modern optics lab lab 6 part 2: interference experiments observe interference by plane-parallel...

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


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.)



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



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).


r

rr

r n

dm

22 sin

cossin2

Thick plates: Use small angle.

Very thin plates: Use angle near 45 degrees.


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.


VI.C Converging the beam with a lens

Top view

Laser

136mm lens 136mm


VI.C Studying the symmetry of the interference pattern for small incident angles

Laser

136mm lens

Screen


VI.C Measuring m/for thick glass plate

Laser

136mm lens

Big screen (make sure angle of incidence is 90)

R



ScreenS

m = 5

= S/R (in Radians)



ScreenS

m = 6

= S/R (in Radians)


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).


VI.C Measuring m/for microscope cover slide (very thin glass)

Laser

136mm lens


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!


The Fabry-Perot Interferometer

Highly reflective mirrors

d

integer where2when

)phase"in " rays outgoing (all

ceInterferen veConstructi

* mmd

d*


d=m

md 2when

ceInterferen veConstructi

)90 toclose angle(incident Assume * dd

Bright


d

dark goeslight outgoing

ce)interferen veconstructilonger (no 21

mirror one movingby bit a d increasingSlowly

mdm


Bright Dark


d

againbright goeslight outgoing

ce)interferen veconstructi(next

)1(2 until moreeven d increasingSlowly

md


Dark Bright

How far do you have to move the mirror to go from the mth to the (m+1)st interference maximum?


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)


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


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)


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.


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!


Aligning an FP interferometer: Use a narrow laser beam

Mirrors not parallel: The reflected beams are too far apart to interfere!

Screen

Screen view


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.


The Michelson Interferometer

Laser

Adjustable (tilt) mirror

Moveable (translational)mirror

Screen

Semi-transparentmirror


The Michelson Interferometer – with lens added

Laser

Adjustable (tilt) mirror

Moveable (translational)mirror

ScreenLens to diverge beam

modern optics lab lab 6 part 2: interference experiments observe interference by plane-parallel...

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