Question

A convex lens of focal length $f$ produces an image 1/n times than that 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

Answer: (D)

$-(n+1)f$
As the image formed by convex lens is real and inverted, so
$m=\frac{v}{u}=\frac{-1}{n}\Rightarrow v=\frac{-u}{n}$
$\begin{array}{l}\therefore \frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{-n}{u}-\frac{1}{u}=\frac{1}{f}\\ \Rightarrow \frac{-1}{u}(n+1)=\frac{1}{f}\\ \Rightarrow u=-(n+1)f\end{array}$