Like does it get CPU nanometer level small

Or is it not. So. Infinite. At all

Without giving is a lot of thought, my first reaction is it isn't infinite. It's the reflection of light over and over and over again. The mirror absorbes a bit of it each time so it will fade out.

1. You'd need specialized dielectric lab mirrors that lose almost zero energy. A normal mirror absorbs some photons as heat and eventually all of it.

2. It's my understanding that from the perspective of light everything is instantaneous. A photon takes millions of Earth years to travel from the core of it's star to the surface. But from the perspective of the photon it is created, emitted, and hits it target all instantaneously. Unless the light is generated spontaneously from a non-material source you would have to break the laws of relativity. The light has to bounce exactly perpendicular to the mirror to bounce infinitely. As such your light source would inevitably interrupt its path.

If you had perfect mirrors set up in the perfect way, it would behave like light going through the vacuum of space without any obstructions.

Light is quantum mechanically incapable of going perfectly in a straight line; any light beam will diverge over time. This means telescopes have a maximum resolution depending on their diameter and the distance to the object. So for an infinite series you would need an infinitely wide telescope to see any detail.

Though realistically you're not getting anywhere near that because the mirrors or the air between them will absorb and scatter the light.