Question

# A child is standing in front of a straight plane mirror. His father is standing behind him, as shown in the fig. The height of the father is double the height of the child. What is the minimum length of the mirror required so that the child can completely  see his own image and his fathers image in the mirror? Given that the height of father is $$2H$$.

A
H/2
B
5H/6
C
3H/2
D
None of these

Solution

## The correct option is B $$5H/6$$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,$$\dfrac{2l}{H-x}=\dfrac{l}{x}$$$$\implies x=\dfrac{H}{3}$$Hence the minimum length of mirror required=$$\dfrac{H}{2}+\dfrac{H}{3}=\dfrac{5H}{6}$$Physics

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