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The Michelson-Morley experiment questions
If light is a wave, nineteenth-century physics reasoned, it must travel through a medium, and the Earth must be moving through that medium. Michelson and Morley built an interferometer sensitive enough to detect that motion and found nothing, and the null result became a starting point for special relativity.
17 original questions · 49 marks · the michelson-morley experiment notes · Turning points
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Describe the principle of the Michelson interferometer.
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A half-silvered mirror splits one light beam along two equal arms at right angles to mirrors that return them (1); the recombined beams interfere, and the fringe pattern registers any difference in the two round-trip times (1).State the two postulates of Einstein's theory of special relativity.
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One: physical laws have the same form in all inertial frames (1). Two: the speed of light in free space is invariant, the same for every inertial observer (1).State what is meant by an inertial frame of reference.
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A frame of reference moving at constant velocity, without acceleration or rotation (1), in which Newton's first law holds: objects with no resultant force stay at rest or move uniformly (1).Explain why nineteenth-century physicists expected light to require a medium, the ether.
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Every known wave travelled through a medium: sound through air, ripples through water (1). Light, established as a wave, was therefore assumed to need a medium of its own filling all space, which was named the ether (1).State what the Michelson-Morley experiment was designed to detect.
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The Earth's absolute motion through the ether, appearing as an ether wind blowing across the apparatus (1).A boat travels at 4.0 m s−1 in still water on a river flowing at 2.4 m s−1. Calculate the round-trip times for 48 m straight across and back, and 48 m downstream and back, and state the relevance to the Michelson-Morley experiment.
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Across: cross-stream speed √(4.02 − 2.42) = 3.2 m s−1 (1)
t = 96/3.2 = 30 s (1)
Along: 48/1.6 + 48/6.4 = 37.5 s (1)
A medium's motion separates the two round trips, which is exactly what the interferometer's two arms were built to detect for light in the ether (1)For an effective arm length of 11 m and an ether wind equal to the Earth's orbital speed of 3.0 × 104 m s−1, the expected time difference is roughly Δt ≈ (L/c)(v2/c2). Evaluate Δt and the corresponding path difference.
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v/c = 10−4, so Δt ≈ (11/(3.0 × 108)) × 10−8 (1)
Δt = 3.7 × 10−16 s (1)
Path difference cΔt = 1.1 × 10−7 m, about a fifth of a wavelength of visible light, well within the instrument's sensitivity (1)Explain why the apparatus was rotated through 90° during the experiment.
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Rotation swaps which arm lies along the supposed ether wind (1), reversing the predicted time difference between the arms (1). The fringes should therefore shift visibly as the apparatus turns, without needing the two arms to be perfectly equal in length (1).The experiment was repeated at different times of year. Explain why this mattered.
The interferometer was mounted on a massive stone block floated on liquid mercury. Suggest why.
State and explain whether each of the following is an inertial frame of reference: (a) a train travelling at a steady 55 m s−1 on a straight track; (b) a car rounding a bend at constant speed; (c) a rocket accelerating uniformly upwards.
State and explain the two conclusions drawn from the failure of the Michelson-Morley experiment to detect any fringe shift.
A spacecraft approaching Earth at 0.40c switches on a landing light. Using the second postulate, state the speed at which the light arrives at Earth, and explain why the everyday rule for adding velocities fails here.
Explain why the Michelson-Morley result, though "null", is counted among the most important measurements in physics.
Michelson's first interferometer of 1881 had an effective arm length of only 1.2 m and could just detect a path-difference change of 0.05 wavelengths of the light used (λ = 5.5 × 10−7 m). The expected time difference from an ether wind of v = 3.0 × 104 m s−1 is Δt ≈ (L/c)(v2/c2), with c = 3.0 × 108 m s−1. Deduce whether this first instrument could have detected the ether wind, and hence suggest why the 1887 apparatus used repeated reflections to give an 11 m effective arm.
Every other wave known in 1887 travelled through a material medium. Explain how an electromagnetic wave is able to travel through empty space.
Describe the Michelson-Morley experiment and explain the significance of its result. Your answer should include the principle of the interferometer, the reason the apparatus was rotated, and the conclusions drawn.
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