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?
If the disc is sufficiently flat then any minisun at any altitude covers an infinite area. However there are obstacles like hills in the way if the terrain is halfway like Earth, and once the minisun's rays are hitting at a low enough angle the light intensity will be too low for crops.
If you assume that a 15 degree angle is about the lowest you can usefully use then the radius of the area covered is about 3.7 times the altitude. Put it on a 2 mile tall mountain and you can grow crops in about a 7.5 mile radius, but likely most of that land is poor for crops and a lot of it will be in shadow from lesser peaks and hills. Put it on a floating fortress 2 miles above flat land and you illuminate the same area but probably with a lot more production.
Unless there are a huge number of these minisuns then most land is unilluminated and will freeze; you'll lose almost every river and winds off the cold lands will be startlingly icy. All the seas will freeze over too. There won't be much rain, snow or other precipitation.
You may also consider that the intensity of the light decreases with distance; and the illumination strongly depends on the angle of illumination. When the source of light is 30 degrees above the horizon, the illumination already drops by factor of two.
A shard that creates perpetual daylight in its vincinity, at large distance may look like just a bright star on the horizon, and somwewhere between would be a twilight zone.
The radii of various zones depend not only on the elevation, but also on the strength of the shard.