Which is the correct expression for horizontal distance between instrument and staff for an anallatic telescope? (S = staff intercept, K = multiplying constant, C = additive constant)
Correct Answer: D. 100S
📚 Detailed Explanation: Anallatic Telescope Horizontal Distance = 100S
Why D (100S) is correct: For an anallatic lens telescope, the multiplying constant K = 100 and the additive constant C = 0. Substituting into the tachymetry distance formula D = KS + C gives D = 100S.
Stadia Tachymetry Distance Formula
Standard formula: D = KS + C
where: D = horizontal distance (m)
K = multiplying constant (= f/i; f = focal length, i = stadia interval)
S = staff intercept (upper hair reading – lower hair reading)
C = additive constant (= f + d)
where: D = horizontal distance (m)
K = multiplying constant (= f/i; f = focal length, i = stadia interval)
S = staff intercept (upper hair reading – lower hair reading)
C = additive constant (= f + d)
For ANALLATIC lens telescope:
K = 100 (designed to give exactly 100 for simplicity)
C = 0 (the anallatic lens shifts the front focal point to the instrument centre,
making the additive constant zero)
Simplified formula: D = 100 × S + 0 = 100S
What Is the Anallatic Lens?
| Feature | Without Anallatic Lens | With Anallatic Lens |
|---|---|---|
| Multiplying constant K | Approximately 100 but varies | Exactly 100 |
| Additive constant C | f + d (typically 30–50 cm) | Exactly 0 |
| Distance formula | D = KS + C (C must be measured) | D = 100S (no C to add) |
| Purpose | Standard internal focusing telescope | Simplifies field calculation |
- Anallatic lens: K = 100, C = 0 → D = 100S.
- Staff intercept S = upper hair reading − lower hair reading.
- The anallatic lens eliminates the additive constant, making distance measurement simpler.