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.

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.

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