I can use air play through apps, but can't mirror. How do I fix?

I have an iPhone 5 and AppleTV 3rd generation. I know I'm on the same wifi network because I can stream YouTube videos and my music and use the remote app, but the option for mirroring isn't there when I double click home and slide through the settings—all I see are the usual volume and music controls. I've also tried flicking my router off and on, any other tips?