Question

The image of a tree just covers the length of a plane mirror $4\text{cm}$ tall when the mirror is held $35\text{cm}$ from the eye. The tree is $28\text{m}$ from the mirror. What is its height?

• A. $300\text{cm}$
• B. $225\text{cm}$
• C. $324\text{cm}$
• D. $350\text{cm}$

Answer 1

The correct option is C $324\text{cm}$


The image of the top of the tree is reflected to the eye from the top of the mirror and the image of the bottom of the tree is reflected to the eye from the bottom of the mirror.

It can easily be shown that the triangle formed by the eye and the mirror is similar to the triangle formed by the eye and the image of the tree.
$\Rightarrow \frac{\text{Height of mirror}}{\text{Height of image}}=\frac{\text{distance between the eye and the mirror}}{\text{distance between the eye and the image}}$
$\frac{4}{\text{Height of image}}=\frac{35}{35+2800}$
$\text{Height of the image}=4\times \frac{2835}{35}=324\text{cm}$

In a plane mirror, the height of the image is the same as the height of the object.
$\text{Height of the tree}=324\text{cm}$