There is a similar question, but it is about Pathfinder and not for shadowy illumination.
My question is how far can a character see (without low-light vision) in shadowy illumination? How many feet?
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The process follows the linked question, though the 3.5e rules are very slightly different.
Firstly, shadowy illumination does not change how far someone can see. It simply provides concealment inside sight range.
In an area of shadowy illumination, a character can see dimly. Creatures within this area have concealment relative to that character. A creature in an area of shadowy illumination can make a Hide check to conceal itself.
A creature can see as far as their Spot skill allows. Spotting something gets harder by -1 per 10 feet of distance. One could reasonably assume it's DC0 to see something just standing there. We'll assume taking 10, but of course you can always roll to try to make it sweeter.
Spot checks may be called for to determine the distance at which an encounter begins. A penalty applies on such checks, depending on the distance between the two individuals or groups.
And finally, the maximum distance at which you can detect someone with Spot varies by terrain. It starts at 6d6×40 feet for plains.
Bringing these together, on the plains, in shadowy illumination, then if what you're trying to see isn't hiding you can see for whichever is least:
So to see a Medium sized (+0) menhir (DC 0) in a field at twilight, if you have a Spot of +8 (180') and the DM rolls a 23 on 6d6 (920') then you spot it at 180', assuming you're taking 10. You'd see it at the same distance during the day.
To see a Medium sized orc assassin (Stealth +7) in that same field at twilight, as the shadowy illumination gives him concealment he can hide. So instead of starting at DC 0 we're starting at DC 17 if he's taking 10. Your Spot of +8 means that, again assuming taking 10, you'll see him when he comes within 10 feet of you!
The terrain "max distance" roll is just a cap, which won't always come into play. Other than that, the simplified version is to assume that