Question

A convex lens of focal length 20 cm and a concave lens of focal length $f$ are mounted coaxially 5 cm apart. Parallel beam of light incident on the convex lens emerges from the concave lens as a parallel beam. Then $f$ in cm is:

• A. 35
• B. 25
• C. 20
• D. 15

Answer 1

The correct option is D 15

Given: A convex lens of focal length 20 cm and a concave lens of focal length $f$ are mounted coaxially 5 cm apart. Parallel beam of light incident on the convex lens emerges from the concave lens as a parallel beam.

To find the value of $f$ in cm

Solution:

As per given criteria,

Focal length of the convex mirror, $f_c=20cm$

As the parallel beam is first incident on convex lens parallely, it will form an image at a distance of $v$ from it, such that

$\frac{1}{v}-\frac{1}{-\infty }=\frac{1}{20}⟹v=20cm$

This image acts as object for concave lens, but as the distance between the convex lens and the concave lens is $5cm$.

The object distance for the concave lens will be $20-5=15cm$

Applying lens formula for concave lens of focal length, $f$, we get

$\frac{1}{\infty }-\frac{1}{15}=\frac{1}{-f}⟹f=15cm$

Hence the focal length of the concave lens is 15cm.