1. P33 - 1 Class 33: Outline Hour 1: Interference Hour 2: Experiment 13: Interference

2. P33 - 2 Last time: Microwaves (mw) This time: Visible (red) light: How in the world do we measure 1/10,000 of a cm?

3. P33 - 3 We Use Interference This is also how we know that light is a wave phenomena

4. P33 - 4 Interference: The difference between waves and bullets No Interference: if light were made up of bullets Interference: If light is a wave we see spreading and addition and subtraction

5. P33 - 5 Interference: The difference between waves and bullets Link to interference applet

6. P33 - 6 Interference Interference: Combination of two or more waves to form composite wave – use superposition principle. Waves can add constructively or destructively Conditions for interference: 1.Coherence: the sources must maintain a constant phase with respect to each other 2.Monochromaticity: the sources consist of waves of a single wavelength

7. P33 - 7 Demonstration: Microwave Interference

8. P33 - 8 Interference – Phase Shift Look here as function of time Consider two traveling waves, moving through space: Look here as function of time Constructive Interference Destructive Interference

9. P33 - 9 Microwave Interference Link to mpeg

10. P33 - 10 Interference – Phase Shift What can introduce a phase shift? 1.From different, out of phase sources 2.Sources in phase, but travel different distances 1.Thin films 2.Microwave Demonstration 3.Double-slit or Diffraction grating

11. P33 - 11 PRS Question: Interference

12. P33 - 12 Extra Path Length In Phase Here Still in Phase Here (m=0, ±1, ±2…)

13. P33 - 13 Extra Path Length In Phase Here Not in Phase Here (m=0, ±1, ±2…)

14. P33 - 14 Thin Film Interference - Iridescence

15. P33 - 15 Thin Film Interference - Iridescence

16. P33 - 16 Thin Film Interference

17. P33 - 17 Thin Film: Extra Path d Extra path length ~ 2d Oil on concrete, non-reflective coating on glass, etc.

18. P33 - 18 Phase Shift = Extra Path? What is exact relationship between  L &  ?

19. P33 - 19 Two Transmitters

20. P33 - 20 Microwave Interference Link to mpeg

21. P33 - 21 Two In-Phase Sources: Geometry

22. P33 - 22 Interference for Two Sources in Phase (1) Constructive: (2) Destructive:

23. P33 - 23 In-Class: Lecture Demo From our lecture demo, we measure: L ~ 1.16 m; d ~ 0.24 m; y destructive ~ ? m Estimate the wavelength & frequency of our microwaves For m = 0 (the first minimum): Just Found:

24. P33 - 24 How we measure 1/10,000 of a cm is smaller by 10,000 times. But d can be smaller (0.1 mm instead of 0.24 m) So y will only be 10 times smaller – still measurable Question: How do you measure the wavelength of light? Answer: Do the same experiment we just did (with light)

25. P33 - 25 The Light Equivalent: Two Slits

26. P33 - 26 Young’s Double-Slit Experiment Bright Fringes: Constructive interference Dark Fringes: Destructive interference

27. P33 - 27 PRS Question Double Slit Path Difference

28. P33 - 28 Lecture Demonstration: Double Slit

29. P33 - 29 Diffraction

30. P33 - 30 Diffraction Diffraction: The bending of waves as they pass by certain obstacles No spreading after passing though slits Spreading after passing though slits No Diffraction Diffraction

31. P33 - 31 Single-Slit Diffraction Destructive interference: “Derivation” (Motivation) by Division: Divide slit into two portions: Don’t get confused – this is DESTRUCTIVE!

32. P33 - 32 Intensity Distribution

33. P33 - 33 Putting it Together

34. P33 - 34 PRS Question: Two Slits with Width

35. P33 - 35 Two Slits With Finite Width a With more than one slit having finite width a, we must consider 1.Diffraction due to the individual slit 2.Interference of waves from different slits

36. P33 - 36 Two Slits With Finite width a Zero Order Maximum First Order Maximum First Diff. Minimum

37. P33 - 37 Lecture Demonstration: Double Slits with Width

38. P33 - 38 Babinet’s Principle Case I: Put in a slit, get diffraction Case II: Fill up slit, get nothing Case III: Remove slit, get diffraction By superposition, the E field with the slit and the E field with just the filling must be exact opposites in order to cancel: So the intensities are identical:

39. P33 - 39 Experiment 13: To Do Download Excel File! 1.Single Slit – 4 different slits. Use known width a and zeroes y destructive to Estimate wavelength of red light 2.Human Hair (Babinet says just single slit). Use red (from 1) and zeroes y destructive to Estimate thickness of hair 3.Double Slit – 4 different slits. Use known spacing d and zeroes to Estimate wavelength of red light 4.CD Track Spacing (Diffraction Grating) Estimate track spacing