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Question

# A person AB of height 170 cm is standing in front of a plane mirror. His eyes are at height 164 cm. At what distance from P should a hole be made in the mirror so that he cannot see his hairs?

A
167 cm
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B
161 cm
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C
163 cm
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D
165 cm
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Solution

## The correct option is A 167 cmTo see the image of hair, the rays incident from hair must reach the eye of the person after reflection. Let the hole be made at a point M on the mirror where light coming from hair is reflected. From the geometry of the diagram, PM=BC ⇒PM=BE+CE ⇒PM=BE+(AE2) [∵ In ΔAEM, AM=ME ( Isosceles triangle ) and MC is the perpendicular bisector of AE ] ⇒PM=164+(62) ∴PM=167 cm Hence, option (a) is the correct answer.

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