Question

A thin rod of length $f/3$ is placed along the optic axis of a concave mirror of focal length $f$ such that its image which is real and elongated, just touches the rod. The magnification is _______.

Answer 1

From fig

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\frac{-3}{5f}+\frac{1}{u}=-\frac{1}{f}\frac{1}{u}=-\frac{1}{f}+\frac{3}{5f}=\frac{2}{5f}u=\frac{5f}{2}m=\frac{finallength}{initiallength}=\frac{f}{2}.\frac{3}{f}=1.5$