Heat forming acrylic (aka plexiglass) is pretty simple. Just get the temperature up around 220°F and it's pliable. I put it into the kitchen oven. Don't rely on the oven temperature, though, use something with a probe to tell if you've got the real temp. For one thing, you can put the probe right down where the mirror is, not just floating around in the air inside the oven. Also, when I was researching this I found some warnings about fumes. I think that's only if you overheat because I never smelled or sensed anything. Maybe I've silently shortened my life by 20 years.
I tried a couple different methods of using a form. The first couple tries were "open-faced," meaning I laid the acrylic on top of something and counted on the weight of the material itself to cause it to sag into the form. It isn't really heavy enough for that, so I moved to a two-part form. It takes longer to heat that way because of the mass of the form itself. Another disadvantage of this method is that you have to be able to force the mirror into shape before you heat it, which means no 2D curves (like a bowl, if you see what I mean). Actually, you probably could do that by putting the acrylic sheet between the halves of the form and then weighing the top part down. Like the open-faced method, but with extra weight. Drill a hole in the form so the temp probe can sit right on the acrylic.
The above should give pretty nicely formed acrylic sheet even in complex shapes. Unfortunately it's totally unworkable for acrylic mirror. I'm not sure if it's the acrylic or the mirror backing, but the heat stresses the material such that you don't get a smooth reflection anymore. For a while I thought it was imperfections in the form, but various experiments ruled that out. (You can get bumps and ridges from a rough form, though, which can be eliminated by loosening the form a little or by lining the form with some kind of bumper material. I used a sliced up silicone baking sheet.)
Also: I never got far enough to have this problem, but eventually you'll run out of space in the oven. Multi-part forms? Some other heating method?
The curve I wanted wasn't 2D, so how about cold forming (aka "bending")? I have not yet determined the point at which the acrylic cracks or deforms. I haven't even determined if there's some point short of complete destruction where the mirror breaks down, a la the heat deformation. It seems to be pretty sturdy and stable, but then I'm not making tiny radius curves. If you imagine bending a yard stick, that's about what it seems like, or maybe a little stiffer. Put another way: I have a square of acrylic mirror that's 2'x2' bent into a curve about the same as the side of a 55 gallon drum and I haven't see any problems with it. (This is the 1/8" thick stuff. There's also a 1/4" thick stuff that I've never tried.)
The trick with cold forming is that you have to hold it in place somehow. Even drilling a hole through the acrylic will deform it, although only in the immediate area surrounding the hole. I started with a sandwich method--cutting two parts and then cramming the mirror between. That works, but you have to have some method of securing the bread of the sandwich that doesn't involve drilling through the mirror. Also, you cover up some portion of the mirror surface.
Of course, you can drill through the mirror, but in that case why even have the top piece of bread? That's what I switched to: Put the mirror on an open-faced form and drill a few well-placed holes to secure it down. Don't overtighten, because the force isn't distributed over a wide area like with the sandwich, so the local area can get quite deformed. Maybe a reason to have the top piece of bread after all. Or maybe just some rubber washers or silicone baking sheet for padding.
You can't get too fancy with this method, but for a single, relatively gentle curve it works great.
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