Calculate the combined correction for curvature and refraction (in m) for a distance of 2 km.
Correct Answer: C. 0.269 m
📚 Detailed Explanation: Combined Correction at 2 km = 0.2692 m (Choice C)
Why C (0.269 m) is correct: Using the combined curvature and refraction correction formula with D = 2 km gives Cc = 0.0673 × 4 = 0.2692 m.
Formula: Combined correction Cc = 0.0673 × D² (D in km)
D = 2 km
Cc = 0.0673 × (2)²
Cc = 0.0673 × 4
Cc = 0.2692 m ≈ 0.269 m
Quick Reference Table
| Option | Value | Formula That Gives It |
|---|---|---|
| A. 0.045 | 0.045 | 0.0112 × 2² = 0.0448 (refraction only) |
| B. 0.135 | 0.135 | Not a standard formula result at 2 km |
| C. 0.269 | 0.2692 | 0.0673 × 4 = 0.2692 — CORRECT combined correction |
| D. 3.14 | 3.14 | Wrong magnitude entirely; no valid formula |
- Combined correction at 2 km: 0.0673 × 2² = 0.269 m.
- At Q41 the same correction (0.2692 m) was used to correct the observed staff reading.
- Curvature alone: 0.0785 × 4 = 0.314 m; refraction alone: 0.0112 × 4 = 0.045 m; net = 0.314 − 0.045 = 0.269 m.