A pin of length 2.00 cm is placed perpendicular to the principal axis of a converging lens. An inverted image of size 1.00cm is formed at a distance of 40.0 cm from the pin. Find the focal length of the lens and its distance from the pin.

the image is formed at a distance from the object, -u + v =40cm

The height of the object, h0 = 2cm

The height of the image, h1= 1cm

The magnification is given by

Now, using lens maker’s formula,