modern optics lab lab 9: interferometer experiments fabry-perot or michelson interferometer...

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


About Electronic Fringe Counting

Etc.

Photo Sensitive Detector (PSD)

time

IPSD


Simples Method: One level comparator

time

IPSD

1 2 3


Problems with single level comparator: Unwanted counts from noise

time

IPSD

1 2 3 4 5 6


Double Level Comparator (Schmitt-Trigger)

time

IPSD

1 2 3


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.


Laser

Adjustable (tilt) mirror

Photo-sensitive diode

Semi-transparentmirror

Experiment 1: Wavelength Measurement with Michelson Interferometer

Schmitt-Trigger

Oscilloscope

Counter



Experiment 1: Wavelength Measurement with Fabry-Perot Interferometer

Schmitt-Trigger

Oscilloscope

CounterLaser


Laser


Screen


Experiment 2: Measure the Index of Refraction of Air with a Michelson Interferometer

Pressure gauge

Relief valve

Hand Pump

Pump isolationvalve



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



Finding Pm

P (mm Hg) m (count)

… 0

… 5

… 10

15

20

25

etc.

m

P

Slope of graph = m/P



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


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


Laser




Experiment 3: Measure the Index of Refraction of a Glass Plate with a Michelson Interferometer

Glass Plate

Angle ScaleSchmitt-Trigger

OscilloscopeCounter


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(


Experiment 4: Separation of Sodium Doublet – Rough Adjustment

Sodium Lamp

Mirror tilt adjustment screws


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.


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.


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.


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.



The two ring sets move apart at slightly different rates their separation changes



Eventually one ring set catches up with the other and they overlap completely You will see about half as many rings in that position.



Finally, the fast ring set surpasses the slower ring set and eventually they will be interleaved again.


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.


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

modern optics lab lab 9: interferometer experiments fabry-perot or michelson interferometer...

Documents

modern optics lab lab

psd slide

p slide

pressure of air

index of refraction

wavelength of laser

wavelength measurement

wavelength change