modern optics lab lab 9: interferometer experiments fabry-perot or michelson interferometer...
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Modern Optics LabLab 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 LabLab 9: Interferometer Experiments
About Electronic Fringe Counting
Etc.
Photo Sensitive Detector (PSD)
time
IPSD
Modern Optics LabLab 9: Interferometer Experiments
Simples Method: One level comparator
time
IPSD
1 2 3
Modern Optics LabLab 9: Interferometer Experiments
Problems with single level comparator: Unwanted counts from noise
time
IPSD
1 2 3 4 5 6
Modern Optics LabLab 9: Interferometer Experiments
Double Level Comparator (Schmitt-Trigger)
time
IPSD
1 2 3
Modern Optics LabLab 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 LabLab 9: Interferometer Experiments
Laser
Adjustable (tilt) mirror
Photo-sensitive diode
Semi-transparentmirror
Experiment 1: Wavelength Measurement with Michelson Interferometer
Schmitt-Trigger
Oscilloscope
Counter
Modern Optics LabLab 9: Interferometer Experiments
Photo-sensitive diode
Experiment 1: Wavelength Measurement with Fabry-Perot Interferometer
Schmitt-Trigger
Oscilloscope
CounterLaser
Modern Optics LabLab 9: Interferometer Experiments
Laser
Adjustable (tilt) mirror
Screen
Semi-transparentmirror
Experiment 2: Measure the Index of Refraction of Air with a Michelson Interferometer
Pressure gauge
Relief valve
Hand Pump
Pump isolationvalve
Modern Optics LabLab 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.
box oflength where, 2
ll
mn
P 2
11)(lP
mP
P
nPn
Pm
Modern Optics LabLab 9: Interferometer Experiments
Experiment 2: Measure the Index of Refraction of Air with a Michelson Interferometer
Finding Pm
P (mm Hg) m (count)
… 0
… 5
… 10
15
20
25
etc.
m
P
Slope of graph = m/P
Modern Optics LabLab 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.
P 2
1)(lP
mPn
n(P)
P
Modern Optics LabLab 9: Interferometer Experiments
Hints for deriving : P 2
1)(lP
mPn
(6). and (5) steps from results using dP
dm,n Express (7)
count fringedm ;chamber oflength e wher
, 2dm
dn that ce)interferen veconstructi(for Show (6)
)n & P offunction a (as....dP
dn,n Express (5)
.....dP
dn derivative theTake (4)
P. offunction a as n Express (3)
constant a is C where(given), 1n (2)
Density Gas ; eTemperaturT ; Pressure P
;Constant Gas IdealR ; MassMolar M where
law) gas ideal (use R
M that Show (1)
air
air
airair
air
air
air
air
P
ll
P
C
T
P
Modern Optics LabLab 9: Interferometer Experiments
Laser
Adjustable (tilt) mirror
Photo-sensitive diode
Semi-transparentmirror
Experiment 3: Measure the Index of Refraction of a Glass Plate with a Michelson Interferometer
Glass Plate
Angle ScaleSchmitt-Trigger
OscilloscopeCounter
Modern Optics LabLab 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)
mt
mtn
)cos1(2
)cos1)(2(
Modern Optics LabLab 9: Interferometer Experiments
Experiment 4: Separation of Sodium Doublet – Rough Adjustment
Sodium Lamp
Mirror tilt adjustment screws
Modern Optics LabLab 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 LabLab 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 LabLab 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 LabLab 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 LabLab 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 LabLab 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 LabLab 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 LabLab 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 LabLab 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 (d2). 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 (d1).
Determine the doublet separation as follows:
Alternatively, you can measure from one interleaved pattern to the next.
21
2
21 2 dd
d1d2