Compute the scale of an aerial photograph when the flying height of an aircraft is 7500 m and the focal length of the camera is 15 cm:

Question

Accepted Answer

The scale of an aerial photograph is calculated as the ratio of the focal length of the camera to the flying height above the ground. The formula is:

Scale (S) = Focal Length (f) / Flying Height (H)

Given:
*   Focal Length (f) = 15 cm = 0.15 m (converting cm to meters)
*   Flying Height (H) = 7500 m

Therefore,
S = 0.15 m / 7500 m
S = 1 / 50000

This means the scale of the aerial photograph is 1 : 50,000. Therefore, Option 2 is the correct answer.

Now, let's explain why the other options are incorrect:

*   **Option 1: 1 : 15,000:** This scale would imply a much lower flying height relative to the focal length. If the scale were 1:15,000, then 0.15m / H = 1/15000, which means H = 0.15 * 15000 = 2250m. This contradicts the given flying height of 7500m.

*   **Option 3: 1 : 25,000:** This scale would imply a flying height that is different from the given 7500m. If the scale were 1:25,000, then 0.15m / H = 1/25000, which means H = 0.15 * 25000 = 3750m. This contradicts the given flying height of 7500m.

*   **Option 4: 1 : 30,000:** This scale also implies a flying height different from the given 7500m. If the scale were 1:30,000, then 0.15m / H = 1/30000, which means H = 0.15 * 30000 = 4500m. This contradicts the given flying height of 7500m.

Only Option 2, 1 : 50,000, correctly reflects the scale calculated using the given focal length and flying height.