What should be the minimum height (m) of a lighthouse so that it can be visible from a distance of 3 km?
Correct Answer: B. 0.605 m
📚 Detailed Explanation: Minimum Lighthouse Height Visible from 3 km = 0.605 m
Why B (0.605 m) is correct: For an object to be visible from a horizontal distance d (in km), it must be high enough to be above the combined effect of earth curvature and atmospheric refraction at that distance. Using the line-of-sight visibility formula h = 0.0673 × d² gives the minimum height required.
Formula: Minimum height h = 0.0673 × d² (d in km, h in metres)
This is the same as the combined curvature and refraction correction.
This is the same as the combined curvature and refraction correction.
Given: d = 3 km
h = 0.0673 × (3)²
h = 0.0673 × 9
h = 0.6057 m ≈ 0.605 m
Why Other Options Are Wrong
| Option | Value | Derivation |
|---|---|---|
| A. 0.101 m | 0.0112 × 3² = 0.101 | Refraction correction only; ignores curvature |
| B. 0.605 m | 0.0673 × 9 = 0.606 ≈ 0.605 | CORRECT — combined correction |
| C. 0.673 m | 0.0673 × 10 = 0.673 | Correct formula but d = √10 (wrong) |
| D. 0.707 m | 0.0785 × 3² = 0.707 | Curvature only; ignores the partial correction from refraction |
- Minimum height = combined correction = 0.0673 × d² (d in km).
- For d = 3 km: h = 0.0673 × 9 = 0.605 m.
- This is how lighthouse heights are determined to ensure visibility over a given nautical range.