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} $