Hint: the speed of light is finite

@NiharKarve Sure... but how finite?

Signal travels in body, muscles move, light is reflected on body, light travels to the mirror, bounces around, light travels to retina, stuff happens in eye, signals propagate in brain, ...

@Emil So the answer is... there is lag?

I think the lag from moving to and reflecting on a mirror is the smallest. I don't know how long the "bounce time" inside the mirror is, but light moves very quick but not instantly as far as I know.

Light travels at c (299,792,458 mps) in a vacuum. The refractive index of air is about 1.0003 so light travels in air about 90,000 mps slower than c

Technically the crowd won't see is movements exactly when he makes them even if they are facing him, for the same reasons that it takes even longer for the signal to get to them via the mirror.

the lag is 1 nanosecond per foot (one way), so a mirror at the end of a 400' field has lag of 0.8 microseconds.

Your entire body has both input and output lag. Researchers that connected a GUI to muscles reported that participants felt like the cursor was moving pre-emptively (before they thought about it). Your brain compensates for the lag.

There always is a lag between the light being reflected of someone and the moment it reaches your eyes (about 1 nanosecond/feet). Even when you are talking face to face with your friend sitting 3 ft from you, you are seing his movements ~3ns after he did them. The thing is your brain takes a lot more time to process this info (in the order of ms), so you'll never conciously notice the light travel time lag.

"Will they see his movements exactly when he makes them, just as if they had been simply facing him" - what makes you think they will see his movements exactly when he makes them if they are facing him? The mirror in your scenario is essentially irrelevant. All it does it extend the distance over which the light must travel. It doesn't magically change the laws of physics so that light goes from infinite speed to a finite speed.

You've just reinvented Lidar. en.wikipedia.org/wiki/Lidar

Here's an example: A youtuber tried to record himself 20 km away from a camera. Calculate the lag in the recording.

"Sure... but how finite?" - finite enough that, if the Sun suddenly disappeared, there'd be an 8 minute lag before we stopped seeing it.

Replace the mirror with the man shouting instructions and there will be a noticeable (but still quite short) delay.

Do you ever get in a zoom call and watch your own camera and you can see yourself blinking? It'd be like that, but imperceptible.

@JEB That could be an answer.

That lag needs to be accounted for in audio systems, but light is too fast to make that necessary

What do you mean exactly with long distance in with a long distance between them and the mirror? The mirror cannot be beyond their horizon, or they would not see it. Even if the mirror were tall enough to be beyond their horizon and still visible, they would see the mirror's top part. Certainly they could not see what that person is doing.

It would be kind of cool to put a camera on mars pointing at earth... Then when a murder happens on earth you could ask the camera to replay the appropriate point when the light reached it and know the murderer. You'd need a good camera though.

Here's a good one. You put two mirrors facing each other say 1KM apart , with a speck of dirt at the bottom, you move your head so your looking at the spec after its bounced between the mirrors 4.4×10^23 times. Your now looking at the speck as it was 93 billion years ago at the beginning of the big bang... apart from its not there the light will not have arrived yet, you will have a 93 billion year wait.