From Apples web site
Retina display
3.5-inch (diagonal) widescreen Multi-Touch display
960-by-640-pixel resolution at 326 ppi
800:1 contrast ratio (typical)
500 cd/m2 max brightness (typical)
The built in camera captures at 720p so I’d try producing a video at that resolution first and check the playback. Compression will also matter, the higher the bit rate, the harder for the phone to playback.
Hope this helps.