Yes I thought of that and forgot to mention I was looking for something static. But thanks anyway.

I think you will get a very hot mirror indeed! If not sufficiently cooled down...

@DescheleSchilder Why? Just like a black piece of paper gets very hot when you shine light on it?

@NorbertSchuch Yes, indeed. The mirror takes energy from the incoming light, so...

@DescheleSchilder Strange. I just checked a few black surfaces in my home and none of them felt particularly hot.

@NorbertSchuch That's strange indeed. But black surfaces (not to be confused with black bodies) are different from frequency shifting mirrors.

Indeed, the former exist.

@NorbertSchuch But suppose they existed, where would the absorbed energy go? Into the mirror. Won't this energy accumulate?

@DescheleSchilder I think the point Norbert tries to make is that the black surface absorbs almost all photons completely and thus the energy they are absorbing is larger than that of the mirror, so by logic conclusion the mirror won't get any hotter than a black surface now.

Of course you can use a rotating mirror rather than have the whole thing moving through space, but there's still a pretty low limit on the frequency shift you'll get out of this

@llama: if by rotating you mean an axis perpendicular to the sight direction, like a turnstile, I thought of it too but yes, low limit, especially from a practical mechanic design point of view.

@NorbertSchuch, You've never sat down on a hot car seat on a sunny day?

@SolomonSlow While this might make parts of you turn red, it has nothing to do with a redshift.

@NorbertSchuch, I must have misunderstood your reason for saying, "I just checked a few black surfaces in my home and none of them felt particularly hot."

@SolomonSlow Irony.

@Deschele Schilder: not sure that would amount to a lot of energy, but you are right regarding energy storage. What energy is not reflected must go somewhere.

@Winston I actually think now that it won't get too hot. Precisely for the reason mentioned above. Your question made a lot of people thinking! including me (I was thinking about the possibility to use gravitational redshift, but it really can't be done, i.e. not in this universe) I'm really curious if such a mirror exists and what you would see. .

@DescheleSchilder: Just added a simple simulation to the question body.