Relief displacement on a vertical aerial photograph: A triangulation station has R.L. = 500 m. On a truly vertical photo taken from altitude 2000 m above datum, its image lies 4 cm from the principal point. What is the relief displacement (radial) on the photo?

Introduction / Context:Relief displacement is the radial shift of an image point from the principal point on a vertical aerial photograph caused by terrain elevation. Understanding this displacement is essential in planimetric corrections, radial line plotting, and height extraction.

Given Data / Assumptions:

• Vertical photograph (tilt neglected).
• Altitude above datum H = 2000 m.
• Point elevation h = 500 m (above datum).
• Radial distance of image from principal point r = 4 cm.

Concept / Approach:For a vertical photo, the relief displacement d (measured radially outward) is approximated by d = (r * h) / H, with r and d in the same photo units. Positive h causes displacement away from the principal point.

Step-by-Step Solution:Use d = (r * h) / H.Substitute r = 4 cm, h = 500 m, H = 2000 m.Compute the ratio h/H = 500/2000 = 0.25.Compute d = 4 cm * 0.25 = 1.0 cm = 10 mm.

Verification / Alternative check:If the point had zero elevation (h = 0), displacement would be zero. Here, positive elevation produces a positive outward displacement, consistent with field experience.

Why Other Options Are Wrong:2–8 mm underestimate the computed displacement; 10 mm matches the formula exactly with the given numbers.

Common Pitfalls:Mixing datum-referenced altitude with height above ground, or mixing units (centimetres on photo vs metres on ground) without using the dimensionless ratio h/H.

Final Answer:10 mm.