Suppose a transparent vessel long is placed in one arm of a Michelson interferometer. The vessel initially contains air at and . With light of vacuum wavelength , the mirrors are arranged so that a bright spot appears at the center of the screen. As air is slowly pumped out of the vessel, one of the mirrors is gradually moved to keep the center region of the screen bright. The distance the mirror moves is measured to determine the value of the index of refraction of air, n. Assume that, outside of the vessel, the light travels through vacuum, and that if none of the mirror are moved, the central region of the screen changes would from bright to dark and back to bright times—that is, bright fringes are counted (not including the initial bright fringe). Calculate the distance that the mirror would be moved as the container is emptied of air.
