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?
the guard will never be able to see her
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 ∠BNC=∠SNP. So the right triangles BNC and SNP are similar, hence sides are in the same ratio.
Therefore, BC,d2, the distance B is away from the mirror when first visible to S.