Question

A combination of concave and convex lens in contact is placed over a plane mirror. When a pin $P$ is placed as shown in the figure, the image is formed at the position of the pin itself. The focal length of the convex lens is 10 $cm .$ Then the focal length of the concave lens is:

• A. $40 cm$
• B. $\frac{40}{3} cm$
• C. $20 cm$
• D. $\frac{20}{3} cm$

Answer 1

Answer: (B)

Since the image of the pin is formed at the position of the pin itself, therefore light rays incident on the plane mirror normally which means that the rays falling over the lens will emerge parallel to its principal axis. Hence, the object point itself is the focus of combined lens.

Therefore focal length of combined lens is $F =40 cm$ If $f_{1}$ and $f_{2}$ are the focal lengths of convex and concave lens respectively.
$\frac{1}{F}= \frac{1}{f_{1}}+\frac{1}{f_{2}}$
$\frac{1}{ f _{2}}=\frac{1}{ F }-\frac{1}{ f _{1}}$
$f _{2}=\frac{ Ff _{1}}{ f _{1}- F }=\frac{40 \times 10}{10-40}=-\frac{40}{3} cm$
Negative sign indicates concave nature of the lens.