a child is standing in front of a straight plane mirror his father is standing behind him whose height is double the father.what should be the minimum length of the mirror so that the child can see his father's image
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The length of mirror is the distance between points A and B.
To see the bottom most point of himself, the boy of height H needs to have mirror at least at a distance of H/2 from the bottom.
Thus the point B is established.
Also to see the top most point of his father, the child must have a point of mirror at a distance x from a point directly in front of him such that,
H−x
2l
=
x
l
⟹x=
3
H
Hence the minimum length of mirror required=
2
H
+
3
H
=
6
5H
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