Am I correct in assuming it takes the 'normal' view a lens would have on 35mm format and focuses the whole of that image onto a smaller sensor?
If so, it seems logical. It's something I thought about a few years ago when I was temporarily a digital photographer - not as a business idea, just one of the idle thoughts I have occasionally!
Some people might be querying the faster claim. It's because the lens now actually has a shorter focal length but the aperture diameter range stays the same. Simply, aperture (f No.) = focal length / aperture diameter).