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Question

A man is 160 m tall and his eyes are 10 cm below the top of his head. In order to see this entire height right from top to head, he uses a plane mirror kept at a distance 1 m from him. The minimum length of the plane mirror is

A
80 cm
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B
90 cm
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C
100 cm
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D
70 cm
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Solution

The correct option is A 80 cm
Total height of man (H)=160 cm
(Including eyes)
Distance between head and eyes,
HE=10 cm
Distance between feet and eyes,
FE=150 cm


Considering man as an extended object in front of mirror, man will be able to see his entire image when the light incident on mirror from his head and feet reaches his eyes after reflection.

From the symmetry of incident and reflected rays(i=r)
HM=EM & EP=PF

At points M & P of mirror, MO and PD will be the perpendicular bisectors of length HE and EF respectively.
NP=ED=EF2
and, MN=OE=EH2
Minimum required length of mirror will be,
Lmin=NP+MN
Lmin=EF2+EH2
Lmin=1502+102=80 cm
Hence, option (a) is the correct answer.

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