Question

Figure shows an overhead view of a corridor with a plane mirror M mounted at one end. A burglar B sneaks along the corridor directly toward the center of the mirror. If d = 3.0 m, how far from the mirror will she be when the security guard S first sees her in the mirror?

• A. the guard will never be able to see her
• B. $\frac{d}{2}$
• C. $\frac{3d}{2}$
• D. $d$

Answer 1

The correct option is B

$\frac{d}{2}$

As the burglar B keeps moving towards the mirror, the field of view keeps on increasing. When the boundary of the field of view just reaches the guard S, the diagram is as below:

The angle i = r, therefore $\angle BNC=\angle SNP$. So the right triangles BNC and SNP are similar, hence sides are in the same ratio.
Therefore, $\frac{BC}{CN}=\frac{SP}{PN}$
Or, $\frac{BC}{\frac{d}{2}}=\frac{d}{d}$
Therefore, $BC,\frac{d}{2}$, the distance B is away from the mirror when first visible to S.