Modern Optics Lab
Lab 6 Part 2: Interference Experiments
Topics
 Observe interference by plane-parallel plates: Measure the thickness of
the plates based on the theory.
 Michelson and Fabry-Perot interferometers: Determine the wavelength of
the laser (again).
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Interference by Plane-Parallel Plates
Path length difference:
Qi
n=1
Destructive interference:
  2d
n  sin
2
2
  m
Constructive interference:   m   1 2
d
Qt
n >1
(Remember: The light undergoes a 180º phase
shift due to reflection at the bottom.)
Qi
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Interference by Plane-Parallel Plates
Constructive interference:

m
2d
m   2  2d
n  sin Q i 
2


m
Q r
2

dm
dQ r
1

2

  m
 d  
2  Q r
n  sin
2
2d
2
Qi
n  sin Q r 
2

2
2 d sin Q r cos Q r

n  sin Q i
2
2
 n  sin Q i

 sin Q cos Q
r
r

2
2
1
2
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Interference by Plane-Parallel Plates
  m
 d  
2  Q r
 n  sin Q i

 sin Q cos Q
r
r

2
2
Plate
Lens
Qi
Q
Use a lens to focus laser beam on plate (avoiding thicknessaveraging) and simultaneously have it diverge after leaving the
plate (making it possible to see multiple interference maxima).
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
Variation of fringe density with reflected
angle
m
100
Q r

2 d sin Q r cos Q r

n  sin Q r
2
2
# of fringes per degree
80
60
5mm
1mm
.1mm
40
Thick plates: Use small angle.
20
Very thin plates: Use angle near 45
degrees.
0
0
20
40
60
Reflected Angle
80
100
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Setting up the Glass Plate Experiment – Zero
Degree Adjustment
Make sure that the glass plate reflects light back into the laser to find the zero
degree incident angle position. Also, make sure the laser hits the glass plate at
a place where there is air behind the glass plate – no metal pieces.
Top view
Glass plate
Laser
Short component holder
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Converging the beam with a lens
136mm lens
Laser
136mm
Top view
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Studying the symmetry of the interference
pattern for small incident angles
136mm lens
Laser
Screen
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Measuring m/Q for thick glass plate
136mm lens
Laser
R
Big screen (make sure angle of incidence is 90)
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Measuring m/Q for thick glass plate
m = 5
S
Q = S/R (in Radians)
Screen
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Measuring m/Q for thick glass plate
m = 6
S
Q = S/R (in Radians)
Screen
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Measuring m/Q for microscope slide
136mm lens
Laser
Tape microscope slide to component
holder (you can use a tiny piece of
double stick tape).
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
VI.C Measuring m/Q for microscope cover slide
(very thin glass)
136mm lens
Laser
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
Using the micrometer to measure thickness
Please be gentle to the micrometer! It is a delicate instrument!
40
0
5
10
35
30
25
40
0
5
10
35
30
Thickness = 11.5mm + 0.33mm
= 11.83mm
25
11.5mm
0.33mm
0.32mm
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
The Fabry-Perot Interferometer
d
d*
Constructi
ve Interferen ce
(all outgoing
rays " in phase" )
when 2 d  m 
*
Highly reflective mirrors
where
m  integer
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
Assume
d  d (incident
*
angle close to 90  )
d=m/2
Bright
Constructi
ve Interferen ce
when 2 d  m 
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
d  d (incident
*
Assume
angle close to 90  )
d
Bright  Dark
Slowly increasing

 m  1

outgoing
d a bit by moving
 2d  m
one mirror
(no longer constructi ve interferen
light goes dark
ce)
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
d  d (incident
*
Assume
angle close to 90  )
d
Dark Bright
Slowly increasing
d even more until 2 d  ( m  1) 
(next constructi ve interferen

outgoing
ce)
light goes bright again
How far do you have to move the mirror to go from the mth to
the (m+1)st interference maximum?
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
In summary: When the mirror is moved, the outgoing laser spot “blinks” as
you go from constructive to destructive to constructive interference.
d
2d=m
2d=(m+1)
2d=(m+2)
Etc.
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
Using a Diverging Laser Beam
Bright
2d*=(m+1)
d
Dark
(m+1) >2d*>m
2d*=2d=m
Bright
(m+1) >2d*>m
Dark
2d*=(m+1)
Bright
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
Moving Mirror by a bit Using a Diverging Laser Beam
Dark
(m+2) >2d*>(m+1)
Bright
d
2d*=(m+1) 
(m+1) >2d*>m
Dark
2d*=(m+1) 
Bright
(m+2) >2d*>(m+1)
Dark
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
As you move the mirror, the center of the pattern alternates between
bright and dark.
The rings move outwards as “new” center maxima “pop up” and the
outermost rings “disappear”.
Etc.
Count=0
Count=1
Count=2
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
Accuracy of Fabry-Perot Interferometer Wavelength
Measurement
Suppose you can adjust the mirror with a micrometer screw to an accuracy
of ± 0.1mm:
If you move the mirror by /2 (count=1), your wavelength will be accurately
measured to within 0.1mm*2 = 200nm (quite poor considering a laser
wavelength of around 600nm).
If you move the mirror by 1000* /2 (count=1000), you will calculate your
wavelength by dividing the distance the mirror was moved by 1000.
 Your accuracy will be 0.1mm/500=0.2nm. That is a quite useful accuracy!
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
Aligning an FP interferometer: Use a narrow laser beam
Screen
Screen view
Mirrors not parallel: The reflected
beams are too far apart to interfere!
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
Aligning an FP interferometer
Vertical tilt needs adjustment
Horizontal tilt needs adjustment
Both horizontal and vertical tilt needs
adjustment
Adjust mirror tilts until all spots coincide. Then add the
lens to the setup. Move lens left/right/up/down until
you illuminate the center of the ring pattern. You can
also do some fine adjustment of the tilt to try to get a
nicer ring pattern.
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
The Michelson Interferometer
Screen
Semi-transparent
mirror
Moveable
(translational)
mirror
Laser
Adjustable (tilt) mirror
Modern Optics Lab
Lab 6 Part 2: Interference Experiments
The Michelson Interferometer – with lens added
Lens to
diverge
beam
Screen
Moveable
(translational)
mirror
Laser
Adjustable (tilt) mirror