Photogrammetry MCQ with answer and solution

Concept

Relief displacement is the shift in the position of an object on a photograph due to its height above the ground. It is measured from the principal point (center) of the photograph.

Formula

d = (h × r) / H

Step-by-step solution

1. Identify the given values: Height of the minar (h) = 88 m Relief displacement (d) = 8.8 mm = 0.88 cm Distance of the top from the principal point (r) = 10 cm 2. Use the relief displacement formula: d = (h × r) / H 3. Rearrange the formula to find the flying height (H): H = (h × r) / d 4. Put the values into the formula: H = (88 m × 10 cm) / 0.88 cm 5. Calculate the result: H = 880 / 0.88 = 1000 m Answer: (B) 1000 m

Explanation

The relief displacement (d) is directly proportional to the object's height (h) and its distance from the center (r). By using the standard formula d = hr/H, we find that the camera was at a height of 1000 m. This ensures the geometry of the photograph matches the physical height of the minar.

Why the other options are wrong

A: This value is too low and would result in a much larger relief displacement. C: This value is too high and would result in a smaller relief displacement. D: This value is double the required height, which would halve the displacement.

Shortcut

Notice that d (0.88 cm) is exactly 1/100th of h (88 m). So, H must be 100 times r (10 cm), which is 1000 cm... wait, keep units consistent! 0.88/88 = 10/H gives H = 1000.

Common mistake

Students often forget to convert relief displacement (mm) and distance (cm) into the same units before dividing.