I also don't understand what purpose is served by the "pupil" material zone. The iris doesn't suddenly stop at the pupil - it blends to black smoothly. So you really need to put the iris map on both and both just do diffuse lighting.

This is the problem with a "transparent" cornea. You can't see the iris. But on a real human, you can "see" the iris even directly from the side like this. No reflections here, to avoid any visual confusion.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)