The document discusses Michelson's interferometer. It begins by explaining interference and interference fringes. It then describes how Michelson's interferometer works by splitting light into two beams using a beam splitter, sending the beams to mirrors with one fixed and one movable, and recombining the beams to produce an interference pattern. Key applications of Michelson's interferometer include measuring the wavelength of light, measuring small wavelength separations, detecting gravitational waves, and its role in the Michelson-Morley experiment.

1. MICHELSONS INTERFEROMETER
 .INTERFERENCE
 .INTERFERENCE FRINGES
 .INTERFEROMETERS
 .MICHELSONS INTERFEROMETER
 .APPLICATIONS AND USES

2. .INTERFERENCE
 It is the phenomenon which is associated with the wave
nature of light.
 The phenomena of modification of intensity of light
obtained by the superposition of two or more beams of
light is called as interference.
 If the resultant intensity is zero or less than we expect
from the separate intensities ,we have destructive
interference while if it is greater we have constructive
Interference.

3. .INTERFERENCE FRINGES

4. Real fringe
Can be intercepted on a screen placed
anywhere in the vicinity of the interferometer
without a condensing lens system.
Virtual fringe
Cannot be projected onto a screen without
a condensing focusing system. In this case,
rays do not converge.

5. Non-localized fringe
. Exists everywhere
. Result of point/line source
Localized fringe
- Observed over particular surface
- Result of extended source

6. .INTERFEROMETERS
An interferometer is an optical device which utilizes
the effect of interference. Typically, it starts with
some input beam, splits it into two separate beams
with some kind of beam splitter (a partially
transmissive mirror), possibly exposes some of these
beams to some external influences (e.g. some
length changes or refractive index changes in a
transparent medium), and recombines the beams on
another beam splitter.

7. .TYPES OF INTERFEROMETERS
• Mach–Zehnder Interferometer
• Michelson Interferometer
• Fabry–Perot Interferometer
 Sagnac Interferometer
 Common path Interferometer

8. .MICHELSONS INTERFEROMETER
• A Michelson interferometer is a tool to produce interference between
two beam of light. It is the most common design for optical
interferometry, and was invented by Albert Abraham Michelson.
• The Michelson interferometer produces interference fringes by
splitting a beam of monochromatic light, such that one beam hits a
fixed mirror and the other hits a movable mirror. When the reflected
beams are combined, an interference pattern is formed.
• To create interference fringes on a detector, the paths have to be of
different lengths, or composed of different materials.
• Michelson interferometers are relatively simple in operation, and
possess the largest field of view for a specified wavelength. They also
possess a relatively low temperature sensitivity.

9. (1852-1931)
Albert Abraham Michelson
A.A Michelson. Conjectured that if the speed of light relative to
the hypothetical ether was indeed constant, then the Earth’s
orbital velocity relative to this ether should exhibit observable
relativistic effects. He devised and constructed an optical
interferometer with which he presumed he would then be able
to detect the relative motion of Earth against the static ether.
That is , since Earth’s orbital velocity is approximately 107000
km/h, Michelson anticipated that his interferometer would
exhibit measurable change over the course of a year due to the
substantial difference In velocity relative to the static
background ether.

10. Figure 1: A Michelson Interferometer

11. Figure 2: Schematic Representation of Michelson Interferometer

12. .CONSTRUCTION
• The main optical parts consist of two highly polished mirrors M1 & M2 and a
plane-parallel plate of glass G1(compensator plate) & a beam splitter .
• Sometimes the rear side of the beam splitter is lightly silvered, so that light
coming from the source is divided into (1)a reflected & (2) a transmitted beam
of equal intensity.
• The mirror M1 is fixed to a movable carriage and can be moved along the well
machined ways or tracks .This slow and accurately controlled motion is
accomplished by means of the screw .
• To obtain the interference fringes ,the mirrors M1 & M2 are made exactly
perpendicular to each other .
• Even when this adjustments have been made , fringes will not be seen unless
two important requirements are fulfilled. First the light must originate from
an extended source and second, the light must in general be monochromatic
or nearly so .

