Modern Physics For Scientists And Engineers
Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 1, Problem 1.17P

To determine

To find:

The expected shift ΔN when the apparatus is rotated through 90°.

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One of the difficulties with the Michelson Morley experiment is that several extraneous effects (mechanical vibrations, variations of temperature, etc) can produce unwanted shifts in the interference pattern, masking the expected shift of interest. Suppose, for example, that during the experiment the temperature of one arm of the interferometer were to rise by deltaT. This would increase the arm’s length (L) by delta(L) =aLdeltaT, where a=10-5 is the arm’s coefficient of expansion. a) Symbolically, express the shift delta(N) that this temperature change would cause (in terms of a, L, deltaT, and lamda).b) Calculate deltaN for lamda=590nm, L=50cm, and deltaT=0.01 C. c) Make a conclusion about the importance of careful temperature control in the experiment by comparing result in b) with the expected shift deltaN (without temperature correction). Hint: we calculated the expected shift in class for different dimensions of the Michelson Interferometer.
Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 µs. They are produced when cosmic rays bombard the upper atmosphere about 10 km above the earth’s surface, and they travel very close to the speed of light. The problem we want to address is why we see any of them at the earth’s surface. (a) What is the greatest distance a muon could travel during its 2.2 µs lifetime? (b) According to your answer in part (a), it would seem that muons could never make it to the ground. But the 2.2 µs lifetime is measured in the frame of the muon, and muons are moving very fast. At a speed of 0.999c, what is the mean lifetime of a muon as measured by an observer at rest on the earth? How far would the muon travel in this time? Does this result explain why we find muons in cosmic rays? (c) From the point of view of the muon, it still lives for only 2.2 µs, so how does it make it to the ground? What is the thickness of the 10 km of atmosphere through which the muon…
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