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  4. The figure shows an overhead view of a corridor with a plane mirror MN mounted at one end. A burglar B sneaks along the corridor directly towards the centre of the mirror. If d=3 m , how far from the mirror will the burglar be when the security guard S can first see him in the mirror? <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-x9qxeou0babp.png />

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Q. The figure shows an overhead view of a corridor with a plane mirror $MN$ mounted at one end. A burglar $B$ sneaks along the corridor directly towards the centre of the mirror. If $d=3 \, m$ , how far from the mirror will the burglar be when the security guard $S$ can first see him in the mirror?

Question

NTA AbhyasNTA Abhyas 2020Ray Optics and Optical Instruments

Solution:

Solution
$\tan \theta=\frac{\mathrm{X}}{\left(\frac{\mathrm{MN}}{2}\right)}$ (in the smaller triangle)
$tan \theta =\frac{3 m}{3 m}$ (in the bigger triangle)
$\therefore \frac{x}{\text{1.5}}=\frac{3}{3}$
$\therefore x=\text{1.5}m$