The correction for refraction for a distance 'D' between the staff and instrument is proportional to:
Correct Answer: C. proportional to square of D
📚 Detailed Explanation: Refraction Correction Is Proportional to the Square of Distance (D²)
Why C (proportional to square of D) is correct: The formula for atmospheric refraction correction is Cr = 0.0112 × D² (D in km). Since D appears squared, the correction is proportional to D². If the distance doubles, the refraction correction quadruples.
Refraction correction formula: Cr = 0.0112 × D² (D in km)
Proportionality test:
D = 1 km: Cr = 0.0112 × 1 = 0.0112 m
D = 2 km: Cr = 0.0112 × 4 = 0.0448 m (4× larger when D doubles)
D = 3 km: Cr = 0.0112 × 9 = 0.1008 m (9× larger when D triples)
Conclusion: Cr ∝ D² (proportional to square of distance)
Comparison with Curvature Correction
| Correction | Formula | Proportional to |
|---|---|---|
| Curvature (Cc) | 0.0785 × D² | D² |
| Refraction (Cr) | 0.0112 × D² | D² |
| Combined | 0.0673 × D² | D² |
- Cr = 0.0112 × D² → proportional to square of distance (D²).
- Both curvature and refraction corrections are proportional to D².
- Refraction correction = exactly 1/7 of curvature correction at any distance.