Modern Optics Lab 9 Interferometer Experiments Topics FabryPerot
Modern Optics Lab 9: Interferometer Experiments Topics Ø Fabry-Perot or Michelson Interferometer • Adjusting • Measuring the wavelength of laser using an electronic fringe counter Ø 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 Ø Michelson Interferometer • Measuring the index of refraction of a glass plate using an electronic fringe counter Ø Fabry-Perot Interferometer • Measuring the separation of the sodium doublet
Modern Optics Lab 9: Interferometer Experiments About Electronic Fringe Counting Etc. Photo Sensitive Detector (PSD) IPSD time
Modern Optics Lab 9: Interferometer Experiments Simples Method: One level comparator IPSD time 1 2 3
Modern Optics Lab 9: Interferometer Experiments Problems with single level comparator: Unwanted counts from noise IPSD time 1 2 3 4 5 6
Modern Optics Lab 9: Interferometer Experiments Double Level Comparator (Schmitt-Trigger) IPSD time 1 2 3
Modern Optics Lab 9: Interferometer Experiments Experiment 1: Wavelength Measurement with either Fabry-Perot or Michelson Interferometer Ø Choose either the Fabry-Perot or the Michelson Interferometer to do this activity. Ø Use electronic counting to get an accurate measurement of the wavelength of the laser.
Modern Optics Lab 9: Interferometer Experiments Experiment 1: Wavelength Measurement with Michelson Interferometer Schmitt. Trigger Counter Photo-sensitive diode Oscilloscope Laser Semi-transparent mirror Adjustable (tilt) mirror
Modern Optics Lab 9: Interferometer Experiments Experiment 1: Wavelength Measurement with Fabry-Perot Interferometer Laser Photosensitive diode Schmitt. Trigger Oscilloscope Counter
Modern Optics Lab 9: Interferometer Experiments Experiment 2: Measure the Index of Refraction of Air with a Michelson Interferometer Screen Semi-transparent mirror Laser Pressure gauge Relief valve Adjustable (tilt) mirror Pump isolation valve Hand Pump
Modern Optics Lab 9: Interferometer Experiments Experiment 2: Measure the Index of Refraction of Air with a Michelson Interferometer Ø 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). Ø 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. Ø Change in pressure DP change in index of refraction Dn Ø Dn causes a shift of fringes Dm (due to wavelength change in the box) Ø First find Ø Then use the equation n(P) to calculate n for various pressure. Ø Plot n versus P.
Modern Optics 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 … 10 m 15 20 25 etc. P Slope of graph = Dm/DP
Modern Optics 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 9: Interferometer Experiments Hints for deriving :
Modern Optics Lab 9: Interferometer Experiments Experiment 3: Measure the Index of Refraction of a Glass Plate with a Michelson Interferometer Schmitt. Trigger Counter Photo-sensitive diode Angle Scale Oscilloscope Laser Semi-transparent mirror Glass Plate Adjustable (tilt) mirror
Modern Optics Lab 9: Interferometer Experiments Experiment 3: Measure the Index of Refraction of a Glass Plate with a Michelson Interferometer Ø Measure thickness t of the glass plate with the caliper. Ø Make sure that initially the glass plate is exactly perpendicular to the laser beam. Ø 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. Ø 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. Ø Record the fringe count m. Ø Reset the fringe counter. Ø Rotate glass plate back to zero and make sure you get the same m as before. Ø Calculate n: (Hint: You could use a spreadsheet)
Modern Optics Lab 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Rough Adjustment Sodium Lamp Mirror tilt adjustment screws
Modern Optics 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 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 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 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 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 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 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 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Measuring the Average Wavelength Ø Ø Ø 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 9: Interferometer Experiments Experiment 4: Separation of Sodium Doublet – Measuring Double Separateion Ø Ø Ø 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). d 2 d 1 Ø Determine the doublet separation as follows: Ø Alternatively, you can measure from one interleaved pattern to the next.
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