Question

To form a virtual image twice the size of the object, using a convex lens of focal length, $\left(f\right)$ $20cm$, the object distance $\left(u\right)$ must be ______.

• A. $u<20cm$
• B. $u>40cm$
• C. $20cm\le u\le 40cm$
• D. $u=20cm$

Answer 1

The correct option is A $u<20cm$

Given:
Focal length $\left(f\right)=20cm$.
Image size $h_i$ is twice the object size $h_o$
$\therefore h_i=2\left(h_o\right)$
or, magnification, $m=\frac{h_i}{h_o}=\frac{v}{u}=2$
$\Rightarrow v=2u$, where $u$ is the object distance and $v$ is the image distance.
According to lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
or $\frac{1}{2u}-\frac{1}{u}=\frac{1}{20}$
or $u=-10cm$
Therefore object lies in between focus and optical centre.
That is, inorder to form a virtual image twice the size of the object, $u<20cm$