Download and install the OS X Mountain Lion v10.8.5 Supplemental Update.
MacBook Air (Mid 2013): FaceTime HD Camera might not work after OS X v10.8.5 update
The FaceTime HD Camera on your MacBook Air (Mid 2013) stops working with 32-bit applications (such as Skype, iMovie, Final Cut Pro, and QuickTime Player) after installing the OS X Mountain Lion v10.8.5 update.
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