A person 180 cm tall wants to see his full image in a plane mirror. What is the minimum length of th

Question

A person 180 cm tall wants to see his full image in a plane mirror. What is the minimum length of the mirror required.\

Professor PC Thomas Classes · Answer

The course of rays by which a person sees his image in a plane mirror is shown in the figure. The length of the mirror required to see his full image is $A B$. To find $A B$ we make use of principles of similar triangles. $\Delta$ les OAB and OIM are similar.\ $\frac{\mathrm{AB}}{\mathrm{IM}}=\frac{\mathrm{OA}}{\mathrm{OI}}=\frac{\mathrm{d}}{2 \mathrm{~d}}=\frac{1}{2}$\ $\mathrm{AB}=\frac{\mathrm{IM}}{2}=\frac{\mathrm{h}}{2}=\frac{180}{2}=90 \mathrm{~cm}$\ The mirror must be placed at such a height equal to his forehead. The distance between the mirror and the person is immaterial.\