Question

An image $\frac{2}{3}$ the size of the object is formed by a convex lens at a distance of 12 cm from it. Find the focal length of the lens.

Answer 1

For real and inverted image, the magnification will be negative. $\therefore m=\frac{-2}{3}$.
We know that, $m=\frac{v}{u}\Rightarrow \frac{-2}{3}=\frac{12}{u}\Rightarrow u=\frac{12\times 3}{-2}=-18cm$
Now, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{12}-\frac{1}{-18}=\frac{1}{f}\Rightarrow \frac{5}{36}=\frac{1}{f}\Rightarrow f=\frac{36}{5}=7.2cm$
Therefore the focal length is 7.2 cm.