The Michelson-Morley experiment aimed to detect the motion of the Earth through the hypothesized luminiferous ether by measuring fringe shifts in an interferometer when the apparatus was rotated. However, the experiment yielded a null result, finding no difference in the speed of light in different directions. This contradicted the ether theory and provided early experimental evidence for Einstein's theory of relativity by showing there was no ether drag. The null result meant the Earth's speed could not be measured relative to the ether, disproving its existence and revolutionizing our understanding of space and time.

1. Special Theory of Relativity-Lecture– 2
B.Sc Physics - First Year - First Semester
Topic: Michelson-Morley Experiment

2. Michelson-Morley Experiment
Michelson – Morley
experiment is aimed to
determine the velocity of the
earth with respect to ether
frame that means, to detect the
real existence of ether, which
was proposed by Huygens.
Source: wikipedia

3. Michelson and Morley conducted this experiment by using Michelson interferometer.
Michelson-Morley Experiments laid the experimental foundations of theory of relativity.
Source: wikipedia

4. The principle of the experiments lies finding the shift in
fringes in the Michelson interferometer due to difference in
time taken by light to travel along and opposite to the
direction of motion of the earth.
The time taken by a beam of light to travel along the
direction of motion of the earth is greater than that to travel
distance opposite to the direction of motion of the earth.

5. d
S
V
1
M
2
M
G
1
A
A
D
B B
d
GB
GA 

2
T T
G
Experimental Arrangement:
The experimental
arrangement of Michelson –
Morley is shown in figure. S is
a monochromatic light source.
The monochromatic light from
S is incident on a semi silvered
glass plate G, which is kept at
an inclined angle of 450 with
the light. The light falls on the
semi silvered glass plate and
split into two rays, they are
reflected and transmitted rays.

6. The reflected ray (ray1)
towards the plane mirror M1,
which is at a distance of d from
the glass plate G. The
transmitted ray (ray2) travels
towards plane mirror M2, which
is also at a distance of d from
glass plate G.
The two rays are
incident normally on the
mirrors M1 and M2 respectively
and they are reflected back
along their original paths and
meet at the surface of the semi
silvered glass plate G.
d
S
V
1
M
2
M
G
1
A
A
D
B B
d
GB
GA 

2
T T
As these rays(ray1 &ray2) satisfy the interference
conditions, hence an interference pattern can be
observed by the telescope T.
G

7. d
S
V
1
M
2
M
G
1
A
A
D
B B
d
GB
GA 

2
T T
If the experimental setup at
rest in ether, then the two
reflected rays take equal time to
reach Glass plate G. But the
whole setup is moving along with
the earth.
Consider the direction of
motion of earth is in the direction
of the initial beam.
Due to the motion of the
earth, the optical paths travelled
by the two rays are not the same.
Then the reflections at the
mirrors and do not take
place at A and B, but take place at
A’ and B’ respectively.
So, the time taken by the two rays to travel to
the mirrors and back to G is different.
1
M 2
M

8. d
S
V
1
M
2
M
G
1
A
A
D
B B
d
GB
GA 

2
T T
Let the velocities of the
light and the apparatus (earth)
are c and v respectively. it is
obvious from fig. that the
reflected ray 1 from glass plate G
will move along GA’ and strikes
the mirror M1 at A’ instead of A
due to the motion of the earth.
After reflection the total
path taken by the ray is GA'Gˈ
G
From the ∆GA’D, we have
(GA')2 = (GD)2 + (A'D)2 But, GD = AA’
∴ (GA')2 = (AA')2 + (A'D)2 ----(1)

9. d
S
V
1
M
2
M
G
1
A
A
D
B B
d
GB
GA 

2
T T
G
If t is the time taken by the ray
to move from G to A’, then eq.(1)
becomes
(ct)2 = (vt)2 + (d)2
⇒ t2(c2-v2) = d2
2
2
v
c
d
t



If is the time taken by the ray1 to
travel whole path GA’G’, then
1
t

10. d
S
V
1
M
2
M
G
1
A
A
D
B B
d
GB
GA 

2
T T
G
)
2
(
2
1
c
2d
t
1
c
2d
1
2
c
2d
2
2
2
1
2
1
2
2
2
2
2
2
1

























c
v
c
v
c
v
c
d
v
t
t

11. d
S
V
1
M
2
M
G
1
A
A
D
B B
d
GB
GA 

2
T T
G
Let the experimental setup is
moving with earth velocity v in the
direction of incident light. Then the
transmitted light ray 2 is travelling
with a velocity (c - v) from glass
plate G to plane mirror M2 with
respect to interferometer.
Similarly, it is reflected from M2
with a velocity of (c + v) and falls
on G. The distance between G and
M2 is d.
Then t2 is time taken by ray 2 to
reach G’, then

12. d
S
V
1
M
2
M
G
1
A
A
D
B B
d
GB
GA 

2
T T
G
  
v
c
v
c
v
c
v
c
d
v
c
d
v
c
d
t










)
(
2










2
2
2
2
2
1
2
c
2dc
c
v
c
dc
v
1
2
2
1
2









c
v
c
d
)
3
(
1
2
2
2
2 










c
v
c
d
t

13. Therefore, the difference in the times of intervals of ray1 and ray2 is
Δt = t1 – t2



















2
2
2
2
2
1
2
1
2
1
c
2
c
v
c
d
c
v
d
t
t
t









 2
2
2
2
2
1
1
2
c
v
c
v
c
d
)
4
(
2
2
3
2
2
2












c
dv
c
v
c
d
t

14. The Optical path difference between two rays is given by
Optical path difference = velocity x ∆ t
2
2
3
2
c
dv
c
x 

c
dv
If the wave length of the light is 𝜆, then the path difference in
terms of wave length =
2
2
c
v
d

.

15. The path difference gives the fringe shift. When the apparatus is
rotated to 90°, hence the mirrors M1 and M2 exchange their positions.
It means initially if a ray travels lesser distance by rotating, it travels
longer distance. Hence, the path difference becomes negative. By
rotating the apparatus the resultant path difference results the fringe
shift to equal to
2
2
2
c
v
d


16. In the above experiment,
cm
-5
10
X
5
.
5


cm/sec
10
X
3 6

v
Therefore, theoretically it was expected a shift in fringes was less than
half a fringe. But, Michelson and Morley could observe a shift about
0.01 of fringe. This shift is within the limits of the error of observation.
cm
10
10 3

 m
d
sec
/
m
10
3X 10

c
0.4
)
10
X
3
(
X
10
X
5
.
5
)
10
X
3
(
X
10
X
2
n
shift
Fringe 2
10
5
-
2
6
3




17. They have repeated the experiment at different places on the earth and
at different seasons of the year, but they could not find any shift. This is
known as null result.
The null result gives that it is impossible to measure the speed of the
earth relative to ether, i.e., there is no relative motion between earth and
ether. Experimentally it is proved that, there is no ether drag and this leads
to the total rejection of ether hypothesis.
To explain this, Albert Einstein has proposed Special Theory of
Relativity.

18. ASSIGNMENT
1. Describe Michelson-Morley Experiment.
What is the significance of the negative result