# 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?

Question:

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.

Solution:

Focal length of the convex lens, f1 = 30 cm

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:

$\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$

$\frac{1}{f}=\frac{1}{30}-\frac{1}{20}=\frac{2-3}{60}=-\frac{1}{60}$

$\therefore f=-60 \mathrm{~cm}$

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.