Camera Turns On By Itself

I was working on my Mac Mini when I noticed that my Logitech camera was on (red light around lens). I also noticed that there was a number in the upper right corner of the FaceTime app icon (badge?). When I clicked on the app, nothing happened. I had to quit it and restart to get it to come up. When I did, I saw that my sister had tried to contact me, but when I spoke to her later, she said she hadn't. I suspect her son was playing around or acutally trying to contact me. At any rate, I don't like the camera comming on without my permission. Is there anyway to stop it from doing so?