Question

The image of a tree just covers the length of a plane mirror tall when the mirror is held 35cm from the eye. The tree is 28m from the mirror. What is its height?

Short answer

The height is $3.24m$.

Step-by-step solution

Calculate the height using lateral magnification method

Given that height of the image of the tree is $h\text{'}=4cm$, the distance between the tree and the mirror is $s=28m$and from the eye is $s_{mirror}=35cm$.

The whole situation is shown in the following figure

Using the concept of lateral magnification

$$\begin{gathered} \frac{h\text{'}}{h}=\frac{s_{mirror}}{s_{tree}} \\ h=\left(\frac{s_{tree}}{s_{mirror}}\right)h\text{'} \\ h=\left(\frac{s_{mirror}+s}{s_{mirror}}\right)h\text{'} \\ h=\left(\frac{0.35+28}{0.35}\right)\times 0.04 \\ h=3.24m \end{gathered}$$

So, the height is $3.24m$.