1. Modern Optics Lab Lab 6 Part 2: Interference Experiments  Observe interference by plane-parallel plates: Measure the thickness of the plates based on the theory.  Michelson and Fabry-Perot interferometers: Determine the wavelength of the laser (again). Topics

2. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Interference by Plane-Parallel Plates n >1 d ii tt n=1 Path length difference: Destructive interference: Constructive interference: (Remember: The light undergoes a 180º phase shift due to reflection at the bottom.)

3. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Interference by Plane-Parallel Plates Constructive interference:

4. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Interference by Plane-Parallel Plates Plate ii  Lens Use a lens to focus laser beam on plate (avoiding thickness- averaging) and simultaneously have it diverge after leaving the plate (making it possible to see multiple interference maxima).

5. Modern Optics Lab Lab 6 Part 2: Interference Experiments Thick plates: Use small angle. Very thin plates: Use angle near 45 degrees.

6. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Setting up the Glass Plate Experiment – Zero Degree Adjustment Top view Laser Glass plate Short component holder Make sure that the glass plate reflects light back into the laser to find the zero degree incident angle position. Also, make sure the laser hits the glass plate at a place where there is air behind the glass plate – no metal pieces.

7. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Converging the beam with a lens Top view Laser 136mm lens  136mm

8. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Studying the symmetry of the interference pattern for small incident angles Laser 136mm lens Screen

9. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Measuring  m/  for thick glass plate Laser 136mm lens Big screen (make sure angle of incidence is 90  ) R

10. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Measuring  m/  for thick glass plate Screen S  m = 5  = S/R (in Radians)

11. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Measuring  m/  for thick glass plate Screen S  m = 6  = S/R (in Radians)

12. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Measuring  m/  for microscope slide Laser 136mm lens Tape microscope slide to component holder (you can use a tiny piece of double stick tape).

13. Modern Optics Lab Lab 6 Part 2: Interference Experiments VI.C Measuring  m/  for microscope cover slide (very thin glass) Laser 136mm lens

14. Modern Optics Lab Lab 6 Part 2: Interference Experiments Using the micrometer to measure thickness 0 5 10 30 35 40 25 0 5 10 30 35 40 25 11.5mm 0.32mm 0.33mm Thickness = 11.5mm + 0.33mm = 11.83mm Please be gentle to the micrometer! It is a delicate instrument!

15. Modern Optics Lab Lab 6 Part 2: Interference Experiments The Fabry-Perot Interferometer Highly reflective mirrors d d*

16. Modern Optics Lab Lab 6 Part 2: Interference Experiments d=m  Bright

17. Modern Optics Lab Lab 6 Part 2: Interference Experiments d Bright  Dark

18. Modern Optics Lab Lab 6 Part 2: Interference Experiments d Dark  Bright How far do you have to move the mirror to go from the m th to the (m+1) st interference maximum?

19. Modern Optics Lab Lab 6 Part 2: Interference Experiments d In summary: When the mirror is moved, the outgoing laser spot “blinks” as you go from constructive to destructive to constructive interference. 2d=m 2d=(m+1) Etc. 2d=(m+2)

20. Modern Optics Lab Lab 6 Part 2: Interference Experiments Using a Diverging Laser Beam d 2d*=2d=m (m+1)  >2d*>m 2d*=(m+1) Bright 2d*=(m+1) Bright (m+1)  >2d*>m Dark

21. Modern Optics Lab Lab 6 Part 2: Interference Experiments Moving Mirror by a bit Using a Diverging Laser Beam d 2d*=(m+1)  Bright Dark (m+2)  >2d*>(m+1) Dark (m+1)  >2d*>m 2d*=(m+1)  (m+2)  >2d*>(m+1)

22. Modern Optics Lab Lab 6 Part 2: Interference Experiments As you move the mirror, the center of the pattern alternates between bright and dark. The rings move outwards as “new” center maxima “pop up” and the outermost rings “disappear”. Count=0Count=1 Count=2 Etc.

23. Modern Optics Lab Lab 6 Part 2: Interference Experiments Accuracy of Fabry-Perot Interferometer Wavelength Measurement Suppose you can adjust the mirror with a micrometer screw to an accuracy of ± 0.1  m: If you move the mirror by /2 (count=1), your wavelength will be accurately measured to within 0.1  m*2 = 200nm (quite poor considering a laser wavelength of around 600nm). If you move the mirror by 1000*  /2 (count=1000), you will calculate your wavelength by dividing the distance the mirror was moved by 1000.  Your accuracy will be 0.1  m/500=0.2nm. That is a quite useful accuracy!

24. Modern Optics Lab Lab 6 Part 2: Interference Experiments Aligning an FP interferometer: Use a narrow laser beam Mirrors not parallel: The reflected beams are too far apart to interfere! Screen Screen view

25. Modern Optics Lab Lab 6 Part 2: Interference Experiments Aligning an FP interferometer Vertical tilt needs adjustment Horizontal tilt needs adjustment Both horizontal and vertical tilt needs adjustment Adjust mirror tilts until all spots coincide. Then add the lens to the setup. Move lens left/right/up/down until you illuminate the center of the ring pattern. You can also do some fine adjustment of the tilt to try to get a nicer ring pattern.

26. Modern Optics Lab Lab 6 Part 2: Interference Experiments The Michelson Interferometer Laser Adjustable (tilt) mirror Moveable (translational) mirror Screen Semi-transparent mirror

27. Modern Optics Lab Lab 6 Part 2: Interference Experiments The Michelson Interferometer – with lens added Laser Adjustable (tilt) mirror Moveable (translational) mirror Screen Lens to diverge beam