W14D2: Interference and Diffraction Experiment 6

1. W14D2:Interference and DiffractionExperiment 6 Today’s Reading Course Notes: Sections 14.4-14.9

2. PS 11 is only for practice. It will not be graded. Next Reading Assignment W14D3 Course Notes: Sections 14.9-14.11 Final Exam Mon May 20 9 am-12 noon in Johnson Athletic Center Review Sessions TBA Announcements

3. Outline Review Interference Diffraction Interference and Diffraction Experiment 6

4. Interference – Phase Shift constructive destructive What can introduce a phase shift? • From different, out of phase sources • Sources in phase, but travel different distances because they come from different locations 4

5. Microwave Interference http://youtu.be/-O8V2QHkaLI http://web.mit.edu/viz/EM/movies/light/distant.avi 5

6. ReviewThe Light Equivalent:Two Slits

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

8. Two In-Phase Sources: Geometry 8

9. Interference for Two Sources in Phase Constructive: Destructive: 9

10. Intensity Distribution What is intensity of two waves out of phase? Use Average Intensity:

11. Average Intensity Average intensity:

12. Diffraction

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

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

15. Intensity Distribution

16. Concept Question: Lower Limit? Using diffraction seems to be a useful technique for measuring the size of small objects. Is there a lower limit for the size of objects that can be measured this way? • Yes – and if we used blue light instead of red light we can measure even smaller objects than the ones we measure using red light • Yes – and if we used blue light instead of red light we couldn’t even measure objects as small as the ones we measure using red light • No

17. Concept Q. Answer: Lower Limit? Answer: 1. we have the condition that There is a lower limit imposed by the condition, namely that Once the feature size a is as small as the light wavelength you can’t go to an angle large enough to satisfy the above equation for any m > 0. Blue light has a shorter wavelength than red light, so you can measure smaller sizes using blue light.

18. Interference & DiffractionTogether

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

20. Lecture Demonstration:Double Slits with Diffraction http://tsgphysics.mit.edu/front/?page=demo.php&letnum=P%2010&show=0

21. Two Slits With Finite Width

22. Interference & Diffraction

23. Con. Q.: Interference & Diffraction Coherent monochromatic plane waves impinge on two long narrow apertures (width a) that are separated by a distance d with d > a. • The resulting pattern on a screen far away is shown above, with distantly-spaced zeroes of the envelope, as indicated by the length X above, and closely-spaced zeroes of the rapidly varying fringes, as indicated by the length Y above. • Which length in the pattern above is due to the finite width a of the apertures? • X • Y • X and Y • Neither X nor Y

24. Concept Q. Ans.: Inter. & Diffraction • Answer: 1. The ‘envelope’ length X depends on slit width. • You could infer this in two ways. • Slit width a < slit separation d. Angles and size scale inversely, so the bigger features come from a. • Interference patterns are roughly equal in magnitude while diffraction creates a strong central peak. So the envelope is from diffraction.

25. Worked Problem: Interference In an experiment you shine red laser light (600 nm) at a slide and see the following pattern on a screen placed 1 m away: You measure the distance between successive fringes to be 20 mm a) Are you looking at a single slit or at two slits? b) What are the relevant lengths (width, separation if 2 slits)? What is the orientation of the slits?

26. Solution: Interference (a) Must be two slits a d

27. Solution: Interference At 60 mm…

28. Concept Q.: Changing Wavelengths You just observed an interference pattern using a red laser. What if instead you had used a blue laser? In that case the interference maxima you just saw would be • closer together. • further apart. • came distance apart.

29. Concept Q. Ans.: Changing Colors Answer: 1. Closer Together Blue light is a higher frequency (smaller wavelength) so the angular distance between maxima is smaller for blue light than for red light

30. Experiment 6, Part I:Measure Laser Wavelength 30

31. Experiment 6, Part II:Interference from a CDDiffraction Gratingd = distance between openings 31

32. From 2 to N Slits

33. Experiment 6, Part II:Diffraction Grating: CD

34. Experiment 6, Part III:Measure Hair Thickness Single hair strand acts as a single slit (Babinet’s Principle)