# Is the focal length of a mirror always shorter than the radius of curvature?

Is the focal length always shorter than the radius of curvature? If so, is there a reason for that?

This is to help me when drawing ray diagrams.

I am asking for spherical and plane mirrors.

I would be happy to find out for lenses as well, though do lenses have a centre of curvature ?

If the source of light was at the center of the curvature of a spherical mirror, i.e., at the distance $R$ from the mirror, the light would be reflected right back, because the incident and reflected angles will be $90^\circ$, i.e., it would converge at the source.
From the above, it should be obvious that, if the light source is moved further away from the center, the reflected light would be converging closer to the mirror. Following this logic, it should be clear that the focus of the mirror, which is a converging point of the reflected light coming from infinity, should be even closer to the mirror, i.e., the focal length should be less than $R$ (actually, about $\frac R 2$).