Introduction
The Michelson–Morley experiment attempted to detect Earth's motion through the hypothetical luminiferous ether.
Light was split into two perpendicular beams. Scientists expected interference fringes to shift when the apparatus rotated.
Principle of the Experiment
If Earth moves through ether with velocity v, then:
- Light moving parallel to Earth’s motion should have a different travel time.
- Light moving perpendicular to Earth’s motion should take another time.
This time difference should create a shift in interference fringes.
Experimental setup
The apparatus contains:
- A monochromatic light source
- Beam splitter G
- Two perpendicular arms of equal length L
- Mirrors M_1 and M_2
- Telescope/screen for interference fringes
The beam splitter divides light into two beams:
- One beam travels parallel to Earth’s motion
- Other beam travels perpendicular to Earth’s motion
After reflection, the beams recombine and produce interference fringes
However, almost no shift was observed.
EXPERIMENT ANIMATION
How the Experiment Works
- Light from source S reaches the beam splitter.
- The beam splitter divides light into two perpendicular beams.
- One beam travels upward toward mirror M₁.
- The second beam travels horizontally toward mirror M₂.
- Both beams reflect back and recombine.
- Interference fringes are observed through telescope T.
- The apparatus is rotated to detect ether wind.
Procedure of Michelson–Morley Experiment
Step 1: Monochromatic Light Source
A monochromatic light source is used to produce a beam of light. The light beam falls on a partially silvered glass plate called the beam splitter.
Step 2: Splitting of Light Beam
The beam splitter divides the incident light into two equal parts:
- One beam travels along the arm parallel to the motion of Earth.
- The second beam travels along the perpendicular arm.
Step 3: Reflection by Mirrors
The two light beams travel equal distances toward mirrors \(M_1\) and \(M_2\).
After reaching the mirrors, the beams are reflected back toward the beam splitter.
Step 4: Recombination of Light Beams
The reflected beams recombine at the beam splitter and enter the telescope.
Due to interference between the two beams, interference fringes are produced.
Step 5: Rotation of Apparatus
The entire apparatus is slowly rotated through \(90^\circ\).
After rotation:
- The arm previously parallel to Earth's motion becomes perpendicular.
- The perpendicular arm becomes parallel.
Step 6: Observation of Fringe Shift
If ether existed, the velocity of light along the two paths would change after rotation.
This would produce a shift in interference fringes.
The fringe shift was carefully observed through the telescope.
Step 7: Experimental Result
No significant fringe shift was observed.
This null result indicated that:
- Ether does not exist.
- The speed of light is constant in all directions.
Michelson–Morley Experiment Derivation
The Michelson–Morley experiment was performed to detect the presence of ether and to study the effect of Earth's motion on the speed of light.
Assumptions
- Velocity of light = \(c\)
- Velocity of Earth through ether = \(v\)
- Length of each arm of interferometer = \(L\)
1. Time Along Parallel Arm
Consider the arm parallel to the motion of Earth.
Forward Journey
Effective velocity of light:
\[ c-v \]Time taken:
\[ t_1 = \frac{L}{c-v} \]Backward Journey
Effective velocity of light:
\[ c+v \]Time taken:
\[ t_2 = \frac{L}{c+v} \]Total Time Along Parallel Arm
\[ T_p = \frac{L}{c-v} + \frac{L}{c+v} \] Taking LCM, \[ T_p = \frac{L[(c+v)+(c-v)]}{c^2-v^2} \] \[ T_p = \frac{2Lc}{c^2-v^2} \] \[ T_p = \frac{2L}{c\left(1-\frac{v^2}{c^2}\right)} \] Using binomial approximation, \[ (1-x)^{-1} \approx 1+x \] Therefore, \[ T_p \approx \frac{2L}{c} \left( 1+\frac{v^2}{c^2} \right) \]2. Time Along Perpendicular Arm
For the perpendicular arm, light travels diagonally.
