Download Lecture 12 | 1 Version 3.6 Michelson

L e c t u r e 12 | 1
Michelson-Morley Experiment
Suppose that light makes a round trip ABA between two points A and B separated by distance l. The
velocity of light relative to the apparatus is
to the left, and
to the right. The effect of
earth’s motion is to delay the return of the light signal by
For earth in orbit
and if we take
then
an interval much too small
to be measured directly. Rather than measure the time of transit of one light beam, Michelson
observed the difference between the transit times of two beams.
M2
M1
A
B
E
Time taken by beam 1 to travel BM1B
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L e c t u r e 12 | 2
D
B
B
Let us say time taken by light to travel from B
during this time is
to
be hence distance travelled by earth
Solving for
Thus time taken to travel
to
Thus time difference for two beams to reach the same spot according to ether hypothesis
The interference patter produced by the two beams will thus be shifted from the position it would
have occupied if the earth were stationary with respect to ether, i.e., if
. However, since this
no-shift postion cannot be realized( the earch cannot be stopped from orbiting). Micheson and
Morley rotated the interferometer through 900. This interchanged the role of two beams, causing a
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L e c t u r e 12 | 3
path difference in two directions. Therefore as a result of rotation, the path difference would change
by .
It was expected that the effect would be graphable as a sine wave with two peaks and two
troughs per rotation of the device. This is because during each full rotation, each arm would be
parallel to the aetherial wind twice (facing into and away from the wind giving identical readings)
and perpendicular to the wind twice. Additionally, due to the Earth's rotation, the wind would be
expected to show periodic changes in direction and magnitude during the course of a sidereal day.
Because of the motion of the Earth around the Sun, it was expected that yearly cycles would
also be detectable in the measured data.
The change in the delay between the two positions
readily calculated. If
and the corresponding fringe shift can be
is the wavelength of the illuminating light, a time delay of
pattern by one fringe. Thus the time delay of
will shift the pattern by
will shift the
fringes.
Since
and c are constant the only factor which can be increased to incerase
is
which Michelson and Moreley did by reflecting beams back and forth through eight round trips. The
eintire appratus was set floating on mercury in order to avoid any jerks due to rotation . A glass slab
was also introudced in order to adjust the path length of the order of wavelength. But
was
observed experimntally which implies =0.
In this experiment Michelson and Morely increased the effective length l to 11m by
reflecting the beams back and forth several times. The wavelenght of light was
.
Taking
and
we have
Thus , a shift of the pattern by 0.4 of a fringe was expected. Their apparatus was so sensitive
that it could detect a shift of 0.01 of a fringe. However, no fringe shift was observed on rotating the
interferrometer. The experiment has since been repeated by various groups at different palaces and
times.
Another scientist, Miller worked on increasingly larger interferometers, culminating in one
with a 32 m (effective) arm length that he tried at various sites including on top of a mountain at the
Mount Wilson observatory.
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