they simply reflect the light back over and over. if you have a certain amount of infinite mirrors they will slowly turn a green-ish colour – because the material they are made out of will absorb a tiny amount of the light unevenly, leaving more of the green than the rest of the spectrum. this is very slight, though.
generally, infinite mirrors can bounce light forever – there is nothing stopping them, if we can find a material that absorbs no light whatsoever. it’s nothing special.
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