Question

An image 2/3 of 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

The image formed is real (convex lens forms diminished real image)

\(h_i=\frac{2}{3}h_0\)

\(\frac{h_i}{h_o}=\frac{2}{3}\)

\(\frac{h_i}{h_0}=\frac{-v}{u}\)

\(\frac{2}{3}=\frac{-12}{u}\)

\(u=\frac{-12\times3}{2}=-18\,cm\)

\(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)

\(\frac{1}{f}=\frac{1}{12}-\frac{1}{-18}\)

\(=\frac{3+2}{36}\)

\(f=\frac{36}{5}=7.2\,cm\)