I am in the process of creating a custom campaign setting for my players, with the main premise being that the sun has shattered, leaving most of the world in perpetual night, while a host of nations have obtained a "sun stone", a shard of the broken sun, which keeps a reasonable swath of territory in perpetual daylight.
Assuming I go the mythological route and assume the world is a flat disc, how much territory would a "miniature sun" cover from different elevations? Say, from the top of a mountain? Or from the top of a floating city/fortress?
are you hoping for an accurate estimate, because it depends on how bright the sun is. every doubling of distance away from the sun would be 1/4 as bright(on average), so directly under the sun would have to be pretty intense for it to travel any distance and be meaningfully bright.(the mathematics on why this is is because while the distance doubles the surface area quadruples)
if it shines like i star, you probably could see the other suns on a flat disc from VERY far away.
air scatter would be negligible until a great distance away.
If you wanted to handwave physics in favor of mythology, you could throw distance out and use landmark shadows, so you'd end up with valleys that were dark holes in the enlightened region, big cones of darkness behind mountains, etc. If you sketch a crude map, just starting with your Sunstone in the center, and some locations of other tall features, and shade out the areas behind them, you might end up with an interesting set of light borders.
If your world is a flat disc, the effective range of a light source is infinite if it doesn't run into any sort of barrier (such as a hill or mountain of higher elevation than the place you put the light on).
The main issue is how bright the light is at any given distance.
