I have actually tried this, and it is not as comfortable as it sounds. I have a projector and used a mirror to project the picture directly on the white ceiling above my bed (I tried this once when I was home sick and uncomfortable even sitting up for longer periods).
The problem is that when you have the picture directly above, you have to lie on your back to see the picture properly, and cannot change position easily (e.g. to lie on your side or belly instead). That is very tiring for your back after a while.