The ratio of the focal length of the objective lens to the stadia interval is called:
Correct Answer: B. multiplying factor
📚 Detailed Explanation: Focal Length / Stadia Interval = Multiplying Factor
Why B (multiplying factor) is correct: In stadia tachymetry, the distance formula is D = (f/i)S + (f + d). The ratio f/i is defined as the multiplying factor (also called the multiplying constant K). It is typically designed to equal 100 for simple calculation.
Stadia Distance Formula Components
| Symbol | Name | Definition | Typical Value |
|---|---|---|---|
| f | Focal length of objective | Distance from optical centre to focal point | 20–30 cm |
| i | Stadia interval | Distance between the two stadia lines on the reticle | ~1/100 of f |
| f/i | Multiplying factor (K) | Ratio of focal length to stadia interval | 100 |
| f + d | Additive constant (C) | f = focal length, d = distance from lens centre to instrument centre | 30–50 cm |
| S | Staff intercept | Upper stadia reading − Lower stadia reading | Varies |
Stadia distance: D = (f/i) × S + (f + d) = K × S + C
where K = f/i = multiplying factor (typically 100)
C = f + d = additive constant (typically 0 with anallatic lens)
where K = f/i = multiplying factor (typically 100)
C = f + d = additive constant (typically 0 with anallatic lens)
- f/i = multiplying factor (also called multiplying constant K).
- Typically K = 100 (designed by making stadia interval = f/100).
- f + d = additive constant C; zero in anallatic telescopes.