Question

A concave lens of focal length $f$ produces an image $\left(1/n\right)$ times the size of the object. The distance of the object from the lens is

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

Answer 1

The correct option is D $(n-1)f$

magnification, $m=\frac{1}{n}$

$\Rightarrow \frac{1}{n}=\frac{v}{u}$

$v=\frac{u}{n}$

from lens formula

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

$=\frac{n}{u}-\frac{1}{u}$

$\Rightarrow \frac{1}{f}=\frac{(n-1)}{u}$

$\Rightarrow f=\frac{u}{n-1}$

$u=f(n-1)$