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

• A. True
• B. False

Answer 1

The correct option is A True

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