Question

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

Answer 1

Focal length of the convex lens,f1=30cm
The focal length of the concave lens,f2=-20cm
The focal length of the system of lenses=f
The equivalent focal length of a system of two lenses in contact is given as:

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$

=$\frac{1}{f}=\frac{1}{30}-\frac{1}{20}$

=$\frac{2-3}{60}$=$\frac{-1}{60}$ ∴ƒ=-60cm
Hence, the focal length of the combination of lenses is 60cm. The negative sign indicates that the system of lenses acts as a diverging lens.