Question

A boy is standing in front of a straight plane mirror. His uncle is standing behind him as shown. The height of the boy is 3 feet and that of the uncle is 6 feet. What is the minimum length of the mirror required so that the boy can completely see his uncle’s image in the mirror?

• A. 1 feet
• B. 2 feet
• C. $\frac{1}{2}$ feet
• D. $\frac{3}{4}$ feet

Answer 1

The correct option is B 2 feet

Let AB represent the uncle, CD represent the boy and GF represent the mirror.
The boy can see complete image of his uncle in the mirror when rays of light from point A and B, after reflection from mirror (GF), reach the point C (eye of the boy) as shown in the figure.
Let H be any point on the mirror such that GH = x and HF = y.
Now, AB = 6 feet, CD = 3 feet
Al = 3 - x
FE = 3 - y
CH = 3 feet
BE = IG = 6 feet
In ΔHCG and ΔAGI,
$\frac{GH}{CH}=\frac{AI}{IG}$$\rho \frac{x}{3}=\frac{3-x}{6}$$\rho x=1feet$$In\Delta CFHand\Delta BFE$,
$\frac{HF}{CH}=\frac{EF}{BE}\rho \frac{y}{3}=\frac{3-y}{6}\rho y=1feet$
= GF = x + y = (1 + 1) feet = 2 feet
Hence, the correct answer is option (b).