  We treat the problem of a Michelson interferometer in the field of a plane
gravitational wave in the framework of general relativity. The arms of the
interferometer are regarded as the world lines of the light beams, whose motion
is determined by the Hamilton-Jacobi equation for a massless particle. In the
case of a weak monochromatic wave we find that the formula for the delay of a
light beam agrees with the result obtained by solving the linearized coupled
Einstein-Maxwell equations. We also calculate this delay in the next
(quadratic) approximation.
