If I stand in front of a mirror, the light takes a finite, albeit small, amount of time to reach my eye.
So I am seeing myself as I looked some small fraction of time in the past.
Now if I stand with a second mirror behind me, I can see an infinite number of images of myself, each slightly older.
If I had my arm raised, and then I lowered it, can I still see an image of myself with raised arm?
I may be missing the point here, but at first thought you'd need an awfully big telescope, for starters. Assuming you could lower your arm in 1/10 of a second, the image of your "arm up" self would be about 18,600 miles away. Certainly you couldn't see that without some help. Aside from that, there are plenty of practical issues at play, such the telescope getting in its own line of sight, etc.