13. .WORKING
• We see from Figure 2 that light from a source strikes a partially silvered beam
splitter , causing part of the beam to be transmitted toward a mirror, M1 ,
fixed to a moveable carriage.
• The remainder of the beam is reflected from the beam splitter toward a fixed
mirror, M2. A glass compensation plate along the path toward M1 ensures that
the two paths are effectively identical.
• The two beams, once reflected from M1 and M2, re-converge at the Beam
splitter.
• A precision micrometer screw is connected to the M1 carriage and allows the
optical path length along the M1 branch to be altered over a few mm. Fine
adjustment screws on M2 allow fine tuning such that the beams from each
branch can be overlapped at the viewing screen.

14. • When recombined and aligned, the beams fall on the
interferometer’s viewing screen where the resultant light exhibits
interference effects dependent on the length differences between
the two paths .
• If the distances from the beam splitter to mirrors M1 and M2
differ by distance d, then the total difference in the path lengths
traveled by the two beams of light is 2d.
• When the distance 2d is equal to an integer multiple of the
light’s wavelength, constructive interference is observed at the
viewing screen as the crests of the two beams overlap, and a
bright spot or ring is seen as the viewing screen.
Mathematically this condition is described by the equation
2d = mλ
Where λ is the wavelength of the light and m is an integer .

15. • In actuality, due to differences between internal and external
reflections at silvered surfaces, a phase reversal of one of beam
may result, in which the distance 2d is a half integer multiple of the
light wavelength, destructive interference is observed at the
viewing screen.
• Mathematically this condition is described by the equation
2d = (m+1/2)λ
Maxima:0,1,2,...)(m
2
1
cos2
Minima:0,1,2,...)(mcos2










md
md
m
m

16. 
d
m
2

• As d is increased new fringes appear at the center
and the existing fringes move outwards, and
finally move out of the field of view.
• For any value of d, the central fringe has the
largest value of m.

17. 1. Measurement of wavelength of light
)(md 02 0  
md 2
m
d
nmmdd




2
2 0


2 cosd m 
Move one of the mirrors to a new position d’ so that the order of the
fringe at the centre is changed from mo to m.

18. 2. Measurement of wavelength separation
of a doublet (λ1 and λ1+λ)
   1112 qpd )(md 02 0  
If the two fringe patterns coincide at the centre: (Concordance)
The fringe pattern is very bright

19. Concordance
112 pd 
   1q

20. 2. Measurement of wavelength separation
of a doublet (λ1 and λ1+λ)
   1112 qpd )(md 02 0  
As d is increased p and q increase by different amounts, with
pq 
)2/1( pq
When
the bright fringes of λ1 coincide with the dark fringes of λ1+λ, and
vice-versa and the fringe pattern is washed away (Discordance).

21. Discordance
112 pd 
= (q+1/2)  1

22. 2. Measurement of wavelength separation
of a doublet (λ1 and λ1+λ)
   1112 qpd
      112 12 nqnpd
      1112 12 nndd
 12
2
1
2 dd 



)(md 02 0  
- Δ can be measured by increasing d1 to d2 so that the two sets of fringes,
initially concordant, become discordant and are finally concordant again.
- If p changes to p+n, and q changes to q+(n-1) we have concordant fringes
again.

23. .APPLICATIONS AND USES
 The key applications of a Michelson interferometer are as follows:
 In the Michelson-Morley experiment, which led to the development of the
special theory of relativity.
 In astronomical interferometry.
 In optical coherence tomography.
 In analyzing the upper atmosphere, by revealing temperatures and winds, and
by measuring the Doppler widths and shifts in the spectra of airglow and
aurora.
 As a component in the helioseismic and magnetic imager to study solar
variability, and to illustrate the sun‘s interior, along with the many aspects of
magnetic activity.
 For the detection of gravitational waves .
 As a tunable narrow band filter.
 As the core of Fourier transform spectroscopy.

24. LIGO - Laser Interferometer Gravitational Wave Observatory
To detect Gravitational waves, one of the predictions of Einstein’s General Theory of Relativity
Hanford Nuclear Reservation, Washington, Livingston, Louisiana
Arm length: 4 Km
Displacement Sensitivity: 10-16 cm
When Gravitational
waves pass through the
interferometer they will
displace the mirrors!

25. “
”
THANK YOU VERY MUCH
Success is the ability to go from one failure to
another with no loss of enthusiasm.
Sir Winston Churchill
Created and Presented By:
Prabhukrupa chinmaya Kumar
M.Sc Physics
1st year
GITAM UNIVERSITY