How big does a mirror have to be for an astronaut on the moon to notice it?

Answer

The important parameter is the amount of light that is sent to the astronaut. Ordinary sunlight on a mirror is far too dim to be visible to the eye. The reflection on large ice surfaces in the mountains can of course be seen. Perhaps more interesting is the “Lunar Laser Ranging” experiment, which does just the opposite: they placed mirrors on the moon; by now aiming a laser at these mirrors from the earth, we get very little light back (one photon every few seconds, according to wikipedia); too little for our eyes, but visible to detectors that can measure the distance between Earth and moon very precisely.