Michelson - Morley Experiment - B.Sc Physics - I Year- Mechanics

Michelson - Morley Experiment - B.Sc Physics - I Year- Mechanics

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

2. Dept.of Physics., KGC Hanamkonda 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. Dept.of Physics., KGC Hanamkonda Michelson and Morley conducted this experiment by using Michelson interferometer. Michelson-Morley Experiments laid the experimental foundations of theory of relativity. Source: wikipedia

4. Dept.of Physics., KGC Hanamkonda 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. Dept.of Physics., KGC Hanamkonda d S V G 1 A D B 2 T T 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 45 with the light. The light falls on the semi silvered glass plate and split into two rays, they are reflected and transmitted rays.

6. Dept.of Physics., KGC Hanamkonda The reflected ray (ray1) towards the plane mirror M 1, which is at a distance of d from the glass plate G. The transmitted ray (ray2) travels towards plane mirror M 2, which is also at a distance of d from glass plate G. The two rays are incident normally on the mirrors M 1 and M 2 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 G 1 A D B 2 T T As these rays(ray1 &ray2) satisfy the interference conditions, hence an interference pattern can be observed by the telescope T.

7. Dept.of Physics., KGC Hanamkonda d S V G 1 A D B 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.

8. Dept.of Physics., KGC Hanamkonda d S V G 1 A D B 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 M 1 at A ’ instead of A due to the motion of the earth. After reflection the total path taken by the ray is GA'Gˈ 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. Dept.of Physics., KGC Hanamkonda d S V G 1 A D B 2 T T 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 ⇒ t 2 (c 2 -v 2 ) = d 2 If is the time taken by the ray1 to travel whole path GA ’ G ’ , then

10. Dept.of Physics., KGC Hanamkonda d S V G 1 A D B 2 T T

11. Dept.of Physics., KGC Hanamkonda d S V G 1 A D B 2 T T 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 M 2 with respect to interferometer. Similarly, it is reflected from M 2 with a velocity of ( c + v ) and falls on G. The distance between G and M 2 is d. Then t 2 is time taken by ray 2 to reach G ’ , then

12. Dept.of Physics., KGC Hanamkonda d S V G 1 A D B 2 T T

13. Dept.of Physics., KGC Hanamkonda Therefore, the difference in the times of intervals of ray1 and ray2 is Δt = t 1 – t 2

14. Dept.of Physics., KGC Hanamkonda The Optical path difference between two rays is given by Optical path difference = velocity x ∆ t If the wave length of the light is 𝜆 , then the path difference in terms of wave length = .

15. Dept.of Physics., KGC Hanamkonda The path difference gives the fringe shift. When the apparatus is rotated to 90°, hence the mirrors M 1 and M 2 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

16. Dept.of Physics., KGC Hanamkonda In the above experiment, 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.

17. Dept.of Physics., KGC Hanamkonda 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. Dept.of Physics., KGC Hanamkonda ASSIGNMENT Describe Michelson-Morley Experiment. What is the significance of the negative result Thank You