The focus, or focal point of a lens or parabolic mirror is the point onto which collimated light parallel to the axis is focused. Although the focus is conceptually a point, physically, the focus has a spatial extent, called the Airy disc, or blur circle, due to the width of the aperture of the imaging optics. The focus of an elliptic mirror is either of two points at which light from one point converges on the other. The focus of a hyperbolic mirror is either of two points at which 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 light appears to be emanating from, after it travels through the lens or reflects from the mirror. A convex parabolic mirror will reflect a beam of collimated light to make it appear as if radiating from the focal point or conversely, reflect the rays directed toward the focus as a collimated beam. A convex elliptical mirror will reflect light directed towards one focus as if radiating from the other focus, both of which are behind the mirror. A convex hyperbolic mirror will reflect rays eminating from the focal point in front of the mirror as if eminating from the focal point behind the mirror. Conversely, it can focus rays directed at the focal point that is behind the mirror towards the focal point that is front of the mirror as in a Cassegrain telescope.
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.
See also: focus (geometry)