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During the day, a character can see a distance of 960ft. This is modified by their Perception, giving a bonus of 5% for each level of Perception score (including modifiers) that they have. If they have a negative Perception score, then they have a negative modifier.
This is no Dim light during full daylight.
On an overcast day, then vision distance is halved, plus half this distance is dim. This means most people can see clearly out to 240ft, and dimly out to 480ft.
Terrain can affect how far you can see, since it is assumed trees, bushes, hills etc block line of sight beyond a certain point. Such terrain causes a dim effect, due to targets being partially concealed.
Twilight occurs after the upper rim of the sun meets the true horizon. At this point there is still enough light to not impact vision, due to light being reflected back down from the sky.
From sunset to about 6 degrees below the horizon is defined as civil twilight, and there is enough light to carry on as normal.
From 6 degrees to 12 degrees below the horizon, light is dimmed but otherwise good enough for most circumstances. Vision is limited to 400m.
From 12 degrees to 18 degrees these is still a meagre amount of light, but generally artificial light sources are required.
The Moon can provide enough light to cast shadows when full, but rapidly decreases in brightness as the phase moves towards new. Note that a quarter Moon (half the face showing) doesn't provide half the light as the full Moon, but due to the direction the Moonlight is being reflected it only provides one twelfth.