We probably all know someone who has been hit in or near the eye while playing Badminton. The shuttle is flying so fast that this happens all too often, usually of course while playing at the net. A selection of information and links is presented here. Much more can be found by general web searches. Unlike most other injuries in badminton, eye injuries can be permanent and irreversible.
Bottom line: if you play net a lot and don't wear glasses, you might want to take a look at the excellent polycarbonate goggles that are available. These can be very light yet provide excellent protection and visibility.
If you decide to look into eyeware, here's some good starting links