Suppose that you cut a piece out of a metallic sphere. The inside of this object forms a converging (concave) spherical mirror. Actually, most quality mirrors are not spherical in shape, but have a parabolic cross-section, . This distinction will not be particularly important at this time, since both mirrors will work pretty-much the same way as long as the object used to create an image is small compared to the size of the mirror.
The point that used to be the center of the ball is now called the center of curvature of the mirror. The point in the center of the mirror is called the vertex (or center) of the mirror, and the line joining the vertex and the center of curvature is called the axis of the mirror. The distance between the center of curvature and the mirror is called the radius of curvature of the mirror. The point located on the mirror axis halfway between the vertex and the center of curvature is called the focus , and the distance from the focus to the vertex of the mirror is called the focal length of the mirror.
The (important) relationship between the radius of curvature and focal length can be summed up:
radius = 2(focal length)
r = 2f
portion of the outside of a metallic sphere forms a
diverging (convex) spherical mirror. A diverging mirror has a vertex,
axis, center of curvature, focus, and all the rest - just like a
converging mirror - except for one thing. The focus and center of
curvature of a converging mirror are in front of the mirror - on the
same side as you. Light rays that reflect from the surface of a
converging mirror can pass through the focus and center of curvature
of the mirror. The focus and center of curvature of a diverging
mirror are behind the mirror, and the light rays that reflect from
the surface of the diverging mirror do not pass through them. For
this reason, the focus of a diverging mirror is called a
virtual focus, and the center of curvature is called
a virtual center of curvature.