Question

A thin lens of focal length $10$ cm is cut into two equal halves and are kept as shown in figure. It an object $O$ is placed at distance $10$ cm from the optical centre of combination. then the distance of image from object will be

• A. 5 cm
• B. 7.5 cm
• C. 10 cm
• D. 20 cm

Answer 1

The correct option is C 10 cm

$\begin{array}{c}\frac{1}{f_{eq}}=\frac{1}{f_1}+\frac{1}{f_2}\\ \Rightarrow \frac{1}{f_{eq}}=\frac{1}{f}+\frac{1}{f}\\ =\frac{2}{f}\\ \Rightarrow f_{eq}=\frac{f}{2}5cm\\ \frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ \Rightarrow \frac{1}{v}-\frac{1}{\left(-10\right)}=\frac{1}{5}\\ \Rightarrow \frac{1}{v}=\frac{1}{5}-\frac{1}{10}\\ =\frac{1}{10}\\ v=10cm\\ Hence,\\ optionCiscorrectanswer.\end{array}$