In reply to Paul035:
The Grivel visor is a bit of a faff especially if you put slings over your head as they tend to get caught between the visor and the helmet. It also gets knocked askew quite easily. Jim is on the right track. I use bike glasses because I need a prescription lens.
You are right to be concerned, I am blind in one eye as a consequence of not wearing eye protection whilst climbing.
This is however no reason to get massively alarmed, the main dangers are looking upwards while belaying (thats what happened to me!)brittle ice when climbing, and being on routes below other parties. All are likely to be sorted with Jim's £2.99 safety glasses, if not the eye injury may not be your major concern.