Question

A concave lens of focal length forms an image which is $n$ times the size of the object. The distance of the object from the lens is

• A. $(1-n)f$
• B. $(1+n)f$
• C. $\left(\frac{1+n}{n}\right)f$
• D. $\left(\frac{1-n}{n}\right)f$

Answer 1

The correct option is D

$\left(\frac{1-n}{n}\right)f$

For concave lens $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

where $v$ is the distance of image from the lens, $u$ is the distance of object from the lens and $f$ is the focal length of the lens
$\Rightarrow \frac{u}{v}-1=\frac{u}{f}$
Since, image size is equal to $n$ times the size of object, $\frac{u}{v}$ can be written as $\Rightarrow \frac{u}{u\times n}=\frac{1}{n}$
$\Rightarrow \frac{u}{v}-1=\frac{u}{f}$
$\Rightarrow (\frac{1}{n}-1)=\frac{u}{f}$
$\therefore u=\left(\frac{1-n}{n}\right)f$