How do you calculate the focal point location of a circular mirror? [closed]

I'm trying to find the focal point and center of curvature of a concave mirror. Just using the radius for the center doesn't seem to work. I know C = 2f, but I'm not sure how to find f or C, given the radius of a perfect circle. is r = C and I'm just to drawing it right?

The object should be at the same place (but inverted) if it's placed at the center of curvature right?

When I try to use an optics simulator the rays seem to bounce off something behind the mirror.

closed as off-topic by ACuriousMind♦, JamalS, Kyle Kanos, David Z♦Jan 16 '15 at 21:06

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• A circular mirror is an approximation of a parabolic mirror. This approximation gets worse the further you are from the main/symmetry axis. So you would get better results if you would make the object a lot smaller, such that the parallel beam stays closer to the axis, or use a parabolic mirror. – fibonatic Jan 16 '15 at 16:35

You are correct in the way that you use the center and radius. You are also mostly correct that $C=2f$, however this is only true when the size of the mirror is small, compared to the radius of the mirror. The relationship $C=2f$ holds best for small angular diameters.