A divergent lens has a focal length of 30cm. At what distance should an object of height 5cm from the optical centre of the lens be placed so that its image is formed 15cm away from the lens?

We know that for a divergent lens both u and f are negative. From the lens equation: 1/v = 1/u + 1/f, as both u and f are negative, therefore v will be negative. Given f = -30cm, v = -15cm, so u = fv/(f - v) = (-30)(-15)/(-30 - (-15)) = 450/(-15) = -30cm.

Now, linear magnification m = I/O = v/u, given height of object O = 5cm, I = ?, therefore I/5 = 15/30, or I = 5 × 15/30 = 2.5cm