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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?


  1. d

  2. d2

  3. the guard will never be able to see her

  4. 3d2


Solution

The correct option is B

d2


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, BCCN=SPPN
Or, BCd2=dd
Therefore, BC,d2, the distance B is away from the mirror when first visible to S.

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