A person stands at the centre of a room the walls of which are 3 metres tall. What is the smallest l

Question

A person stands at the centre of a room the walls of which are 3 metres tall. What is the smallest length of the mirror to be fixed on the front wall so that he may see the full length of the hind wall in the mirror.\

Professor PC Thomas Classes · Answer

The course of rays by which a person at the centre sees the hind wall in the mirror is shown in the figure. $	riangle$ les OAB and OIM are similar\ $\frac{\mathrm{AB}}{\mathrm{IM}}=\frac{\mathrm{OA}}{\mathrm{OI}}=\frac{\mathrm{x}}{3 \mathrm{x}}=\frac{1}{3}$\ $\frac{\mathrm{AB}}{3}=\frac{1}{3} \quad \mathrm{AB}=1 \mathrm{~m}$\ Note:- Suppose 1 is the length of the room.\ Let $x=\frac{1}{n}$, Then $A B=\frac{h}{n+1}$\ In this problem $\mathrm{n}=2$.\