Question

An aerial photograph is to be taken from a flying height of $2~\text{km}$ above a flat ground with a camera having a focal length of $200~\text{mm}$. The image format used is $23~\text{cm} \times 23~\text{cm}$. The ground area covered by a single photograph is \underline{\hspace{1.6cm}} $\text{km}^2$.

• A. 5.29
• B. 1.48
• C. 0.95
• D. 2.22

Hint:

For vertical photos over flat terrain: scale $=f/H$. Multiply the photo side by the scale denominator to get the ground side; square it for area (for square formats).

Answer 1

The Correct Option is A

Step 1: Photo scale.
Flying height above ground $H=2~\text{km}=2{,}000~\text{m}=2{,}000{,}000~\text{mm}$. Focal length $f=200~\text{mm}$. Scale $S=\dfrac{f}{H}=\dfrac{200}{2{,}000{,}000}=1{:}10{,}000$.
Step 2: Ground coverage of one side.
Photo side $=23~\text{cm}=0.23~\text{m}$. Ground side $=0.23 \times 10{,}000 = 2{,}300~\text{m}=2.3~\text{km}$.
Step 3: Area.
\[ A=(2.3~\text{km})^2=5.29~\text{km}^2. \] \[ \boxed{5.29\ \text{km}^2} \]