Spherical Mirror -- from Eric Weisstein's World of Physics

The equation of a circle of radius R displaced a distance R to the right along the x-axis is

and solving for x gives

Taking the minus sign and expanding the square root in a binomial series Eric Weisstein's World of Math gives

This approximates a parabola Eric Weisstein's World of Math

where . Since a parabola brings all light to a single focus, the sphere is a good approximation, with a deviation

Mirror, Optical Aberrations, Spherical Aberration