Then you injure the cornea. That's why they use UV lasers for laser surgery, because the cornea absorbs it.

Edit: I recently had a small corneal erosion from my eye drying out over night (eyelid was pulled open by sleeping in a weird posture) and I had 30% vision for 2 days on that eye. The cornea contributes about 40% (iirc could be more) to the total refractive power in the eye. If you have a UV-spot that melts moskitos dancing around on that for half a second...