Watching a DVD from iMac to TV via Airplay mirroring

I have an iMac that supports Airplay Mirroring. It usually works fine, showing exactly what is on the computer screen onto the TV, but I tried to watch a DVD loaded in the computer on the TV via airplay, and although the movie showed fine on the computer, as soon as I turned on Airplay, the picture disappeared, and grey and white checkerboard showed up. Sound still worked fine, but this checkerboard is what showed on the TV. When I turned off Airplay, the movie picture reappeared on the computer screen. Why is this happening? Is it not possible to watch a DVD via Airplay?