What is this optical effect called?

ISTR its something like recursion.

Its a common misconception that the reflections in two mirrors carry on for infinity for us to see. They don't. It could only occur in two exact same sized mirrors facing exactly opposite and could only be observed from an imaginary line from the centre of each mirror, with no object or thing standing in the way.

It is a truth, but an entirely unobservable one.

It is more like a video TV hooked up to a camera that is pointing at the centre of the TV screen and sitting perpendicular to that point. If the pixels on the tv were infinite, the number of TVs visible on the first TV would be infinite.

I've never heard of this effect having a name, but I imagine it would be classed as a type of echo.

Finally a stage will be reached at which the tray becomes smaller such that the bottle becomes still smaller and the label becomes a point.

The Visual Acuity for normal eye is 0.004mm.

Two dots separated by less than this distance will be seen as single dot.

Its called fractals, 100 percent sure. Its defined as a sequence of repeating events.

Infinity,it can be seen easily at home, have one mirror behind you and one mirror in front,you will see loads and loads of your images stretching back into the distance.

i dont think that this is an actual physics optical effect however never seeing this label i cannot be sure

It is not an illusion as it actually exists.