Question

A 5.0 diopter lens forms a virtual image which is 4 times the object placed perpendicularly on the principal axis of the lens. Find the distance of the object from the lens.

Answer 1

$h_i=4h_0$, $\frac{h_i}{h_0}=4$

$\frac{h_i}{h_0}=\frac{v}{-u}\Rightarrow \frac{-v}{u}=4,v=-4u$

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

$\frac{1}{f}=P=5,f=\frac{1}{5}\text{m}=20\text{cm}$

$\frac{1}{-4u}+\frac{1}{u}=\frac{1}{20}$

$\frac{3}{4u}=\frac{1}{20}\Rightarrow u=\frac{60}{4}=15\text{cm}$.