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By means of plotting find: 

(a) the path of a light ray after reflection from a concave and convex spherical mirror (see Fig. 5.4, where F is the focal point, OO' is the optical axis);

(b) the positions of the mirror and its focal point in the cases illustrated in Fig. 5.5, where P and P' are the conjugate points.

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(a) Look for a point O' on the axis such that O' F and O' P make equal angles with O' O. This determines the position of the mirror. Draw a ray from P parallel to the axis. This must on reflection pass through F. The intersection of the reflected ray with principal axis determines the focus.

(b) Suppose P is the object and P' is the image. Then the mirror is convex because the image is virtual, erect & diminished. Look for a point X (between P & P' ) on the axis such that PX and P'X make equal angle with the axis.

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