[clueless (OP)]

You are at the beginning of a long corridor. The corridor is in the shape of a quadratic prism, its width and height 3 m. There is no opening near you, rather a wall (with a side 3 m long) with a ring centered in its middle. The ring is 30 cm in diameter and it is emitting a dim white light. This is the only source of light in corridor. My question is, how long does the corridor have to be so that you won't be able to see the weak light as you move away from the illuminated ring? Approximately how many miles do you have to be distant from the ring-shaped bulb so that all you can see is darkness in the corridor? About 5 miles? You can see the stars in the night sky, which are many light-years distant from Earth, but the star are a lot brighter than some dim bulb. I would be grateful if you could help me on this matter.

[CliffordK]

You would have a few issues.
Illuminating the corridor vs the light source being visible.

Assuming your eyes are dark adapted, then the vision threshold is somewhere around 50 to 100 photons reaching the eyes (I'm not sure of the time frame). 

The brightness of the object will decrease by the square of the distance.  Anyway, after a short distance, you would no longer see significant reflective light illuminating the corridor, but you would still be able to see the source, perhaps for several miles. 

Hmmm, a 10W bulb would put out somewhere around 1x10¹⁹ photons per second, I think.  Can I just divide this by the distance (in meters) squared?  That would give you somewhere around 1x10⁹ meters, or hmmm, somewhere on the order of a million km.  That sounds like too many, but your dim bulb may be visible for at least several miles.  If it is very dim, you may not just notice it without concentrating somewhat looking for the light source (and as mentioned, you'd have to be 100% dark adapted, as one would be in a cave).

Another issue is the horizon.  If the corridor is constructed perpendicular to gravity, then it will have a slow curve with the curvature of the Earth.  You should be able to calculate the circular curvature of the Earth for an exact calculation, but within a few km, the light source would fall over the horizon.  However, it would be possible to construct a corridor or tunnel that was absolutely straight, especially using laser guidance. 

[clueless (OP)]

This is helpful. Thanks.