The image of an object formed by a lens is of magnification -1. If the distance between the object and its image is 60cm, what is the focal length of the lens?

Given m = -1, since m = v/u = -1, -ive sign shows that v is +ive i.e. image is formed on the other side of the lens, and |v| = |u|.

Now distance between object and image = 60cm,
or |u| + |v| = 60
or |u| + |u| = 60
or |u| = 60/2 = 30cm
or u = -30cm and |v| = 30cm or v = 30cm

Now by lens formula, f = uv/(u - v) = -30 × 30 / -30 - 30 = 15cm (+ive focal length means it is a convex lens).

Now if u = -30 + 20 = -10cm, as u (10cm) < f (15cm), it means the object lies between F and C. In this position of the object, the rays from the object cannot meet at any point on the other side of the lens, which is also clear from the position of the image found below.

From lens equation v = uf/(u + f) = -10 × 15 / -10 + 15 = -30cm, -ive sign shows that the image will be formed on the same side of the lens where the object is placed.