Question

A concave lens of focal length (f) 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,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{u}{v}-1=\frac{u}{f}$
Since image size (h') = n $\times$ the size of object (h),
so, $\frac{h^{\prime }}{h}=\frac{v}{u}=nor,\frac{u}{v}=\frac{1}{n}\Rightarrow (\frac{1}{n}-1)=\frac{u}{f}$
$\therefore u=\left(\frac{1-n}{n}\right)f$