Sony NEX shooters rejoiced when Metabones announced a Speed Booster adapter that offered a Full Frame look on the NEX cameras, but also increased the F-Stop of the lens attached. Check out the quick review from ProCinemaTools.com about the Metabones Speed Booster.
So how does this work? In short, it's similar to a Telephoto Extension adapter that multiplies your lenses focal length. The reason why it's able to perform this same technique in 'reverse', is because it is using a lens designed for Full Frame cams, but is directing the image to a much smaller sensor (like the NEX). The Metabones supports electronic functions like Image Stabilization and aperture can be controlled directly from the Sony NEX cameras buttons and dials, but price ranges from $450-$600 dollars (found here).
Recently another Speed Booster'ish Focal Reduction adapter has been released, but it offers no electronic communication. This one is designed for Nikon manual lenses with manual aperture controls to mount to your Sony NEX cameras (metabones does not currently offer Nikon to NEX). You can use this to achieve a Full Frame look from of your Rokinon (Nikon mount) lenses as well. At less than half the price of the Metabones, this adapter is being listed at $198 via eBay (click here)
Focal Reducer Speed Booster Nikon to Sony NEX
When is someone going to make one for the BlackMagic or MicroFour Thirds?