A parabolic mirror is inside of almost every flashlight (actually it's called a paraboloid). If you want to do a fun "gee whiz" experiment, open up your flashlight and remove the mirrored portion. Take out the lightbulb at the focus of the paraboloid, put a match in in its place, and point the mirror at the sun. Your match should burst into flames (even in Kentucky! It just usually works better down here...).
Now I don't want to heat the water to boiling: pasteurization (killing all the nasty microbes) purportedly takes place at 150 degrees Fahrenheit, for 20 minutes. And I don't want to keep emptying and filling a pot; so we want a closed, circulating system that will allow water to circulate through the focal point. And rather than a single focal point, we're using a parabolic trough, that has a line of foci. There's a length of copper pipe that the water in our system runs through. As the water goes through the trough, the water is heated.
I hope that we might be able to heat 5 gallons of water this way. The average human needs about a gallon of clean water per day (two liters or so to drink, and the rest for handwashing, dishes, etc.), so 5 gallons would be about right for a family. So we started with a 5 gallon bucket, a few lengths of garden hose, a piece of 1/2 inch steel pipe painted black (didn't have copper), and a three foot long trough. The trough, though it was supposed to be parabolic, was more v-shaped, because the fiber board we'd used for a backing split.
At first I was just going to patiently await the next attempt with the fiber board, but since the trough was still relatively parabolic at the ends, and since it was ready to go otherwise, I decided to try this "crippled" heater, to see how well it could do. Best case scenario, it would do the job. Actual case scenario: not even close! I got the coldest water in the bucket up to 100 degrees, and the warmest to 120 or so. There's a remarkable heat gradient in the bucket: you stick your hand in, and up top it's warm, whereas it gets quite noticably colder at the bottom of the bucket.
I'm hoping that several things will make the system better:
We're now moving on to the "better surface" phase: replacing the aluminum-foil-on-fiber-board with tin roofing material. It would be nice to have a thin, highly reflective, cheap, and flexible material to use instead: if you know of such a material, please let me know (someone mentioned newspaper printing transfer aluminum -- anyone know anything about that?).
Paraboloids also collect light from stars in telescopes, and are the basis of your satellite dish. Archimedes purported lined up soldiers with polished brass shields in the shape of a parabola, and burned Marcellus's enemy ships in the harbor. That's the number one reason for using parabolas!;)
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