Question

A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm On the other side of the lens, a convex mirror is placed at a distance of $10 cm$ from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of convex mirror?

• A. 25 cm
• B. 50 cm
• C. 10 cm
• D. 20 cm

Answer 1

Answer: (A)

For convex lens, $\frac{1}{v}-\frac{1}{-12}=\frac{1}{10}$
or, $v=60\, cm$
In the absence of convex mirror, convex lens will form the image $I_{1}$ at a distance of $60 cm$ behind the lens. Since, the mirror is at a distance of $10 cm$ from the lens, $I_{1}$ will be at a distance of $60-10=50 cm$ from the mirror, i.e., $M I_{1}=50 \,cm$.

Now as the final image $I_{2}$ is formed at the object $O$ itself, the rays after reflection from the mirror retraces its path, i.e., rays on the mirror are incident normally, i.e., $I_{1}$ is the centre of the mirror, so that
$ R=M I_{1}=50 cm $
Hence, $f=\left(\frac{R}{2}\right)=\left(\frac{50}{2}\right)=25\, cm$