Question

An object $M$ is placed at a distance of $3\text{m}$ from a mirror kept at some height with its lower end at $2\text{m}$ from ground as shown in the figure. There is a person at a distance of $4\text{m}$ from the object. The ratio of minimum height and maximum height of the person required to see the image of the object will be

• A. $3:4$
• B. $1:2$
• C. $2:3$
• D. $1:3$

Answer 1

The correct option is B $1:2$

Ray diagram of the situation based on field of view is shown below.


$\Delta M^{\prime }CP$ and $\Delta M^{\prime }AN$ both are similar triangles. So, we get,
$\frac{PC}{P{M}^{\prime }}=\frac{AN}{N{M}^{\prime }}$
$\Rightarrow \frac{H_{min}}{10}=\frac{2}{3}$
$\therefore H_{min}=\frac{20}{3}\text{m}$
Similarly, in $\Delta M^{\prime }DP$ and $\Delta M^{\prime }BN$
$\frac{PD}{P{M}^{\prime }}=\frac{NB}{N{M}^{\prime }}$
$\Rightarrow \frac{H_{max}}{10}=\frac{4}{3}$
$\therefore H_{max}=\frac{40}{3}\text{m}$
Thus,
$\frac{H_{min}}{H_{max}}=\frac{\left(\frac{20}{3}\right)}{\left(\frac{40}{3}\right)}$
$\Rightarrow \frac{H_{min}}{H_{max}}=\frac{1}{2}=1:2$
Hence, option $\left(b\right)$ is the correct answer.