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# A person 1.6m tall is standing at the centre between two walls three meter high. What is the minimum size of plane mirror fixed on the wall in front of him, if he is to see the full height of the wall behind him?

Last updated date: 20th Jun 2024
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Hint: We are able to see that object from which light falls on our eyes, either directly or indirectly. The light may be reflected or self-produced (in case of luminous objects). In case we want to view a full object having some dimensions, the light from the left and right most corners and from the bottom and top most corner must fall on the eyes.

From this detailed figure, we can see that for minimum width of mirror, the rays from the head of the boy (C), has to strike the extremities of mirror ‘pq’.
Now, from similar triangles, we have;
$\dfrac{AB}{GC} = \dfrac{qB}{qG} = \dfrac{L}{L/2} = 2$
Thus AB = 2GC
Similarly, DE = 2CF
To find;
$qp = GC + CF = \dfrac{AB}{2} + \dfrac{DE}{2}$
$\implies AB + DE = 2qp$
Also $AB + BD + DE = 3$
$BD + AB + DE = BD + 2qp = 3$
Now $GF = BD = pq$
Thus, $pq+2pq = 3$
$\implies pq = 1 m$
Hence, the minimum width of the mirror should be 1 m.