Answer to Question #164490 in Optics for Chukwuemeka amarachi

Question

When a 5cm plane mirror is held 0.5m from the eye the image of the mango tree in the mirror is also 5cm tall. How tall is the mango tree if it 100m from the mirror

Answer 1

As there is a plane mirror,

The distance of the mango tree from mirror should equal to the Image distance in the mirror.

From the above diagram, The formation of image of tree in the mirror is shown-

From similar triangles

$\dfrac{0.5}{100.5}=\dfrac{5\times 10^{-2}}{h}$

$\Rightarrow h=\dfrac{100.5\times 5\times 10^{-2}}{0.5}=10.05m$

Hence The height of mango tree is $10.05{\text{m}}.$