to find separation distance

1. FABRY PEROT ETALON

2. Outline of the
experiment:
Aim of the experiment
Introduction
Theory
Experimental set up
Data
Graphs
Result
Precautions

3. Aim of the experiment
To determine the separation between
the plates of Fabry Perot etalon.

4. INTRODUCTION
Charles Fabry and Alfred Perot designed Fabry Perot
Interferometer in 1899 .
A Fabry Perot Etalon or simply Fabry Perot Interferometer in
which the distance between the two mirrors is kept fixed.
It represents significant improvement over the Michelson
interferometer . If the gap between Etalon mirrors is varied
moving one of the mirror , the instrument is called
Inteferometer .
I f the mirrors are held fixed and adjustment screw are
provided for parallelism then it is called Etalon.
The multiple reflections of light rays inside the partially
reflecting mirrors strengthen the constructive and destructive
interference of the transmitted light resulting in much sharper
rings compared to Michelson inteferometer .

5. Principle:
The main principle of Fabry Perot Etalon is light is
passed through a pair Of parallel , highly reflecting
etalon.
Interference between components of light
undergoing multiple reflections result in extremely well
defined inference fringes .

6. Theory:
Let us consider a monochromatic light illuminating on etalon
. A ray of light incident on M1 gets reflected and
transmitted. The reflected ray continuous to get reflected
inside the parallel reflecting surfaces , and some of the rays
will be transmitted .The transmitted lights are collected on a
screen and rings are observed. It makes use of multiple
reflection which follow interference of thin films due to
transmitted light.

7. Interference condition in Fabry Perot Etalon
Consider two reflecting surfaces M1 and M2 seperated by a distance
‘d’ . Monochromatic light of wavelength ‘λ’ is being incident on M1
making an angle ‘Ө’ With the normal. The ray incident at A0 gets partly
reflected and partly transmitted . The transmitted ray A0 gets reflected at
A1 and some rays are transmitted i.e, E1 . In the Similar way process of
multiple reflection goes on.
optical path difference is given by
( A1A2)+(A2B)=P
From fig.,
cos2Ө=A2B/A1A2
A2B=A1A2COS2Ө
P=A1A2+A1A2COS2Ө
P=A1A2(1+COS2Ө)
=2A1A2COS2Ө
=2dCOSӨ [d=A1A2COSӨ]
If µ is the refractive index of the medium
between Etalon the
P=2µdCOSӨ

8. If the distance travelled inside by the rays becomes equal to integral
multiple of wave length , maximum light gets transmitted inside
mirrors and we observe constructive interference on screen.
nλ=2µdcosӨ where n=0,1,2,3,4………..
If the distance travelled inside equals to (2n+1)λthen we observe dark
bands due to destructive interference.
(2n+1)λ=2µdcosӨ where n= 0,1,2,3,4……….
FORMULA USED:
nλ=2µdcosӨ
Where
λ=Wave length of light used
Ө=Angle of incidence
n=Order of interference
d=separation between the plates
µ=Refractive index between the plates
Fig showing concentric rings

9. Experimental set up
Laser
Etalon Optical bench
lens Scale given on a milky
Transparent plastic plate

10. Procedure
1.With all the components perfectly set as given in previous fig, we can
find a series of very intense concentric circular interference fringes on the
screen.
2.Take the reading of the first bright ring on the left side ‘a’ . Repeat
above procedure for 2,3,…6 fringes . Now take the readings on the right
side of the
fringes ‘b’ and repeat foe different no.of fringes.
3.Difference between a and b gives Angular diameter 2Өn.
4.Calculate Өn and cosӨn and tabulate the results in tabular column.
5.Draw a graph with order of interference on X-axis and cosӨn on Y-axis.
6.Find the slope of the graph calculate the separation between the plates
of etalon.

11. Ring
number
Angular diameter
b-a =2Өn Өn cosӨn
left(a) right(b)
1
2
3
4
5
6
7
5.9
5.3
5.1
4.9
4.6
4.4
4.3
6.1
7.2
7.7
8.2
8.4
8.6
8.8
0.2
1.9
2.6
3.3
3.8
4.2
4.5
0.1
0.95
1.3
1.65
1.9
2.1
2.25
0.99999
0.99986
0.99974
0.99959
0.99945
0.99933
0.99922
Distance between the screen and etalon is 50cm
Tabular column

12. Distance between screen and etalon is 50cm

13. Ring
number
Angular diameter
b-a=2Өn Өn cosӨnLeft Right
1
2
3
4
5
6
5.1
4.7
4.5
4.3
4.1
4.0
6.3
6.7
7.0
7.2
7.4
7.5
1.2
2.0
2.5
2.9
3.3
3.5
0.6
1.0
1.25
1.45
1.65
1.75
0.9999451
0.9998476
0.9999762
0.9996797
0.9995853
0.9995336
Distance between screen and etalon is 45cm

14. Distance between screen and etalon is 45cm

15. CALCULATION
Formula used is nλ=2dcosӨn
d=nλ/2cosӨn
d=(λ/2)(1/slope) [slope=n/cosӨn]
If distance between screen and etalon is 50cm
d=(532*10-9)/(2*1.30714*10-4)
d=203.4977*10-5
d=2.03497mm
If the distance between screen and etalon is 45cm
d=(532*10-9)/(2*8.3428*10-5)
d=3.18mm

16. Precautions
1.Do not touch or contact in any way either the front or back
surfaces of the mirror pieces . Doing so will permanently damage the
mirror coatings.
2. Avoid eye exposure to the direct laser beam.
3.While taking readings Etalon should remain stable, for this it can be
fixed on the rectangular plate.

17. Result and conclusion
Separation the plates of Fabry Perot etalon
When distance between screen and etalon 50cm=2.03497mm
When distance between screen and etalon 45cm=3.188mm
Though the distance between the screen and etalon is varied
the separation between the plates remains constant as both
the etalon plates are fixed.