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Question

# A person of height 200 cm is standing in front of a plane mirror. Find the minimum height of the mirror required, so that the person can see his full size image.

A
50 cm
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B
200 cm
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C
100 cm
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D
It depends on the distance of person from the mirror.
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Solution

## The correct option is C 100 cm Let HF be the height of the person and E be the eye level. Draw the rays HM1 and FM2 incident at the edges of the mirror. Complete ray diagram is as shown in the figure. From the figure, height of mirror M1M2=x+y & height of person HF=2x+2y=2(x+y) ∴M1M2HF=x+y2(x+y)=12 ⇒M1M2200=12⇒M1M2=100 cm Note:- The required height of the mirror is half the height of the person.

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