I recently got one of these which is really great.
http://support.logitech.com/en_au/product/tvcam-hd

 

But got me thinking that it would be great to be able to do the same thing with an iPhone iPad. Something like a mount for a TV but with an out for Lightning-to-HDMI.

 

I've spent some time looking but cannot find anything at all which can do this. Is anyone else if it exists?