On an infinite plane, with gravity the same of that of Earth, how far could light at an arbitrary angle travel until bending to hit the plane? Now, I'm a complete idiot, so bear with me.
I've recently come across the idea that standing an infinite flat Earth would in theory appear the same as standing inside a hollow earth, since light would, due to gravity, bend towards the flat earth.
Here illustrated like so:

However, I have yet to find any source that has an actual way of telling how far this distance would be. I have found calculations for the gravity of an infinite flat earth here and a formula for gravitational lensing here, but I'm not smart enough to understand the latter or how one would somehow combine the two.
So, as this has started to drive me insane, I've decided to turn to people who know more about this than I do.
Basically, there's an infinite flat plane with uniform gravity equivalent to that of earth. Is there any sort of formula or calculation that one could do to to figure out how far along the plane a ray of light would travel if casted at an arbitrary angle?
 A: For a proper calculation you will have to consider a spacetime metric that produces the same gravitational field as in your setup, and then find the null geodesics (paths of light) in this metric. I think this shouldn't be very difficult to calculate.
However we can probably also get an order-of-magnitude estimate just by considering the non-relativistic case of a ballistic trajectory and plugging in $c$ for the velocity. In such a case it is easy to see that the horizontal distance of a projectile shot at a 45 degree angle would be $v^2/g$, so if we plug in $v = c = 3 \times 10^8 m/s$ and $g = 9.8 m/s^2$ , we get a distance of approximately $10^{16}$ meters, or 10 trillion killometers (which is about 1 light year).
A: Keep in mind that if you shine the light horizontally on this long flat planet, the light will hit the ground at exactly the same instant as if you dropped a stone on the ground, or if you shot a bullet horizontally. They will all hit the ground simultaneously.  This is because gravity has nothing to do with the falling object, but with the curvature of space time.  So, if it takes 1/4 second for the stone to hit the ground from dropping it, then it will take 1/4 second for the light to hit the ground.  Then the math is simple, light travels at 300,000,000 meters per second, so 1/4 of that is 75,000,000 meters.
A: The same result will be seen if a ray of light in empty is observed from a uniform accelerating frame. The only ray that doesn't fall back onto the floor of the frame is a ray traveling perpendicularly upward. The ray has to turn around for that, which means it would have zero velocity on a point. Which is impossible. If the ray travels 45 degrees up the horizontal velocity can make up for the loss though. As for any direction apart from 90 degrees. How far will it end up? As the horizontal component varies, it depends. If a ray is shot parallel at height h it takes as long as a stone dropped from h (with zero velocity).
Say a stone "hangs" still in empty space. A ray of light just touching it.  Now we approach this constellation uniformly accelerated. What do we see?
