Question

In the figure shown, $AB$ is a plane mirror of length $40\text{cm}$ placed at height of $40\text{cm}$ from the ground. There is a light source at a point on the ground. Find the minimum height of a man (eye height) required to see the image of the source if he is standing at a point $P$ on the ground as shown in the figure.

• A. $300\text{cm}$
• B. $350\text{cm}$
• C. $200\text{cm}$
• D. $160\text{cm}$

Answer 1

The correct option is D $160\text{cm}$


Let the minimum height be $EP$.
By similar traingles :
$\Delta BCD\simeq \Delta BFE$
So, $\frac{BF}{BC}=\frac{EF}{CD}$
$\Rightarrow EF=3\times CD$
$(\because BF=3BC)$
$\Rightarrow EF=120\text{cm}\Rightarrow EP=160\text{cm}$
Therefore, minimum height of the eye is $160\text{cm}$.