what would be the best way to cut a circle into a plexiglass sheet? I need a 4" wide "lens" because I am making an underwater camera case and I am trying to do it without spending too much.
Mmmm...not really. As long as you don't go nuts with it, you shouldn't have those problems. If you are close to or in Seminole County, I can set you up with some scrap acrylic to practice on. Where in Central Florida are you?
A hole saw isn't going to give you super clean edges (if that is what you are hoping for). Clean edges requires a CNC router or a rotary table (Acrylics Manufacturing in Longwood). But for a low budget project, the edges really shouldn't matter.
The first problem that you will run into is that a standard hole saw has a drill bit in the center of it. It will drill a hole right where you don't want one (in the center of the camera window). You'll need to first cut a hole in a piece of plywood, and then remove the center drill bit. Then you'll need to clamp the sheet of acrylic between that piece of plywood and a second piece of plywood that doesn't have a hole. Now when you cut the acrylic, it won't have a hole in the center. (The hole in the plywood holds the hole saw steady (keeps it from drifting).)