Angular subtense of staff graduations at 20 m On a metric levelling staff, what angular subtense (in radians) does a 10 mm marking correspond to when viewed from a distance of 20 m?

Introduction / Context:Understanding the angular size of staff graduations helps observers estimate reading precision and choose appropriate sight lengths. The basic small-angle relation links linear size, distance, and angular subtense in radians.

Given Data / Assumptions:

• Staff graduation considered: 10 mm = 0.01 m.
• Sight distance D = 20 m.
• Small-angle approximation θ ≈ s / D (radians) for s ≪ D.

Concept / Approach:

Angular subtense θ (radians) equals length divided by distance for small angles. Convert the physical graduation to metres and divide by the sight distance to get θ. Express the result as a simple reciprocal in radians for easy comparison with options.

Step-by-Step Solution:

Verification / Alternative check:

Convert to seconds: 0.0005 × 206265 ≈ 103.1 seconds, consistent with typical staff visibility at moderate sights.

Why Other Options Are Wrong:

1/1000, 1/1500, and 1/2500 rad differ from the computed 1/2000 rad by significant margins.

Common Pitfalls:

Forgetting to convert millimetres to metres; using degrees instead of radians when applying the small-angle relation.

Final Answer:

1/2000 radian