Both arms of a Michelson interferometer are enclosed in pipes so that the air can be removed from the regions between the mirrors and the beam splitter. There is initially a vacuum in both regions, and the mirrors are the same distance from the beam splitter. Air is then let into one of the pipes, and light that travels to and from one mirror now propagates in air while the other part of the interferometer is still in a vacuum. If the interference pattern shifts to the 4000th bright fringe when the air is added, what is the distance from a mirror to the beam splitter? Assume λ =  600 nm.