An image I is formed of a point object O by a mirror whose principal axis is AB as shown in figure.

(a) State whether it is a convex mirror or a concave mirror .
(b)Draw a ray diagra to laacate the mirror and its focus . Write down the step of construction of the ray diagram. Consider the possible two cases.
(1) When distance of I from AB is more than the distance of O from AB and
(2) When distance of O from AB is more than the distance of I from AB

Explanation

(a) As the image is on the opposite side of the principal axis, the mirror is concave. Because convex mirror always forms an erect image.
(b) Two different cases are shown in figure. Steps are as under:
(i) From I or O drop a perpendicular on principal axis, such that CI = CD or OC = CD.
(ii) draw a line joining D and O or D and I show that it meets the prinicipal axis at P. the point P will be the pole of the mirror as a ray reflected from the pole is always symmetrical about principal axis.
(iii) From O draw a line parallel to principal axis towards the mirror so that it meets the mirror at M. joining M to I, so that is intersects the principal axis at F. F is focus of the mirror as any ray parallel to principal axis after reflection from the mirror intersects the principal axis at the focus.