To which degree in your FOV would the plane reach?
Simplified, regardless of your height, the plane would extend to horizontal. Looking around, you would see a perfect half sphere of sky above and half sphere of ground below. Using a theolodite, 180* and 180*.
There are some semantics when you get into when you arrive, how the plane is lit and what the surface material is. If, for example, you and the plan “pop” into existence at the same time, you would see the sky surround you, and then the plane would grow asymptotically from your feet up to the horizon. I don’t really care to do the math, but at 1m if you were observing by eye you probably wouldn’t notice this growth.
Temperature too, heat can bend light.
But what’s more important is atmosphere and just amount of light.
Ahh… Atmosphere. That would blur the horizon to the sky. At very far distances, the scattering and absorption would obscure anything further.
It would look like this: https://i.redd.it/h093236y5iqc1.jpeg
So it would reach to exactly the first half of my FOV?
Yes.
Well, since your eye is above the plane, it would appear that way, but strictly speaking it would only infinitely approach that point and never reach it. But in reality it would make no difference.
Does this infinite plane have mass? If so, the plane would cover your entire field of view, as any line of sight would be bent by its gravity until it once again intersects the plane. It would be like an event horizon of sorts, since there’s no way for light to escape the plane.
I made this point under the assumption that it didn’t have any gravity, but this is very interesting too.
