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What will be the focal length of the camera when the scale of the aerial photograph is 1:4500, the flying height of the aircraft is 3780 meters above MSL and the average height of the terrain is 820 meters above sea level ?

This question was previously asked in
MH SET 2025 Paper 2 Hindi Question Paper (15-Jun-2025)
The correct answer is

657.8 mm

657.8 mm option is correct.

The scale of a vertical aerial photograph is the ratio of image distance to ground distance, and for a level terrain it equals the focal length of the camera divided by the flying height of the aircraft above the ground. Because the flying height is quoted above mean sea level while the terrain sits at its own elevation above MSL, the effective flying height above the ground surface must first be corrected.

Step 1 — effective height above terrain: \(H' = H - h = 3780 - 820 = 2960 \text{ m}\).

Step 2 — apply the scale equation \(\dfrac{1}{S} = \dfrac{f}{H'}\), i.e. \(f = \dfrac{H'}{S}\).

Step 3 — substitute: \(f = \dfrac{2960}{4500} = 0.65778 \text{ m} \approx 657.8 \text{ mm}\).

The alternative values 607.8, 555.9 and 595.7 mm all arise from using the wrong flying height (for example, ignoring the terrain correction and using 3780 m directly, or subtracting an incorrect terrain elevation), which changes the numerator of the scale equation but not the algebra itself.

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