# Describe Michelson - Morley experiment

## Michelson-Morley Experiment

Michelson-Morley experiment, an attempt to detect the velocity of Earth with respect to the hypothetical luminiferous ether, a medium in space proposed to carry light waves. First performed in Germany in 1880–81 by the physicist A.A. Michelson, the test was later refined in 1887 by Michelson and Edward W. Morley in the United States.

### Describe Michelson Morley Experiment

According to Michelson’s experiment theory, the light should travel at different speeds through ether. The speed at which light moves depends on the relative motion through space. Michelson Morley designed an interferometer to spot the minute differences in the arrival time of light beams. Out of all these beams, one can take a long time to reach the sensor while travelling through ether.

The experiment performed compared the speed of light to notice the relative motion of Earth through ether. However, the conclusion of the Michelson Morley experiment comes out to be negative. It means that they found no difference between the speed of light while travelling through ether.

Michelson Morley interferometer sent white light for the actual observations and yellow light from a sodium flame through a half-transparent mirror. The mirror was used to split the coming light beam into two separate beams travelling perpendicular to each other. After leaving this mirror, beams moved out to the long arms end where they faced back reflection into the middle. These two beams then recombine to produce a pattern of constructive and destructive interference.

The viewer will see the two beams of light which have traveled along different arms display some interference pattern. If the system is rotated, then the influence of the “ether wind” should change the time the beams of light take to travel along the arms and therefore should change the interference pattern. The experiment was performed at different times of the day and of the year. NO CHANGE IN THE INTERFERENCE PATTERN WAS OBSERVED!

#### Let Us Calculate the Time Taken by the Transmitted Ray to Travel to the Mirror:

t1 = 1/(c–v)1/(c–v) + 1/(c+v)1/(c+v)

t1 = l∗(c+v+c–v)l∗(c+v+c–v)/ (c2 -v2)

t1 = l*[2c/ (c2 -v2)]

t1 = 2lc/c2 *[1/1 - (v2/c2)]

t1 = 2l/c *[1/1 - (v2/c2)]

t1 = 2l/c *[1 - (v2/c2)]-1

Applying Binomial Theorem on the above equation and neglecting higher power terms gives:

t1 = 2l/c *[1 + (v2/c2)]

Now, time taken by the reflected ray to travel to mirror:

t2 = [1/ (c2 – v2)1/2] + [1/(c2 + v2)1/2]

t2 = 2l/ (c2 – v2)1/2

t2 = 2l/c *[1/ (1– (v2/c2)1/2]

t2 = 2l/c *[1 - (v2/c2)]-1/2

Similarly, applying Binomial Theorem:

t2 = 2l/c *[1 + (v2/2c2)]

Michelson Morley experiment derivation indicates the time difference between two rays:

Δt = t2 – t1

Using the values of t1 and t2:

Δt = 2l/c *[1 + (v2/c2) - 1 - (v2/2c2)]

Δt = l/c *(v2/c2)

After the first attempt, the apparatus is rotated clockwise to 90-degree so that two mirrors can exchange their position. Now the time difference between two mirrors can be given by:

Δt = -l/c *(v2/c2)

Due to the rotation of apparatus, there is a delay in time, which is given by:

Δt – Δt’ = 2l/c *(v2/c2)

This time delay causes the fringe pattern to move. Let N denote the total amount of fringe shift, which can be calculated as:

N = Δδ/2π

N = 2l/λ *(v2/c2)

#### Conclusion

The major objective of the Michael Morley experiment was to verify the ether hypothesis. The experiment has been repeated several times but there was no particular conclusion of the Michelson Morley experiment.