I am studying the Michelson interferometer shown in figure 2 (similar design shown below) of the AMRITA vlabs tutorial. There it is stated that
Since the reflecting surface of the beam splitter BS is the surface on the lower right, the light ray starting from the source S and undergoing reflection at the mirror M2 passes through the beam splitter three times, while the ray reflected at M1 travels through BS only once. The optical path length through the glass plate depends on its index of refraction, which causes an optical path difference between the two beams. To compensate for this, a glass plate CP of the same thickness and index of refraction as that of BS is introduced between M1 and BS.
Can the same condition that the optical path lengths are the same be satisfied by removing the compensator plate and rotating the beam splitter around so that both beam paths travel through glass only once?
Edit: I realize now that I miscounted, badly. With the reflective side of the beam splitter facing the source, the number of journeys through the glass is still 3 for one beam and 1 for the other, hence the need for a compensator plate to add two journeys through the glass remains.