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An
experiment was conducted in 1887 by Michelson and Morley to verify ether
hypothesis.
Experimental set-up
The details of the experimental set up is as follows:
Light beam from the source 'S' is incident at a beam splitter, which is a
semi silvered glass plate. The plate splits the beam into two coherent beams
and out of them one is transmitted and other one is reflected. The
transmitted rays strike the mirror M1 and from there it is reflected back to
plate. The reflected beam strike the mirror M2 and it is also reflected back
to plate. The returned beams from mirror M1 and M2 reach the telescope T. The
superposition of these two rays produce interference pattern, which are seen
through the telescope T.
The separation between the P and M1 and P and M2 is
same and that is equal to 'l' and this separation is called length of the
arm. The light will reflected back from mirrors M1 and M2 respectively
and will interfere at P. This interference pattern is noticed by Telescope T.
Time taken by the light to travel to mirror M1 and
came back to plate P
As the apparatus and the light both are moving in same
direction that is when light is going towards M’2. Thus the relative velocity
will be c – v. After reflection, the apparatus and the light both are moving
in the opposite direction that is when light is going towards P. Thus the
relative velocity will be c + v.
Apply Binomial theorem and neglect higher terms
 .........(1)
time taken for light to travel to M2 and back to
plate
Apply Binomial theorem and neglect higher terms
 ......(2)
Therefore the time difference between the transmitted and
reflected rays will be
Using equations (1) and (2)
 ........(3)
After this the apparatus is rotated through  so that mirrors
will exchange their positions.
In a rotated position the time difference the same two
arms would be given by
 ...(4)
The time delay varies as the apparatus is rotated. The
total delay in rotation is
given by
 ......(5)
this would cause fringe pattern to move during rotation,
which can be observed experimentally.
therefore path difference in rotation is
given by
and phase difference
Fringe Shift
The total amount of fringe shift N on rotation can be
calculated from the time difference
 .......(6)
Then N is calculated by putting l = 11m, v = 10-4 c and
λ = 5500 angstroms
Thus N = 0.4 fringes
The experiment was performed day and night and at different times of year.
Even though the sensitivity of the set up is to detect a shift of 0.01
fringe, no such shift was observed. Similar experiments were repeated by
several groups but the result was same. The above experiment shows that the
speed of light is constant in space irrespective of the direction and speed
of inertial frame.
Explanations for negative result
The following explanations were given for the negative result of
Michelson–Morley experiment.
(i) Ether drag theory: The moving bodies drag the surrounding
ether with them. So, we can say that there is no relative motion between
ether and earth
(iii) Light velocity hypothesis: This hypothesis shows that the
velocity of light from a moving source is the vector sum of velocity of light
and velocity of source light. Based on some astronomical evidences, this
hypothesis was also rejected. In 1905, Einstein proposed that the motion
through ether is a meaningless concept. He does not completely rejected the
idea of ether but expressed that it can never be detected. The motion of an
object relative to a frame of reference has a physical concept.
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