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An evacuated cell of length 10 cm is placed in one arm of a Michelson interferometer...

An evacuated cell of length 10 cm is placed in one arm of a Michelson interferometer using a 589-nm light source. When methane gas is allowed to enter the cell, the interference pattern is observed to shift 75 fringes as the pressure increases to atmospheric value. Calculate the index of refraction of methane. If we remove the evacuated cell then, a shift of 50 fringes will correspond to displacing the movable mirror of the interferometer by what distance?

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