I assume you mean when the mirrors are placed such that they are perpendicular to the direction of motion. In the case, you have to take into account the "length contraction." The distance between the mirrors will not be 0.5 light-seconds any more. It would 0.5/gamma light-seconds. With that in mind, now calculate the factor by which time would be "dilated."
BTW, 'stationary space' is really not a good term to use in relativity. Try something like 'rest frame'.