Question

A concave lens of focal length f produces an image $1/3$ of the size of the object, the distance of the object from the lens is

• A. $2f$
• B. $3f/2$
• C. $4f$
• D. $2f/3$

Answer 1

The correct option is C $4f$

Magnification $m=\frac{1}{3}=-\frac{v}{u}$

$u=-3v$

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\Rightarrow \frac{1}{f}=\frac{1}{v}-\frac{1}{-3v}=\frac{4}{3v}$

$\Rightarrow v=\frac{4f}{3}$

Again $u=-3v=-3\times \frac{4f}{3}=-4f$

$u$ is placed in front of the lens hence the negative sign.

Therefore the correct answer is (C).