1. 1 Chapter 33: Interference and Diffraction Homework: 17, 31, 37, 55 Cover Sections: 1, 2, 3, 4, 6, 7 Omit Sectons: 5, 8

2. 2 Outline:  Phase Difference and Coherence  Interference in Thin Films  Single Slit Diffraction Pattern  Two Slit Interference  Fraunhofer and Fresnel Diffraction  Diffraction and Resolution

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4. 4 33-1 Phase Difference and Coherence Phase Difference: The fractional part of a period which represents the offset in peak positions of waves. Coherence: The existence of a correlation between the phases of two or more waves such that interference effects can be observed. Interference: The variation with distance or time of the amplitude of a wave which results from the superposition of two or more waves.

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6. 6 33-2 Interference in Thin Films

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8. 8 Change in Wavelength n = index of refraction

9. 9  

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12. 12 Condition: Ray 1 and 2 will be out of phase by  radians for 589nm light. Path difference = 2t.

13. 13 33-3 Two-Slit Interference Pattern

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15. 15 central max m = 1 bright fringe y-axis m = 2 bright fringe m = 1 dark fringe m = 2 dark fringe m = 3 dark fringe bright/dark are symmetric L

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19. 19 Example: slit-separation d = 1.5mm. Light = 589nm. Bright fringes occur at: etc.

20. 20 Example: L = 3m. slit-separation d = 1.5mm. Light = 589nm. Bright fringe spacing = y3 – y2 = 1.17 mm

21. 21 Example: slit-separation d = 1.5mm. Light = 589nm. 2 nd Dark fringe occurs at: The 2 nd Dark fringe should occur between 1 st and 2 nd Bright fringes:

22. 22 33-4 Diffraction Pattern of a Single Slit

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24. 24 a = Slit-Width (a ≠ d)

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26. 26 Example: slit-width a = 0.200mm. Light = 589nm. Dark fringes occur at: etc.

27. 27 33-5 Using Phasors to Add Harmonic Waves (Omit)

28. 28 33-6 Fraunhofer and Fresnel Diffraction

29. 29 Fraunhofer and Fresnel Diffraction Patterns Fresnel Pattern: observed near obstacle causing diffraction. Fraunhofer Pattern: observed far from away from the obstacle. The criterion for determining near and far is the convergence angle of the light which makes up the pattern.

30. 30 33-7 Diffraction and Resolution

31. 31 First Diffraction Minimum of a Circular Aperture

32. 32 Rayleigh Criterion …occurs when two point sources of light are close enough together that light coming from them passes through a circular aperture so that the 1 st minimums of the diffraction patterns fall on the central maximum of the other. A single ellipsoid is seen instead of two separate objects.

33. 33 Rayleigh Criterion Formula …is a condition for the angle of convergence of rays emanating from the objects that pass through the aperture. This angle is called “alpha”, and occurs when:

34. 34 Summary: Phase Difference and Path Difference Coherence defined Interference in Thin Films Single Slit and Two Slit Patterns Fraunhofer and Fresnel Diffraction Diffraction limits ultimate resolution

35. 35 33-8 Diffraction Gratings Omit End of 33

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