: Consider a Michelson interferometer $($see below$).$ A gas cell with a length of $5\mathrm{.}0$ centimeter and parallel windows at the ends is placed in one arm. The light has a wavelength of $800$ nm in vacuum. When a gas of initial pressure $105$ N$/$m$2$ in the cell is being pumped out completely by a vacuum pump, $25$ fringes pass by a point on the observation screen. $($a$)$ What is the refractive index of the gas? $(15$ points$)($b$)$ What should be the pressure of the gas in the cell to introduce a delay of five full optical periods between light in the two arms of the interferometer? Assume refractive index linearly varies with pressure. $(15$ points$)$