Most plastics are transparent to UVA, which is like 90% of UV that reaches earth's surface. They only start absorbing at higher UV frequencies. That's why sunglasses have dedicated UV ratings. You can bring your sunglasses to basically any optometrist and test how well they block UV. It takes 20 seconds and they'll probably do it for free.

That makes sense, thanks.

Glass protects from UV bellow 350nm, which leaves 350nm-400nm band open. So additional coating is required. I might be wrong but such factors as glass thickness and the radiation intensity should be also accounted for. Every physical object is mostly an empty space ...

Visual range goes to 380. I'm skeptical that light at 350 is really doing much damage to my eyes.

It actually does not not matter what you see. You can't see UV, and it harms your eyes. What you need is a protection from UV band, and that is exactly what your eye can't see.