What is the correct ratio of refraction correction to curvature correction in levelling?
Correct Answer: C. 1/7
📚 Detailed Explanation: Refraction Correction / Curvature Correction = 1/7
Why C (1/7) is correct: The curvature correction formula is Cc = 0.0785D² and the refraction correction formula is Cr = 0.0112D². Their ratio = 0.0112/0.0785 = 0.1427 ≈ 1/7.
Curvature correction: Cc = 0.0785 × D²
Refraction correction: Cr = 0.0112 × D²
Refraction correction: Cr = 0.0112 × D²
Ratio: Cr / Cc = 0.0112 / 0.0785 = 0.1427 ≈ 1/7
Proof from formula derivation:
Cc = D² / (2R)
Cr = D² / (14R) = Cc / 7
Therefore: Cr = Cc / 7 → Cr/Cc = 1/7
Practical Implication
| Correction | Formula | Ratio to Other |
|---|---|---|
| Curvature (Cc) | 0.0785 × D² | 7 × refraction |
| Refraction (Cr) | 0.0112 × D² | 1/7 of curvature |
| Combined (C) | 0.0673 × D² | 6/7 of curvature; 6 × refraction |
- Refraction correction = 1/7 of curvature correction: Cr = Cc/7.
- Both act on the same D² term, so the ratio is constant regardless of distance.
- Combined correction = Cc − Cr = Cc(1 − 1/7) = 6/7 × Cc = 0.0673D².