lets say you were able to place a mirror in space out at such a distance that the mirror experience cosmological redshift from your perspective. If you were to shoot a laser beam of some wavelength at the mirror then the light reflecting off the mirror would be a longer wavelength than the originating laser because of the relativistic doppler effect. what wavelength would the light be when it got back to you after bouncing off the mirror? would it be the original wavelength or would it be redshifted? if its not the original wavelength then how was energy conserved?