What is the focal length of a convex lens of focal length 30 cm in contact with a concave lens of focal length 20 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

Focal length of the convex lens, f1 = 30 cm and

focal length of the concave lens, f2 = -20 cm

Focal length of the system of lenses = f

The equivalent focal length of a system of two lenses in contact is given as:

1/f = 1/f1 + 1/f2

=> 1/f = 1/30 -1/20 = (2-3)/60 = -1/60

Therefore ,

f = -60 cm

Hence, the focal length of the combination of lenses is 60 cm. The negative sign indicates that the system of lenses acts as a diverging lens.