This document summarizes a physics assignment on key concepts including space, time, motion, frames of reference, and the Michelson-Morley experiment. It defines these concepts and describes the experimental setup and calculations used in the Michelson-Morley experiment. The experiment found no fringe shift, inconsistent with the expected results if the Earth moved through the hypothesized luminiferous ether. This led to the conclusion that the speed of light is constant regardless of motion through the ether, questioning the concept of the stationary ether.

1. Physics assignment
By – ABHAY SINGH PARIHAR
-- ABHISHEK SINHA

2. INDEX
• SPACE
• TIME
• MOTION
• FRAME OF REFRENCE
• MICHELSON MORLEY EXPERIMENT

3. Space

4. • Space is the boundless 3 dimensional extend in which objects and events
have relative position and direction . The concept of space is considered to
be of fundamental importance to an understanding of the physical universe.

5. Time
• It is the measure in which events can be ordered from the past through
the present into the future ,and also the measure of duration of events
and intervals between them.

6. Motion

7. • It is the change of position of objects with respect to time also on its
reference points. Motion is typically described in terms of displacement,
direction, velocity, .acceleration, time and speed

9. • Inertial Frame of Reference
• A frame of reference that remains at rest or moves with constant velocity
with respect to other frames of reference is called Inertial Frame of
Reference. An inertial frame of reference has a constant velocity.
Newton’s laws of motion are valid in all inertial frames of reference.
• Non-inertial Frame of Reference
• A frame of reference is said to be a non-inertial frame of reference when a
body, not acted upon by an external force, is accelerated. In a non-inertial
frame of reference, Newton’s laws of motion are not valid.

10. Michelson Morley experiment
• Aim of the Michelson-Morley experiment: The Michelson-Morley
experiment was done to confirm the presence of hypothetical
medium called ether.

11. Experimental setup

14. Experimental setup -
• The light is emitted from source S and is incident on a collimating lens G .
The L will make the light parallel and the beams will now incident on a plate
P which is inclined at an angle of 450. The P will divide the light into two
parts, one reflected part and other transmitted beam. The reflected beam will
incident on a mirror M1 and transmitted on M2 .

15. • The separation between the P and M1 and P and M2 is same and that is
equal to l (suppose) and this separation is called length of the arm. The light
will reflected back from mirrors M1 and M2 respectively and will interfere at
P. This interference pattern is noticed by Telescope T.

16. MICHELSON – MORLEY ‘S EXPERIMENTAL SETUP

17. Derivation and Discussion of Michelson-
Morley experiment:
• As the observer is assumed to be on ether and he is studying the motion of
the earth with respect to ether. Thus the light beam when incident on G and
reflected towards M1. It will catch the M1 at new position M’1 at A’
(according to Michelson-Morley). Then the light gets reflected back to G’ .

18. Calculation for time taken for reflected path that is
from G to A and then A to G:
• Take triangle ABP’ and apply Pythagoras theorem:
• (A’G)2 = (DA’)2 + (GD)2
• Where AB is the path covered by light in time t and AP’ is path covered by
the Plate P in same time t. BP’ is the length of the arm that is equal to l.
• Thus the equation becomes
• c2t2 = l2+ v2t2

19. • or t2 = l2 /(c2 – v2 )
• or t2 = l2/ c2 (1 – v2 / c2 )
• t = l/ c [(1 – v2/ c2)]1/2 or
• t = l/c [(1 – v2 / c2 )]-1/2
• This is the time taken by light from A to B. Same time will be taken from B to C.
Therefore, the total time for the reflected path will be
• t1 = 2t
• or t1 = 2l[(1 + v2 /2 c2 )]/c (1)

20. Calculation for time taken for transmitted
path that is from G’ to M’2 and then M’2 to G’:
As the apparatus and the light both are moving in same direction that is when light is
going towards M’2. Thus the relative velocity will be c – v. After reflection, the
apparatus and the light both are moving in the opposite direction that is when light is
going towards P. Thus the relative velocity will be c + v.
Thus the time taken from A to M’2 and from M’2 to C will be
t2 = l/(c – v) + l/(c + v)
Further solving, we get
2l(1 – v2/ c2)-1/c

21. • Apply binomial theorem to the RHS and neglect higher terms, we get
• t2 = 2l(1 + v2/ c2)/c ……………..(2)
• Therefore the time difference between the transmitted and reflected rays will be
• ∆t = t2 – t1
• Put equations (1) and (2)
• ∆t = 2l(1 + v2/ c)/c – 2l[(1 + v2 /2 c2)]/c
• Or ∆t = lv2 /c3

22. • Path difference for the transmitted and reflected rays will be
• ∆x1 = c∆t
• ∆x1 = c lv2/c3
• Or ∆x1 = lv2/c2 ………(3)
• After this the apparatus is rotated through 900 so that mirrors will
exchange their positions and path difference is again calculated. It
will come out

23. • ∆x2 = -lv2/c2 ………….. (4)
• Therefore the total path difference will be
• ∆x = ∆x2 – ∆x1
• ∆x = 2 lv2/c2 ……………(5)
• Then the number of fringe shift is calculated by following relation (fringes
are the pattern obtained by interference of two more rays that is by
constructive and destructive interference):
• N = path difference/wavelength of light

24. • N = ∆x/λ
• Putting in equation (5)
• N = 2 lv2/c2 λ …………(6)
• Then N is calculated by putting
l = 11m, v = 3 x 104m/s, c = 3x 108m/s and λ = 5800 angstroms
• Thus N = 0.37 fringes.
• But experimentally N = 0
• Thus the theory and experiment results are not matched.

25. Conclusion from negative result
• The velocity of earth relative to ether is zero.
• The speed of light does not depend on the motion of the source or an
observer.
• The concept of ether to be stationary is wrong.