A perfect mirror means, that all the photons which collided with the mirror will be reflected in the same amount, with the same energy and with the same - except sign - angle. Will the mirror get an impulse from the photons?
Answer
Yes it will.
Assuming the light is incedent normally the change in the photon momentum is $2h\nu/c$, and consequently the momentum of the mirror will change by the same amount.
If the mirror is free to move it will be accelerated by the light and as a result the light will be slightly red shifted. There is more discussion of this in Can relativistic momentum (photons) be used as propulsion for 'free' after the initial generation? though the question is not an exact duplicate.
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