Question

A lens forms a diminished and erect image of an object. The magnification is $\frac{1}{4}$. Find ratio of distance between object and focus and focus and image

• A. 4:1
• B. 1:4
• C. 8:1
• D. 2:1

Answer 1

The correct option is C 8:1

magnification is $\frac{1}{4}=\frac{v}{u}$
$v=-v$
$u=-4v$
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{-v}+\frac{1}{4v}=\frac{1}{f}$
$f=\frac{-4v}{3}$
$ratio=\frac{u-f}{v-f}=\frac{4v-\frac{4v}{3}}{v-\frac{4v}{3}}=\frac{8}{1}$
option $C$ is correct