Calculate the combined correction due to refraction and Earth's curvature in levelling for a distance of 2500 m.
Correct Answer: B. 0.420 m
📚 Detailed Explanation: Combined Curvature and Refraction Correction for 2500 m = 0.420 m
Why B (0.420 m) is correct: The standard formula for combined correction accounts for both earth curvature (which makes staff readings appear too large) and atmospheric refraction (which partially compensates, reducing the error by 1/7). The net combined correction is Cc = 0.0673 × D² where D is in kilometres.
Formula: Combined correction Cc = 0.0673 × D² (D in kilometres)
Individual formulas:
Curvature correction Cc_curv = 0.0785 × D²
Refraction correction Cc_ref = 0.0112 × D² (= Cc_curv / 7, opposite sign)
Combined correction Cc = 0.0785 – 0.0112 = 0.0673 × D²
Given: D = 2500 m = 2.5 km
Cc = 0.0673 × (2.5)²
Cc = 0.0673 × 6.25
Cc = 0.420625 m ≈ 0.420 m
Why Other Options Are Wrong
| Option | Value | What Formula Gives This? |
|---|---|---|
| A. 0.070 m | 0.070 | Approximately Cc_ref = 0.0112 × 2.5² = 0.070 — refraction only, not combined |
| B. 0.420 m | 0.420 | Cc = 0.0673 × 2.5² = 0.420 — CORRECT combined value |
| C. 0.490 m | 0.490 | Approximately Cc_curv = 0.0785 × 2.5² = 0.491 — curvature only, not combined |
| D. 0.168 m | 0.168 | 0.0673 × 1.58² — wrong distance substituted |
- Combined correction: Cc = 0.0673 × D² (D in km).
- For D = 2.5 km: Cc = 0.0673 × 6.25 = 0.420 m.
- Refraction correction = 1/7 of curvature correction; they act in opposite directions; net = 6/7 of curvature = 0.0673×D².