So in this causal chain of light (from a shining object) and (a series of) reflecting objects there is one cause that is principal/independent and other causes that are instrumental/dependent. Each member from the latter is deriving its causal power to illuminate from other causes and finally from the principal cause.
Such causal series must have a first independent cause.
I think that is a really bad interpretation of what happens. It completely misunderstands what is actually happening in this scenario.
First, only the light has the 'power to illuminate' and it does so simply by bouncing off of something and then entering an eye. That is what we *mean* to say that something is illuminated: that light has bounced off of it.
Second, NONE of the other things has any 'power to illuminate'. Instead, they have a 'power to reflect light'. And that power is not transferred, gained, or lost.
Now, the light itself can be caused by some sort of interaction of matter, but that doesn't mean the matter has the 'power to illuminate'. It just means that matter has the 'power to make light'. And that power doesn't get transferred either.
So, the sun has the 'power to make light' and the moon has the 'power to reflect light' and the light has the 'power to illuminate'. No powers are transferred between things. Each thing has its own power (property) and keeps it for the duration of the process.