Question

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

Answer 1

Step 1: Data provided:

Focal length of the convex lens (converging lens), $f_1=30\text{cm}$
Focal length of the concave lens (diverging lens), $f_2=-20\text{cm}$
Focal length of the system of lenses = f

Step 2: Find effective focal length:

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

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$
$\frac{1}{f}=\frac{1}{30}-\frac{1}{20}=\frac{2-3}{60}=-\frac{1}{60}$

$f=-60\text{cm}$

Therefore, $60\text{cm}$ is the focal length of the combination of lenses. Also, the negative sign is an indication that the system of lenses used act as a diverging lens.

Final Answer: A diverging lens of focal length $60\text{cm}$.