Download Lab 9 - University of Utah Physics

Modern Optics Lab
Lab 9: Interferometer Experiments
Topics
 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
Modern Optics Lab
Lab 9: Interferometer Experiments
About Electronic Fringe Counting
Etc.
Photo Sensitive Detector (PSD)
IPSD
time
Modern Optics Lab
Lab 9: Interferometer Experiments
Simples Method: One level comparator
IPSD
time
1
2
3
Modern Optics Lab
Lab 9: Interferometer Experiments
Problems with single level comparator: Unwanted
counts from noise
IPSD
time
1
2
3
4
5
6
Modern Optics Lab
Lab 9: Interferometer Experiments
Double Level Comparator (Schmitt-Trigger)
IPSD
time
1
2
3
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
Experiment 1: Wavelength Measurement with Michelson Interferometer
SchmittTrigger
Counter
Photo-sensitive
diode
Oscilloscope
Laser
Semi-transparent
mirror
Adjustable (tilt) mirror
Modern Optics Lab
Lab 9: Interferometer Experiments
Experiment 1: Wavelength Measurement with Fabry-Perot Interferometer
Laser
Photosensitive
diode
SchmittTrigger
Oscilloscope
Counter
Modern Optics Lab
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
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 DP  change in index of refraction Dn
 Dn causes a shift of fringes Dm (due to wavelength change in the box)
Dn 
 First find
Dm
Dm
, where l  length of box
2l
DP
 Then use the equation n(P) to calculate n for various pressure.
 Plot n versus P.
n( P )  1 
Dn
Dm 
P  1
P
DP
DP 2l
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
…
10
Dm
DP
m
15
20
25
etc.
P
Slope of graph = Dm/DP
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)
n( P )  1 
…
0
…
…
5
…
…
10
…
15
…
20
…
25
etc.
Dm 
P
DP 2l
n(P)
P
Modern Optics Lab
Lab 9: Interferometer Experiments
Hints for deriving
n( P )  1 
Dm 
P
DP 2l
:
MP
(use ideal gas law)
R T
M  Molar Mass ; R  Ideal Gas Constant ;
(1) Show that  
where
P  Pressure ; T  Temperatur e ;   Gas Density
(2) n air  1  C
(given), where C is a constant
(3) Express n air as a function of P.
dn air
 .....
dP
 dn 
(5) Express n air  P, air   .... (as a function of P & n air )
dP 

dn

(6) Show (for constructi ve interferen ce) that air  ,
dm 2l
wher e l  length of chamber ; dm  fringe count
(4) Take the derivative
 dm 
(7) Express n air  P,
 using results from steps (5) and (6).
 dP 
Modern Optics Lab
Lab 9: Interferometer Experiments
Experiment 3: Measure the Index of Refraction of a Glass Plate with a
Michelson Interferometer
SchmittTrigger
Photo-sensitive
diode
Angle Scale
Counter
Oscilloscope
Laser
Semi-transparent
mirror
Glass
Plate
Adjustable (tilt) mirror
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: n 
(2t  m )(1  cos )
2t (1  cos )  m
(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 (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).
d2
d1
1  2 
2

Determine the doublet separation as follows:

Alternatively, you can measure from one interleaved pattern to the next.
2d1  d 2 