Where are angles ‘‘true’’ on photographs under various conditions? Considering angle fidelity on aerial photographs, which statement is incorrect?

Introduction / Context:Angle preservation on aerial images depends on camera attitude and terrain relief. Identifying where (if anywhere) angles are locally true helps in interpreting geometry for mapping and for photo measurements.

Given Data / Assumptions:

• Vertical photo: optical axis normal to photo plane.
• Tilted photo: finite tilt without yaw/roll corrections.
• Relief: variations in terrain elevation exist or not.

Concept / Approach:For a truly vertical photo without relief, central projection reduces locally to orthographic behavior at the plumb point (which coincides with the principal point), making small angles true there. For a tilted photo without relief, angles are true at the isocentre, the point midway (angularly) between principal and plumb directions. However, when relief is present with tilt, perspective distortions vary with elevation; there is no single point such as the principal point at which all ground angles are preserved as true.

Step-by-Step Solution:Assess option (a): vertical, no relief → angles true at plumb point → correct.Assess option (b): tilted, no relief → angles true at isocentre → correct.Assess option (c): tilted with relief → claim that angles are true at principal point → incorrect.Hence (c) is the incorrect statement.

Verification / Alternative check:Photogrammetric texts show that in presence of relief, scale varies radially with height, defeating uniform angle preservation at any single point.

Why Other Options Are Wrong:(a) and (b) are established results; (d) “none” is wrong because an incorrect statement exists, namely (c).

Common Pitfalls:Conflating principal, plumb, and isocentre; these points coincide only in special cases (e.g., perfectly vertical photo over level ground).

Final Answer:In tilted photographs with relief, all angles are true at the principal point