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

Answer:

According to the question –

Focal length of the convex lens is f₁=30cm

Focal length of the concave lens is f₂= -20cm

Focal length of the system of lenses is denoted  by f

The equivalent focal length of the given system of lenses 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=-60cm

As a result, the focal length of the lens combination is 60cm. In addition, the negative sign indicates that the lens system in use is a diverging lens.