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Michelson-Morley Experiment |
In 1887 Albert A. Michelson and Edward W. Morley performed an experiment to determine the velocity of the earth with respect to the hypothesized ether. They used an interferometer which split a beam of light into two perpendicular paths of equal length. Mirrors at the end of both paths reflected the light back where they merged again into a single beam observed through a telescope. If the earth were at rest, the two beams would return perfectly in phase and constructively interfere. But if the earth were moving in the direction of one beam, the time required for that beam to go forward and back would be longer than the time for the perpendicular beam to go across and back.
The concept is similar to that of two boats racing on a flowing river with one boat racing back and forth across the river while the other races an equal distance up and down river. If both boats have the same speed relative to the water, the boat going cross river will win the race. This is because the other boat spends too much time going up stream. Yes, it gains part of this time back on the down stream leg, but not enough to make up for the lost time, because the down stream leg lasts for too short a time.
In the case of the interferometer, this time difference is transformed into a phase shift producing an interference pattern seen through the telescope. If the earth were moving through the ether with a speed equal to its orbital speed around the sun, the phase shift for sodium orange light should be about 20% of a wavelength. By rotating the apparatus 90o a phase shift of twice this amount should be observed through the telescope. Since the experimental apparatus was capable of detecting phase shifts as small as 1% of a wavelength, the conclusion was that the earth was not moving through the ether. Later experiments have confirmed this result with even higher precision.
It would seem that the earth is always at rest with respect to the ether, regardless of its actual motion through space. In other words, light always travels at the same speed c in all directions relative to the earth, regardless of the motion of the earth.
The Michelson-Morley experiment is discussed in greater detail in Serway pp. 6-9 and Tipler pp. 10-14. You can also go to Freeman's More Michelson-Morley Experiment web site if you have an Acrobat Reader on your computer in order to learn more about the Michelson-Morley Experiment. This further study may be necessary for you to work the second problem given below.
Q1. Explaining the Null Result.
Which of the following best explains the null result of the Michelson-Morley
Experiment? (A) The earth just happened to be at rest
when the experiment was performed. (B) The ether was
drug along with the earth so the earth was locally at rest with respect to the
ether. (C) The length of the moving apparatus contracts
in the direction of its motion by a factor of (1-v2/c2)1/2.
(D) More than one of these are equally valid explanations.
(E) None of these explain the null result.
Q2. Which are true? (A) The
Michelson-Morley experiment showed that the earth was always at rest relative
to the hypothesized luminiferous ether. (B) Michelson and Morley carefully
measured the one-way velocity of light in various directions in order to
formulate their conclusions. (C) The Michelson-Morley experiment should have
been accurate enough to detect the motion of the laboratory due to the earth’s
daily rotation on its axis. (D) Two of these. (E) Three of these.
P1. Boat Race.
Two identical boats are racing on a moving river. One boat goes back and forth
across the river while the second goes up and down stream an equal distance
relative to the ground. The river is 100 m across and moving at 10 m/s. The
speed of the boats across the water is 20 m/s. Neglecting any turn around time,
calculate (a) the speed of the first boat with respect to the ground, (b) the
speed of the second boat while traveling up stream, (c) the speed of the second
boat going down stream, (d) the time required for the first boat to cross the
river and get back, (e) the time required for the second boat to go up stream
and back, (f) the time difference by which the first boat beats the second boat
back.
P2. Michelson-Morley Calculations.
Derive the Equations used in the Michelson-Morley Experiment and evaluate the
equations for a typical earth orbiting situation. (a) Show that the time
required for the light to go back and forth across the ether wind is t1
= 2L/c (1-v2/c2)-1/2. (b) Show that the time
required for the light to go up and down wind is t2 = 2L/c (1-v2/c2)-1.
(c) Show that the time difference for v<<c is Lv2/c3.
(d) If the apparatus is rotated 90o, show that the observed change
in path length is expected to be Dx =
2Lv2/c2. (e) Show that the corresponding fringe shift
seen in the telescope of the the interferometer is DN = Dx/l = 2Lv2/lc2. (f) For typical values of L = 11 m, v = 30 km/s,
c = 3.00x108 m/s, and l = 590 nm, show that the expected fringe
shift would be approximately 0.40.
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