OS X Yosemite: Use AirPlay to see your desktop on an HDTV
AirPlay Mirroring lets you send what’s on your Mac to an HDTV wirelessly with Apple TV. If your Mac supports AirPlay Mirroring, an AirPlay Mirroring status icon 
appears in the menu bar of your Mac when an Apple TV is on the same network as your Mac.
Before you begin, see the Apple Support article About AirPlay Mirroring in OS X to find out if your Apple TV and Mac can be used for AirPlay Mirroring.
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Make sure your Mac and your Apple TV are on the same network.
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Click the AirPlay status icon
in the menu bar of your Mac, then choose your Apple TV. Note: If you don’t see the AirPlay status icon in the menu bar, check that your Apple TV is set up correctly. OS X automatically detects an Apple TV when it’s on the same network, and displays the AirPlay status icon in the menu bar. -
From the AirPlay status icon menu, choose This Mac or your Apple TV depending on how you want to match the desktop size of your Mac.
You know that you set up AirPlay Mirroring correctly when the status icon in the menu bar is blue. The blue icon indicates that AirPlay Mirroring is active.