Point `S^(')` is the image of a point source of light S in a spherical mirror whose optical axise is `N_(1)N_(2)` (shown in Figure). Find by construction the position of the center of the mirror and its focus.

Explanation

Since the ray incident on the mirror at its pole is relected symmetrically w.r.t. the major optical axis, let us plot point `S_(1)` symmetrical to `S^(')` and draw ray `SS_(1)` until it intersects the axis at point P(see the following figur). This point will be the pole of the mirror. The optical center C of the mirror can obviously be found as the point of intersection of ray `SS^(')` with axis `N_(1)N_(2)`.
The focus can be found by the usual construction of ray SM parallel to the axis. The reflected ray must pass through focus F (lying on the optical axis of the mirror ) and through `S^(')`.