Step-by-Step Procedure and Outcomes of the Michelson Morley Experiment
Physics is the science of every physical phenomenon we come across in our daily life. From the very beginning, we have learnt about the light and sound that we experience easily. Scientists through various experiments and observations have established the fact that light and sound are electromagnetic waves that travel in waves. Sound waves require a medium to travel while light waves do not need any medium. It can move as effectively as in air as well as in gasses. You must all be familiar with the waves that we see on the water surface when a stone or any object is thrown into it.
At the end of the 19th century, some scientists were curious to know and hypothesised that light, as a transmitting wave, requires a medium as well to travel and it can't travel in a vaccum They suggested the presence of a very special matter called aether in outer space with some distinct characteristics that don't create any drag force against any object moving through it, be it a physical object or light. Since then various experiments have been conducted by many scientists to prove this fact but no one has ever succeeded.
The Experiment of Michelson Morley
Michelson Morley was the pioneer in this field of study. His prediction was based on the fact that sound and light being similar kinds of waves travel at different speeds. He strongly believed that the light waves also travel at different speeds in ether relative to that in a vacuum. And any medium having a density will change the direction of light passing through it due to the phenomenon of refraction. He had also developed an interferometer to experiment on the arriving light beams and prove his theory.
What is the Michelson Morley Experiment?
Sound waves require some medium through which these waves can travel. Maxwell in 1864 showed that light is an electromagnetic wave and hence was supposed that there is an ether that propagates light rays. By observing how light propagates through the ether, one can determine an absolute reference frame. Hence, the Michelson Morley experiment was accomplished to detect ether that was assumed to be the carrier of light waves. The purpose of the Michelson and Morley experiment was to detect the velocity of the Earth to ether. The procedure was based on the optical device named interferometer that compares the path lengths for light rays travelling in perpendicular directions.
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 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 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 Procedure of Michelson Morley Experiment
Michelson claimed that if the speed of light was constant concerning the ether medium through which the Earth moves, then that motion can be detected. It can be sensed by comparing the speed of light perpendicular to and in the direction of the Earth’s motion. The details of Michelson experiment set-up are:
The beam of light gets incident to a half-silvered glass plate. This plate acts as a beam splitter, which splits the light beam into two coherent beams. One beam transmits, and the other reflects. The beam transmitted strikes the mirror, say, M1, and gets reflected. The beam reflected strikes the mirror, say, M2, which again gets reflected. The returned beams reach the telescope, which is used for interference patterns produced by these two rays.
The separation between the plate and two mirrors is the same, which refers to the arm’s length. The light reflected from two mirrors interfere with the mirror.
Now, from the Michelson Morley experiment notes, it can be noticed that the apparatus and light both are moving in the same direction. Thus, the relative velocity will be c - v. After reflection, the apparatus, and light both move in the opposite direction. Hence, in this case, relative velocity will become c + v.
Let Us Calculate the Time Taken by the Transmitted Ray to Travel to the Mirror:
\[T_1 = \frac{L}{c - v}\]
\[T_2 = \frac{L}{c + v}\]
\[T_l = T_1 + T_2\]
\[T_l = \frac{L}{c - v} + \frac{L}{c + v}\]
\[T_l = \frac{(L \times (c + v)) + (L \times (c - v))}{c^2 - v^2} \]
\[T_l = \frac{Lc + Lv + Lc - Lv}{c^2 - v^2} \]
\[T_l = \frac{2Lc}{c^2 - v^2} \]
\[T_l = L \begin{bmatrix} \frac{2c}{c^2 - v^2} \end{bmatrix} \]
\[T_l = \frac{L}{c^2} \begin{bmatrix} \frac{2c}{1 - \frac{v^2}{c^2}} \end{bmatrix} \]
\[T_l = \frac{2L}{c} \begin{bmatrix} 1 - \frac{v^2}{c^2} \end{bmatrix}^{-1} \]
Applying Binomial Theorem on the above equation and neglecting higher power terms gives:
\[T_l = \frac{2L}{c} \begin{bmatrix} 1 + \frac{c^2}{v^2} \end{bmatrix} \]
Now, time taken by the reflected ray to travel to mirror:
\[T_t = \frac{L}{\begin{bmatrix} c^2 - v^2 \end{bmatrix}^{\frac{1}{2}}} + \frac{L}{\begin{bmatrix} c^2 + v^2 \end{bmatrix}^{\frac{1}{2}}} \]
\[T_t = \frac{2Lc}{\begin{bmatrix} c^2 - v^2 \end{bmatrix}^{\frac{1}{2}}}\]
\[T_t = \frac{2Lc}{\begin{bmatrix} c^2 - v^2 \end{bmatrix}^{\frac{1}{2}}}\]
\[T_t = \frac{L}{c^2} \begin{bmatrix} \frac{2c}{1 - \frac{v^2}{c^2}} \end{bmatrix} ^{\frac{1}{2}} \]
\[T_t = \frac{2L}{c} \begin{bmatrix} \frac{1}{1 - \frac{v^2}{c^2}} \end{bmatrix}^{\frac{1}{2}} \]
\[T_t = \frac{2L}{c} \begin{bmatrix} 1 - \frac{v^2}{c^2} \end{bmatrix}^{\frac{-1}{2}} \]
Similarly, applying Binomial Theorem:
\[T_t = \frac{2L}{c} \begin{bmatrix} 1 + \frac{v^2}{2c^2} \end{bmatrix}^{\frac{1}{2}} \]
Michelson Morley experiment derivation indicates the time difference between two rays:
\[\Delta t = T_l - T_t\]
Using the values of Tl and Tt:
\[\Delta t = \frac{2L}{c} \begin{bmatrix} 1 + \frac{v^2}{c^2} - 1 - \frac{v^2}{2c^2} \end{bmatrix}\]
\[\Delta t = \frac{l}{c} \times \begin{bmatrix} \frac{v^2}{c^2} \end{bmatrix} \]
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:
\[\Delta t’ = - \frac{l}{c} \times \begin{bmatrix} \frac{v^2}{c^2} \end{bmatrix} \]
Due to the rotation of apparatus, there is a delay in time, which is given by:
\[ \Delta t - \Delta t’ = \frac{2L}{c} \times \begin{bmatrix} \frac{v^2}{c^2} \end{bmatrix} \]
This time delay causes the fringe pattern to move. Let N denote the total amount of fringe shift, which can be calculated as:
\[N = \frac{\Delta \delta}{2 \pi}\]
\[N = \frac{2L}{\lambda} \times \begin{bmatrix} \frac{v^2}{c^2} \end{bmatrix} \]
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.
