Airplay not working on a 2014 iMac

I have a new 2014 iMac running Mavericks 10.9.2 (fully updated), and an AppleTV (can't remember if it's v2 or v3; it's also fully up to date and is running 6.0.2). Both devices are on the wifi network and work fine independently.

On the iMac the Airplay icon is in the menu bar in the top right; I can connect it to my AppleTV. However, when I do so the TV goes black; whe I disconnect the TV returns to the AppleTV homescreen. Again, connect Airplay to the AppleTV and it goes black again.

Checking the Airplay menu, it's currently set to Extend Desktop. If I click Mirror iMac it completely ignores me and nothing changes; checking the Airplay menu again, it's still registering as Extend Desktop.

The iMac was mirroring just fine about a month ago. I've also tried using Airplay on my iPhone 4 and that displays on the AppleTV perfectly.

Does anyone have any clue as to why this has stopped working?