Question

An object $O$ is placed at a distance of 20 cm from a thin Plano-convex lens of focal length 15 cm. The plane surface of the lens is silvered as shown in Fig. The image is formed at a distance of

• A. 60 cm to the right of the lens
• B. 30 cm to the left of the lens
• C. 24 cm to the right of the lens
• D. 12 cm to the left of the lens

Answer 1

Answer: (D)

The effective focal length of the silvered lens is given by
$\frac{1}{F}=-\frac{2}{f}+\frac{1}{f_{m}}=-\frac{2}{15}+\frac{1}{\in fty}=-\frac{2}{15},$ which gives
$F=-\frac{15}{2}cm.$ The silvered lens behaves like a concave mirror. Using the spherical mirror formula $\frac{1}{v}+\frac{1}{u}=\frac{1}{F},$ we have $\left(\because u = - 20 \, c m \, a n d \, F = - \frac{15}{2} c m\right)$
$\frac{1}{v}+\frac{1}{- 20}=\frac{2}{- 15}$
Which gives $v=-12 \, cm.$ The negative sing indicates that the image is formed to the left of the lens.