Question

A camera of 0.20 m focal length was used to take the vertical photograph of a terrain, whose average elevation is 1000 m. In order to get the scale of 1:5000, at what height above the sea level must the aircraft must fly?

• A. 2000 m
• B. 1000 m
• C. 200 m
• D. 5000 m

Hint:

For a vertical photograph the scale is \(\text{Scale} = \dfrac{f}{H - h}\), where \(f\) is the focal length, \(H\) is the flying height above MSL and \(h\) is the average terrain elevation.

Answer 1

The Correct Option is A

Step 1: List what is given.
Focal length \(f = 0.20\) m, average ground elevation \(h = 1000\) m, and required scale is 1 : 5000. We must find the flying height \(H\) above sea level.

Step 2: Write the scale rule.
For a vertical photo, \[ \text{Scale} = \frac{f}{H - h}. \]

Step 3: Put the scale as a fraction.
\[ \frac{1}{5000} = \frac{0.20}{H - 1000}. \]

Step 4: Cross multiply to free \(H\).
\[ H - 1000 = 0.20 \times 5000 = 1000 \text{ m}. \]

Step 5: Solve for \(H\).
\[ H = 1000 + 1000 = 2000 \text{ m}. \]

Step 6: State the answer.
The aircraft must fly at 2000 m above sea level.
\[ \boxed{H = 2000 \text{ m}} \]