An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be:

Initially:
u_i = 40 cm
f_i = 15 cm
\frac{1}{v_i} + \frac{1}{u_i} = \frac{1}{f}
\frac{1}{v_i} + \frac{1}{40} = \frac{1}{15} \implies v_i = 24 cm
Finally:
u_f = 40 - 20 = 20 cm
f = 15 cm
\frac{1}{v_f} + \frac{1}{u_f} = \frac{1}{f} \implies \frac{1}{v_f} + \frac{1}{20} = \frac{1}{15} \implies v_f = 60 cm
Thus image is shifted by 60 - 24 = 36 cm (away from mirror)
Option (4) is correct.