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Modern Optics LabLab 6 Part 2: Interference Experiments
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).
Topics
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Interference by Plane-Parallel Plates
n >1
d
i
t
n=1
Path length difference:ind 22 sin2
Destructive interference: m
21 mConstructive interference:
(Remember: The light undergoes a 180º phase shift due to reflection at the bottom.)
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Interference by Plane-Parallel Plates
indm 22 sin22Constructive interference:
2
1sin
2
2
1sin
2 2222 ri nd
nd
m
i
rr
rr n
d
d
dmm
22 sin
cossin2
rr
i
r
nmd
cossin
sin
2
22
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Interference by Plane-Parallel Plates
rr
i
r
nmd
cossin
sin
2
22 Plate
i
Lens
Use a lens to focus laser beam on plate (avoiding thickness-averaging) and simultaneously have it diverge after leaving the plate (making it possible to see multiple interference maxima).
Modern Optics LabLab 6 Part 2: Interference Experiments
r
rr
r n
dm
22 sin
cossin2
Thick plates: Use small angle.
Very thin plates: Use angle near 45 degrees.
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Setting up the Glass Plate Experiment – Zero Degree Adjustment
Top view
Laser
Glass plate
Short component holder
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.
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Converging the beam with a lens
Top view
Laser
136mm lens 136mm
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Studying the symmetry of the interference pattern for small incident angles
Laser
136mm lens
Screen
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Measuring m/for thick glass plate
Laser
136mm lens
Big screen (make sure angle of incidence is 90)
R
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Measuring m/for thick glass plate
ScreenS
m = 5
= S/R (in Radians)
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Measuring m/for thick glass plate
ScreenS
m = 6
= S/R (in Radians)
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Measuring m/for microscope slide
Laser
136mm lens
Tape microscope slide to component holder (you can use a tiny piece of double stick tape).
Modern Optics LabLab 6 Part 2: Interference Experiments
VI.C Measuring m/for microscope cover slide (very thin glass)
Laser
136mm lens
Modern Optics LabLab 6 Part 2: Interference Experiments
Using the micrometer to measure thickness
0 5 10
30
35
40
25
0 5 10
30
35
40
25
11.5mm
0.32mm0.33mm
Thickness = 11.5mm + 0.33mm = 11.83mm
Please be gentle to the micrometer! It is a delicate instrument!
Modern Optics LabLab 6 Part 2: Interference Experiments
The Fabry-Perot Interferometer
Highly reflective mirrors
d
integer where2when
)phase"in " rays outgoing (all
ceInterferen veConstructi
* mmd
d*
Modern Optics LabLab 6 Part 2: Interference Experiments
d=m
md 2when
ceInterferen veConstructi
)90 toclose angle(incident Assume * dd
Bright
Modern Optics LabLab 6 Part 2: Interference Experiments
d
dark goeslight outgoing
ce)interferen veconstructilonger (no 21
mirror one movingby bit a d increasingSlowly
mdm
)90 toclose angle(incident Assume * dd
Bright Dark
Modern Optics LabLab 6 Part 2: Interference Experiments
d
againbright goeslight outgoing
ce)interferen veconstructi(next
)1(2 until moreeven d increasingSlowly
md
)90 toclose angle(incident Assume * dd
Dark Bright
How far do you have to move the mirror to go from the mth to the (m+1)st interference maximum?
Modern Optics LabLab 6 Part 2: Interference Experiments
d
In summary: When the mirror is moved, the outgoing laser spot “blinks” as you go from constructive to destructive to constructive interference.
2d=m 2d=(m+1)
Etc.
2d=(m+2)
Modern Optics LabLab 6 Part 2: Interference Experiments
Using a Diverging Laser Beam
d
2d*=2d=m
(m+1)>2d*>m
2d*=(m+1)
Bright
2d*=(m+1)
Bright
Bright
(m+1)>2d*>m
Dark
Dark
Modern Optics LabLab 6 Part 2: Interference Experiments
Moving Mirror by a bit Using a Diverging Laser Beam
d2d*=(m+1)
Bright
Bright
Dark
(m+2)>2d*>(m+1)
Dark
Dark
(m+1)>2d*>m
2d*=(m+1)
(m+2)>2d*>(m+1)
Modern Optics LabLab 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”.
Count=0 Count=1 Count=2
Etc.
Modern Optics LabLab 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 ± 0.1m:
If you move the mirror by /2 (count=1), your wavelength will be accurately measured to within 0.1m*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 0.1m/500=0.2nm. That is a quite useful accuracy!
Modern Optics LabLab 6 Part 2: Interference Experiments
Aligning an FP interferometer: Use a narrow laser beam
Mirrors not parallel: The reflected beams are too far apart to interfere!
Screen
Screen view
Modern Optics LabLab 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 LabLab 6 Part 2: Interference Experiments
The Michelson Interferometer
Laser
Adjustable (tilt) mirror
Moveable (translational)mirror
Screen
Semi-transparentmirror
Modern Optics LabLab 6 Part 2: Interference Experiments
The Michelson Interferometer – with lens added
Laser
Adjustable (tilt) mirror
Moveable (translational)mirror
ScreenLens to diverge beam