Modern Optics Lab Lab 9: Interferometer Experiments  Fabry-Perot or Michelson Interferometer Adjusting Measuring the wavelength of laser using an electronic fringe counter  Michelson Interferometer Measuring the index of refraction of air Derive an equation that can be used to get the index of refraction from fringe-counting as the pressure of air in a box changes  Michelson Interferometer Measuring the index of refraction of a glass plate using an electronic fringe counter  Fabry-Perot Interferometer Measuring the separation of the sodium doublet Topics

Modern Optics Lab Lab 9: Interferometer Experiments About Electronic Fringe Counting Etc. Photo Sensitive Detector (PSD) time I PSD

Modern Optics Lab Lab 9: Interferometer Experiments Simples Method: One level comparator time I PSD 123

Modern Optics Lab Lab 9: Interferometer Experiments Problems with single level comparator: Unwanted counts from noise time I PSD

Modern Optics Lab Lab 9: Interferometer Experiments Double Level Comparator (Schmitt-Trigger) time I PSD 123

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 1: Wavelength Measurement with either Fabry-Perot or Michelson Interferometer  Choose either the Fabry-Perot or the Michelson Interferometer to do this activity.  Use electronic counting to get an accurate measurement of the wavelength of the laser.

Modern Optics Lab Lab 9: Interferometer Experiments Laser Adjustable (tilt) mirror Photo-sensitive diode Semi-transparent mirror Experiment 1: Wavelength Measurement with Michelson Interferometer Schmitt- Trigger Oscilloscope Counter

Modern Optics Lab Lab 9: Interferometer Experiments Photo- sensitive diode Experiment 1: Wavelength Measurement with Fabry-Perot Interferometer Schmitt- Trigger Oscilloscope Counter Laser

Modern Optics Lab Lab 9: Interferometer Experiments Laser Adjustable (tilt) mirror Screen Semi-transparent mirror Experiment 2: Measure the Index of Refraction of Air with a Michelson Interferometer Pressure gauge Relief valve Hand Pump Pump isolation valve

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 2: Measure the Index of Refraction of Air with a Michelson Interferometer  Pump cell to a low pressure, then close the pump isolation valve (only close until you feel resistance and then at most another quarter turn – don’t overtighten).  Watch “fringe count” while slowly letting air back into the cell using the needle valve. When closing the needle valve, only close until you feel resistance – then stop and don’t tighten any further.  Change in pressure  P  change in index of refraction  n   n causes a shift of fringes  m (due to wavelength change in the box)  First find  Then use the equation n(P) to calculate n for various pressure.  Plot n versus P.

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 2: Measure the Index of Refraction of Air with a Michelson Interferometer Finding P (mm Hg)m (count) …0 …5 … etc. m P Slope of graph =  m/  P

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 2: Measure the Index of Refraction of Air with a Michelson Interferometer Finding n(P) and plotting the results P (mm Hg)m (count) …0… …5… …10… 15… 20… 25 etc. n(P) P

Modern Optics Lab Lab 9: Interferometer Experiments Hints for deriving :

Modern Optics Lab Lab 9: Interferometer Experiments Laser Adjustable (tilt) mirror Photo-sensitive diode Semi-transparent mirror Experiment 3: Measure the Index of Refraction of a Glass Plate with a Michelson Interferometer Glass Plate Angle Scale Schmitt- Trigger Oscilloscope Counter

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 3: Measure the Index of Refraction of a Glass Plate with a Michelson Interferometer  Measure the thickness t of the glass plate with the caliper.  Make sure that initially the glass plate is exactly perpendicular to the laser beam.  Make sure that photo-sensitive diode works (move the micrometer screw back and forth and check on the oscilloscope that the Schmitt-Trigger works well.) Reset the counter to zero.  Move rotation stage from 0  to nominal 10  or 15 . Please note that the scale is inaccurate. The corrected values for 5,10, and 15 degrees are written on the interferometer.  Record the fringe count m.  Reset the fringe counter.  Rotate glass plate back to zero and make sure you get the same m as before.  Calculate n: (Hint: You could use a spreadsheet)

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Rough Adjustment Sodium Lamp Mirror tilt adjustment screws

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Fine Adjustment Sodium Lamp Diffuser Note: When you move your eyes left/right or up/down the center dot should NOT change from bright to dark or from dark to bright when the tilts are perfectly adjusted.

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Fine Adjustment Sodium Lamp Diffuser Note: When you bring the mirrors closer together you will see fewer and fewer rings. Try to move the mirrors closer together but don’t get them too close - otherwise the mirrors will touch and everything will go out of alignment again.

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – The double ring pattern There are two sets of rings – one for each of the two yellow emission lines of the sodium lamp (they have only very slightly different wavelengths, so both appear in the same yellow). One of the two ring sets is shown dotted so you can more easily distinguish them.

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Moving the mirrors apart As the mirrors move apart, both ring-patterns move outwards and the center alternately appears bright and dark.

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Moving the mirrors apart The two ring sets move apart at slightly different rates  their separation changes

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Moving the mirrors apart Eventually one ring set catches up with the other and they overlap completely  You will see about half as many rings in that position.

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Moving the mirrors apart Finally, the fast ring set surpasses the slower ring set and eventually they will be interleaved again.

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Measuring the Average Wavelength  Start out in a position where the ring sets overlap.  Record starting position of micrometer screw.  Move the mirrors apart and count fringes (bright dots popping out at the center).  Make sure you only count fringes until the two ring sets start to separate. If you count further, you must be careful not to double count as you now have two ring sets.  Record final position of micrometer screw.  Determine the average wavelength of the sodium double line.

Modern Optics Lab Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Measuring Double Separateion  Start out in a position where the ring sets overlap.  Record the starting position of micrometer screw (d 2 ).  Move the mirrors apart until they separate into two visible sets.  Keep moving the mirrors apart until the two sets recombine into a single set.  Record final position of micrometer screw (d 1 ).  Determine the doublet separation as follows:  Alternatively, you can measure from one interleaved pattern to the next. d1d1 d2d2