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M = +1/5 or -1/5 and v = +18 cm or -18 cm So there are 4 possibilities. But v positive means behind convex mirror and hence, the image has to be erect. Hence m is positive only. There are 3 cases only.

It is a mirror: m = -v/u 1/f = 1/v + 1/u

case 1) m = +1/5 = -v/u let v = +18 cm u = - 5 v = -90 cm 1/f = 1/18 - 1/90 = 4/90 => f = +22.5 cm Convex Mirror.

case ii) m = +1/5 = -v/u let v = -18 cm u = +90 cm not possible. as u is always negative.

case iii) m = -1/5 = -v/u let v = +18 cm u = +90 cm not possible

case iv) m = -1/5 = -v/u u = 5 v v = -18 cm 1/f = -1/18 - 1/90 = -6/90 f = -15 cm concave mirror