Question

A convex lens of focal length $f$ produces a real image $\frac{1}{n}$ times of the size of the object. The distance of the object from the lens is

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

Answer 1

The correct option is D

$-(n+1)f$
As the image formed by convex lens is real and inverted, so

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

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

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