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$$ SERCP$1125\mathrm{.}7.$P$\mathrm{.}056.$MI$.$

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The Michelson interferometer can be used to measure the index of refraction of a gas by placing an evacuated transparent tube in the light path along one arm of the device. Fringe shifts occur as the gas is slowly added to the tube. Assume $620-nm$ light is used, the tube is $4\mathrm{.}90$ cm long, and $162$ fringe shifts occur as the pressure of the gas in the tube increases to atmospheric pressure. What is the index of refraction of the gas? Hint: The fringe shifts occur because the wavelength of the light changes inside the gas$-$filled tube. $($Give your answer to five decimal places.$)$

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