A point object is placed at a distance of 15 cm from a convex lens. The image is formed on the other side at a distance of 30 cm from the lens. When a concave lens is placed in contact with the convex lens, the image shifts away further by 30 cm. Calculate the focal lengths of the two lenses.

the distance between the convex lens and the object, u= 15cm

The distance between image of object and the lens, v= 30cm

Let the focal length of the convex lens is

Let the focal length of the concave lens is

By using lens formula,

Again, Let v = image (final) distance from concave lens = +(30 + 30) = 60 cm

= object distance from concave lens= 30m

By using lens formula,

So, the focal length of convex lens is 10 cm and that of concave lens is 60 cm.