Question

A nature photographer wishes to photograph a 30 meter tall tree from a distance of 60 meters.
What focal-length lens should be used if the image is to fill the 36mm height of the film?

please show formula and steps.

Answer 1

Height of the tree \(\mathrm{h}_{0}=30 \mathrm{~m}\) Height of the image \(\mathrm{h}_{i}=-36 \times 10^{-3} \mathrm{~m}\)

Distance of the object \(\mathrm{d}_{o}=60 \mathrm{~m}\)

The converging lens will form a real inverted image

$$ \begin{array}{c} M=\frac{h_{i}}{h_{o}} \\ \frac{h_{i}}{h_{o}}=\frac{-d_{i}}{d_{o}} \\ \frac{\left(-36 \times 10^{-3}\right)}{(30)}=\frac{\left(-d_{i}\right)}{(60)} \\ d_{i}=\frac{\left(36 \times 10^{-3}\right)(60)}{(30)} \\ =72 \times 10^{-3} \mathrm{~m} \\ =72 \mathrm{~mm} \end{array} $$