 30 Resolution is the distance at which a lens can barely distinguish two separate objects. Resolution is limited by aberrations and by diffraction. Aberrations can be minimized, but diffraction is unavoidable; it is due to the size of the lens compared to the wavelength of the light.

31. 7.5 Limits of Resolution; Circular Apertures Pham Hong Quang Fundamental of Drilling and Production 31 For a circular aperture of diameter D, the central maximum has an angular width:

32. 7.5 Limits of Resolution; Circular Apertures Pham Hong Quang Fundamental of Drilling and Production 32 The Rayleigh criterion states that two images are just resolvable when the center of one peak is over the first minimum of the other.

33. 7.5 Limits of Resolution; Circular Apertures Pham Hong Quang Fundamental of Drilling and Production 33 On the left, there appears to be a single source; on the right, two sources can be clearly resolved.

34. 7.6 X-Ray Diffraction Pham Hong Quang Fundamental of Drilling and Production 34 Spacing between atomic layers in a crystal is the right size for diffracting X-rays; this is now used to determine crystal structure

35. 7.6 X-Ray Diffraction Pham Hong Quang Fundamental of Drilling and Production 35 Bragg’s law, θ is Bragg’s angle

36. 7.6 X-Ray Diffraction Pham Hong Quang Fundamental of Drilling and Production 36

37. 7.6 X-Ray Diffraction Pham Hong Quang Fundamental of Drilling and Production 37

38. 7.6 X-Ray Diffraction Pham Hong Quang Fundamental of Drilling and Production 38

39. 7.6 X-Ray Diffraction Pham Hong Quang Fundamental of Drilling and Production 39

40. 40 Pham hong Quang 40 PetroVietnam Universityg Thank you!