Using Pythagoras theorem, \[ (ct)^2 = L^2 + (vt)^2 \] \[ c^2t^2 - v^2t^2 = L^2 \] \[ t^2(c^2-v^2)=L^2 \] \[ t = \frac{L}{\sqrt{c^2-v^2}} \]This is the time for one-way travel.
Hence total time:
\[ T_s = \frac{2L}{\sqrt{c^2-v^2}} \] Factoring out \(c^2\), \[ T_s = \frac{2L} {c\sqrt{1-\frac{v^2}{c^2}}} \] Using binomial approximation, \[ (1-x)^{-1/2} \approx 1+\frac{x}{2} \] Therefore, \[ T_s \approx \frac{2L}{c} \left( 1+\frac{v^2}{2c^2} \right) \]3. Difference in Time
\[ \Delta T = T_p - T_s \] Substituting values, \[ \Delta T = \frac{2L}{c} \left( 1+\frac{v^2}{c^2} \right) - \frac{2L}{c} \left( 1+\frac{v^2}{2c^2} \right) \] \[ \Delta T = \frac{Lv^2}{c^3} \]4. Path Difference
\[ \Delta x = c\Delta T \] \[ \Delta x = \frac{Lv^2}{c^2} \] When the apparatus is rotated through \(90^\circ\), \[ \Delta x_{\text{total}} = \frac{2Lv^2}{c^2} \]5. Fringe Shift
If \(\lambda\) is the wavelength of light, \[ n = \frac{\Delta x}{\lambda} \] Therefore, \[ n = \frac{2Lv^2}{\lambda c^2} \] Where:- \(n\) = fringe shift
- \(L\) = arm length
- \(v\) = velocity of Earth through ether
- \(c\) = speed of light
- \(\lambda\) = wavelength of light
Conclusion
The expected fringe shift was not observed experimentally. This null result proved that ether does not exist and led to the development of Special Relativity.
Advantages
- Highly accurate optical experiment
- Proved constancy of speed of light
- Foundation of modern physics
Limitations
- Could not detect ether wind
- Required extremely precise measurements
Frequently Asked Questions (FAQ)
1. What is the Michelson–Morley experiment?
The Michelson–Morley experiment was performed to detect the existence of ether, which was believed to be the medium through which light waves travel.
2. Who performed the Michelson–Morley experiment?
The experiment was conducted by Albert A. Michelson and Edward W. Morley in 1887.
3. What is the main aim of the experiment?
The main aim was to detect the motion of Earth through ether by measuring changes in the speed of light in different directions.
4. Which instrument is used in the experiment?
A Michelson interferometer is used in the experiment.
5. What is a beam splitter?
A beam splitter is a partially silvered glass plate that divides a single light beam into two separate beams.
6. Why are two perpendicular arms used?
The perpendicular arms help compare the speed of light in two different directions relative to Earth's motion.
7. What are interference fringes?
Interference fringes are alternate bright and dark bands formed due to the superposition of two coherent light waves.
8. What is fringe shift?
Fringe shift is the movement of interference fringes caused by a difference in the optical path lengths of two light beams.
9. Why was the apparatus rotated?
The apparatus was rotated through \(90^\circ\) to interchange the parallel and perpendicular arms and detect any change in light speed.
10. What was the result of the experiment?
No significant fringe shift was observed. This is called the null result.
11. What does the null result indicate?
The null result indicated that ether does not exist and that the speed of light is constant in all directions.
12. What is the importance of the experiment?
The experiment became one of the foundations for Einstein’s Special Theory of Relativity.
13. What is the formula for fringe shift?
The fringe shift is given by:
\[ n = \frac{2Lv^2}{\lambda c^2} \]where:
- \(L\) = length of interferometer arm
- \(v\) = velocity of Earth through ether
- \(\lambda\) = wavelength of light
- \(c\) = speed of light
14. Why is monochromatic light used?
Monochromatic light produces clear and stable interference fringes.
15. How did the experiment influence modern physics?
The experiment challenged the ether theory and helped in the development of Special Relativity and modern physics.