I'm building a Dyson sphere - a real one, like Freeman Dyson originally proposed, made of swarms of solar collectors in independent orbits that fully surround the star, something like this:
Each collector/habitat will be a truncated triangle, approximately two million kilometers wide by one million high. The inner face of some of the collectors will be inhabited, while others - those further in, exposed to stellar radiation at all times - will be entirely automated.
I'm designing a society to live on one of the habitable plates of the swarm. Being further out, their plate spends most of its time shadowed by other plates, and is only occasionally exposed to the sun. The people of the plate have lost a lot of their advanced knowledge, and they see the star as their life-giving god, the plates closer to it as their heavens, the plates further away as hells.
What I'm trying to work out is exactly how often would they get starlight at different levels of the swarm? How many levels have to be 'above' them for them to get, say 25% sun? Is this something that can be easily calculated, or if not is there an engine or similar I could use to find a result?
Edited to Add:
Detail I neglected to include originally - the closest plates to the star are about 0.5 AU out, and there's around 2 million kilometers separation between each layer of plates.