Tilted photograph geometry — distance from principal point to plumb point For a tilted aerial photograph with lens focal length f and tilt angle θ, the distance of the plumb point from the principal point is:

Introduction / Context:
On a tilted photograph, the plumb point is the foot of the vertical (nadir) on the photo plane. Its location relative to the principal point depends on the tilt angle and focal length.

Given Data / Assumptions:

• Small-angle central projection from a calibrated camera.
• Single-axis tilt for simplicity.

Concept / Approach:

Consider the right triangle formed by the optical axis, the vertical line through the exposure station, and the photo plane. The offset between principal and plumb points equals the distance along the photo plane corresponding to the tilt: offset = f * tan θ.

Step-by-Step Solution:

Verification / Alternative check:

Photogrammetry texts derive this from perspective geometry of a tilted frame.

Why Other Options Are Wrong:

• fsinθ or fcosθ represent other legs of the triangle; f*secθ is not the planar offset.

Common Pitfalls:

• Confusing principal point (intersection of optical axis) with nadir/plumb point.

Final Answer:

f * tan θ.