The position of optical axis `N_(1)N_(2)` of a spherical mirror, the source and the image are known (as shown in Figure ). Find by construction the positions of the center of the mirror, its focus, and the pole for the cases
a. A-source, B-image,
B-source, A-image.

Explanation

a. Let us construct, as in the previous example, the ray BAC and find point C (optical center of the mirror) .Pole P can be found by constructing the path of the ray `APA^(')` reflected in the pole with the aid of symmetrical point ` A^(')`. The position of teh mirror focus F is determined by means of the usual construction of ray AMF parallel to the axis.
b. This construction can also be used to find the center C of the mirror and pole P. The reflected ray BM will pass parallel to the optical axis of the mirror. For this reason, to find the focus, let us first determine point M at which straight line AM, parallel to the optical axis, intersects the mirror, and then extend BM to the point of intersection with the axis at the focus F.