A Man 1.8 M Tall Wishes To See Full-length Image In A Plane Mirror. The Length Of The Shortest Mirror In Which He Can See His Entire Image Is

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Question

A man 1.8 m tall wishes to see full-length image in a plane mirror. The length of the shortest mirror in which he can see his entire image is

0.6 m
0.9 m
1.2 m
1.5 m

diffcult

Solution

Correct option is

0.9 m

Consider a man AB 1.8 m tall standing in front of a plane mirror hanging on a wall and let E be the position of his eyes (see fig.) He can see his full length image in the mirror if the rays which start from A and B reach his eyes after reflection from the mirror. Let P and Q be the midpoints of AEand EB respectively. From P and Q draw perpendiculars PM and QN on the mirror. The rays AM and BN will be reflected along ME and NErespectively. These rays enter the observer’s eyes. Thus enabling him to see his full image A’B’. Thus MN is the shortest length of the mirror. Now

MN = PQ = PE + EQ

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