The anallatic lens is used in a tacheometer to:
Correct Answer: B. Eliminate the additive constant
📚 Detailed Explanation: Anallatic Lens Eliminates the Additive Constant in Tacheometry
Why B (Anallatic lens) is correct: The anallatic lens is a special concave lens placed at a fixed position in the telescope of a tacheometer. Its purpose is to make the additive constant C = 0, so the stadia distance formula simplifies to D = 100S (no additive term to apply).
Role of the Anallatic Lens
| Feature | Without Anallatic Lens | With Anallatic Lens |
|---|---|---|
| Stadia formula | D = KS + C, where C = f + d (30–50 cm) | D = KS + 0 = KS (C = 0) |
| K (multiplying constant) | Still 100 | Still 100 |
| Additive constant C | f + d ≠ 0; must be measured and applied | Zero — eliminated by anallatic lens |
| Computation | D = 100S + C (two terms) | D = 100S (one term; simpler) |
| External tube length | May change with focus (external focussing) | Constant (internal focussing + anallatic lens) |
Why is C eliminated?
The anallatic lens is positioned such that the external principal focus
of the combined objective + anallatic lens system falls at the instrument centre.
This makes the “equivalent focal length” behave as if d = 0,
giving C = f + d = f_equivalent + 0 = 0.
The anallatic lens is positioned such that the external principal focus
of the combined objective + anallatic lens system falls at the instrument centre.
This makes the “equivalent focal length” behave as if d = 0,
giving C = f + d = f_equivalent + 0 = 0.
- Anallatic lens: special concave lens in tacheometer that makes C = 0.
- Result: D = KS = 100S (no additive constant).
- Found only in tacheometers, not ordinary theodolites or levels.