FAQs on Michelson Morley Experiment Simplified for Students
1. What was the Michelson-Morley experiment in simple terms?
The Michelson-Morley experiment, conducted in 1887, was a famous scientific attempt to detect the Earth's motion through a hypothetical medium called the luminiferous aether. It was believed that light waves needed this aether to travel through space, similar to how sound waves need air. The experiment used a device called a Michelson interferometer to compare the speed of light in two perpendicular directions, expecting to find a difference caused by the 'aether wind'.
2. Why was the Michelson-Morley experiment so important to perform? What was the aether theory?
The experiment was critically important because 19th-century physics was built on the idea that all waves need a medium. The aether was proposed as a stationary, invisible substance filling all of space, allowing light to propagate. Scientists reasoned that as the Earth orbits the Sun, it must be moving through this aether, creating an 'aether wind'. The experiment's primary goal was to detect this wind, which would have confirmed the existence of aether and provided an absolute frame of reference for the universe.
3. How does a Michelson Interferometer work?
A Michelson interferometer works on the principle of wave interference. Its main components are:
- A light source that emits a single beam of light.
- A half-silvered mirror (beam splitter) that splits the light beam into two perpendicular paths.
- Two mirrors at the ends of these paths that reflect the beams back.
4. What was the expected result of the Michelson-Morley experiment if the aether existed?
If the aether existed, the beam of light travelling 'against' and 'with' the aether wind (parallel to Earth's motion) would take longer to complete its round trip compared to the beam travelling perpendicular to the wind. This time difference would cause the two returning light waves to be out of sync. As a result, when the apparatus was rotated by 90 degrees, a measurable shift in the interference fringe pattern was expected. This predicted shift was the key evidence the experiment was designed to find.
5. What was the famous 'null result' of the Michelson-Morley experiment?
The famous 'null result' refers to the shocking outcome where the experiment detected no significant shift in the interference pattern. Regardless of the time of day or year the experiment was conducted, the speed of light was measured to be the same in all directions. The expected fringe shift, which should have been easily detectable, was absent. This failure to detect the aether wind is what is termed the null result.
6. What is the main conclusion and significance of the Michelson-Morley experiment?
The main conclusion was that the hypothesis of a stationary luminiferous aether was incorrect. The experiment's significance is immense, as it is often called 'the most famous failed experiment in history.' This failure was crucial because it directly challenged classical physics and paved the way for a new understanding of space, time, and light. Its null result is a cornerstone of experimental evidence supporting Einstein's Theory of Special Relativity.
7. How did the Michelson-Morley experiment's result influence Albert Einstein's Theory of Special Relativity?
The experiment's null result was a foundational problem that Einstein's theory elegantly solved. Instead of trying to explain why the aether was undetectable, Einstein proposed two revolutionary postulates:
- The laws of physics are the same for all observers in uniform motion.
- The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or the observer.
8. What is the formula used to calculate the expected path difference in the Michelson-Morley experiment?
The expected path difference (Δ) between the two perpendicular light beams, assuming the existence of an aether wind, is calculated by the formula: Δ = (L * v²) / c², where:
- L is the length of the interferometer arms.
- v is the velocity of the Earth through the aether.
- c is the speed of light.
9. Does the Michelson-Morley experiment prove that the speed of light is constant?
While the experiment is strong evidence, it's more accurate to say it demonstrates the isotropy of the speed of light, meaning it is the same in all directions. It showed that the speed of light is not affected by the motion of the observer (the Earth). This result, combined with observations of binary stars and other phenomena, forms the experimental basis for Einstein's second postulate, which states that the speed of light in a vacuum (c) is a universal constant.
