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The focus, or focal point of a lens or parabolic mirror is the point onto which collimated light parallel to the axis is focused. The focus of an elliptic mirror is either of two points such that light from one converges on the other. The focus of a hyperbolic mirror is either of two points such that light from one is reflected as if it came from the other. The distance from the lens or mirror surface to the focus is called the focal length.
A diverging (negative) lens, or a convex mirror does not focus a collimated beam to a point. Instead, the focus is the point from which a formerly collimated beam appears to be emanating from, after it travels through the lens or reflects from the mirror.
A lens has two foci, one on either side. By convention, the front focal point is closest to the front surface of the lens, and the back focal point closest to the back surface. Which surface is which is arbitrary.
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