Describe how a Michelson interferometer can be used to measure the index of refraction of a gas (including air).

A Michelson interferometer can be used to measure the index of refraction of a gas by enclosing one of the beam paths in a gas-filled chamber and observing the shift in the interference patterns due to the change in the refractive index. The interferometer should first be calibrated with a reference material. After introducing the gas, carefully count the number of fringe shifts in the interference pattern to determine the change in optical path length. Finally, calculate the refractive index of the gas using the formula \(n_{gas}=\frac{L_{ref}+m\lambda}{L_{ref}}\), where \(L_{ref}\) is the reference path length, \(m\) is the number of fringe shifts, and \(\lambda\) is the wavelength of the light source.