Two inertial frames of reference S and S’ are in the standard configuration, frame S’ having velocity v with respect to frame S. At the instant when their spatial origins O and O’ coincide, a light beam is emitted from O and O’ along the positive x- and x’-axis. The beam is reflected by a mirror M fixed in S at a distance d from O and with its plane perpendicular to the x-axis. Consider the following three events:
(1) Light beam reaches M,
(2) Reflected beam returns to O’,
(3) Reflected beam returns to O.
Calculate the times of these events as measured by observers in frame S. Use the Lorentz transformation to determine the times of these events as measured by observers in frame S’. Show how observers in frame S’ would explain their measurements without reference to frame S.