There are two perfect reflect mirrors facing opposite to each other... I place a lamp which is not lit in between the mirrors... I switch it on and switch it off and remove the lamp from between the two mirrors (assume this is instantaneous)... Now(assuming particle nature) the photons are emitted in all direction... The photons collide elastically with the mirror... As the collision is elastic the energy will be conserved and as the photon is reflected... Mirror will gain momentum too and hence kinetic energy.. But the total energy has to be constant so can we say that speed of light decreased then speed of light ? (If you can describe the situation considering wave nature then it will be helpful too)
What we call reflection is in reality a more complicated process than bouncing a ball to a wall. For the part of the electromagnetic radiation that we call visual light and for low densities of this light the surface electrons are responsible for the absorption and re-emission of this photons.
So yes, mirror will gain momentum and the photons will lose momentum. The photons get simply redshifted.
See this answer too, please.