Transcript Michelson Interferometer

Interferometry
It deals with experimental study of the
phenomenon of interference.
Instruments used in this study are
based on principle of interference and
are called Interferometers.
One of such interferometers was
designed by Michelson and is known
as Michelson Interferometer.
Michelson Interferometer





M1&M2 are highly
polished mirrors placed
perpendicular to each
other.
B&C are two glass
plates placed parallel
to each other at an
angle of 45°.C is
compensating plate.
Plate B is half silvered
S is the source of light
E is the eyepiece
through which
observer observes the
fringes.
working
1) Path difference between
interfering waves
Half of the light from source S
falling on plate B is reflected towards
M1 and other half is transmitted
towards mirror M2. The two rays
coming from M1& M2 interfere and
fringes are formed.
The wave reflected from M1 crosses
the plate B twice before entering the
eyepiece twice while the other wave
falling on mirror M2 travels totally in
air .
Hence an extra path 2(μ-1)t is
introduced in first wave
where t is the thickness of the plate
and μ is the refractive index of the
light wave.
Role of compensating plate


This extra path difference is compensated
by another glass plate C .Thickness and
material of this glass plate is same as that
of plate B. So, this glass plate C is called
Compensating plate .
Now Light from M2 will also pass through
the plate C twice and extra optical path 2(μ1)t produced in plate B is thus compensated
by introduction of plate C.
2) Phase change on reflection







A phase change of π occurs on reflection at M1 and M2
both(Stoke’s Law).Further, the phase changes due to
reflection from silver coating on plate B, in air and in
glass are also equal to π each. Hence, the two emergant
waves will interfere constructively or destructively
according as the path difference(∆) between them is
even or odd multiple of λ/2 i.e.
∆ = (2n)λ/2 = nλ ; maxima
∆ = (2n+1)λ/2
; minima
If plate B is unsilvered, then conditions of maxima &
minima are:∆ = (2n)λ/2 = nλ ; minima
∆ = (2n+1)λ/2
; maxima
The observer sees a virtual image M2’ of M2.Therefore,
one of the interfering beams comes by reflection from
M1 & other from M2 as if it had come from M2’.
Adjustment of Michelson
Interferometer

Michelson Interferometer is said to be
in normal adjustment when imageM2’
of M2 is exactly parallel to M1. In this
case, the fringes would be concentric
circles. To make this adjustment ,the
distances of mirror M1 and M2 from
plate B is adjusted nearly the same.

When M1 &M2 are
not exactly
perpendicular to
each other ,two
pairs of images
(1,2) ,(3,4) are
formed.


M1&M2 are turned
in proper direction
until the pair of
images coincide as
shown in figure.
The adjustment is
said to be perfect if
circular fringes do
not expand or
contract.
Forms of fringes

The fringes may be straight lines,
parabolas, circles ,ellipse depending
on distance between M1 and M2’ and
angle α between them.
Circular fringes


These fringes are
produced when α=0
as shown in fig (a) &
(c)
When M1and M2’
coincide the path
difference becomes
zero and field of view
is perfectly dark as
shown in fig (b)
Localized fringes
When M1& M2’ are
inclined the air film is
wedge shaped
When M1 intersects
M2’ in middle straight
line fringes are
observed.
In other positions, the
shape of fringes is
curved-- convex
towards thin edge of
wedge as shown in
figure.
Determination of wavelength of
monochromatic light by
Michelson Interferometer:


The mirrors M1 andM2 are adjusted so as to
get a pattern of circular fringes. Telescope is
focused on center of bright
fringe.Then,mirrorM1 is displaced parallel to
itself either in forward or in backward
direction . In doing so, fringe pattern also
gets shifted to one side in the field of view.
Corresponding to displacement d=λ/4 of the
mirror ,the path difference in interfering
beams changes by 2d= λ /2 so that center
of dark fringe will coincide with crosswire .


Let l be known distance through which
mirror M1 is displaced and m the number
of fringes which shift across the crosswire.
Then change in path difference is 2l and
2l=mλ
λ=2l/m
Thus the value of wavelength λ of
monochromatic light can be determined
by measuring l and counting m in the
experiment.