Question

An object ,a convex lens of focal length $20cm$ and a plane mirror are arranged as shown in figure. How far behind the mirror is the final image formed ?

• A. $20cm$
• B. $30cm$
• C. $40cm$
• D. $50cm$

Answer 1

Answer: (C)

$40cm$

From lens formula, $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\Rightarrow \frac{1}{v}=\frac{1}{f}+\frac{1}{u}$

$=\frac{1}{20}-\frac{1}{12}$

$=\frac{1}{4}(\frac{1}{5}-\frac{1}{3})$

$=-\frac{1}{4}\left(\frac{2}{15}\right)$

Image distance for convex lens, $v=-30cm$

Distance of image formed by lens from mirror $=40cm$

$\therefore$ Final image formed behind the mirror $=40cm$