They're called "cat" lenses or catadioptric lens. The advantage is that they're shorter because the focal length is "folded" inside the barrel and they're lighter too boot. I've see images with them and they're reasonably sharp. The disadvantage is that you can't adjust the f stop because there's only 1 aperture. You can use neutral density filters to "stop" down the lens. The images from these lenses have very distinct circles of confusion.