Use iPhone 5S as webcam w/Mac Mini and older Cinema Display

Hi. I hope this is the right forum. Not sure if this is easier than I'm making it or impossible. I have a Mac Mini that I'm using with a Cinema Display. The Display doesn't have a built-in camera. Not sure if newer ones do. Anyway, I'm going to start taking music lessons from someone using Google Hangouts. Rather than buy an expensive webcam, I was hoping to use the iPhone. I wanted to have it send my teacher streaming video of me while I see him on the display. Not sure if this is a big deal. I already bought one app that was supposed to do this and so far the app can't find the Mini, even though it is plugged directly into it. I see that there is a Hangouts app I can download but that seems to use just the iPhone. I think you can see what I'm trying to do here. Thanks in advance.