Question

A point object O is placed at a distance of $20$cm from $2$ convex lens of focal length $10$cm as shown in figure. At what distance x from the lens should a concave mirror of focal length $10$cm, be places so that final image coincide with the object?

• A. $10$cm
• B. $40$cm
• C. $20$cm
• D. Never

Answer 1

Answer: (C)

$20$cm

$\begin{array}{c}u=-20cm\\ f_1=1cm\\ \frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ \frac{1}{v}+\frac{1}{20}=\frac{1}{10}\\ \frac{1}{v}=\frac{1}{10}-\frac{1}{20}\\ =\frac{2-1}{20}\\ v=20cm\\ \text{Final image coincide with the object at}=20cm\end{array}$