Q53. For a tacheometer, the additive and multiplying constants are respectively:
📚 Detailed Explanation: The Ideal (Anallactic) Tacheometer Constants
This question asks for the constants of an idealised, anallactic-lens-equipped tacheometer — the design target that manufacturers aim for to make field distance calculations as simple as possible.
An ideal tacheometer fitted with an anallactic lens is specifically designed so that the additive constant C = 0 (the anallactic lens internally repositions the effective optical centre so the f+d offset vanishes) and the multiplying constant K = 100 (the standard design target discussed in Q42). With these values, the distance formula simplifies to the cleanest possible form: D = 100 × S, with no additive correction needed at all.
Why the Other Options Are Wrong
A — 0 and 0: While the additive constant is correctly 0, a multiplying constant of 0 would make the distance formula always give D = 0, which is meaningless — the multiplying constant must be a substantial, non-zero value (typically 100) to be useful.
B — 100 and 100: An additive constant of 100 (in whatever length unit) would be an unusually large fixed offset, inconsistent with the anallactic lens’s specific purpose of driving the additive constant to zero, not to 100.
C — 100 and 0: This option reverses which constant equals which standard value — the additive constant should be 0 (not 100) and the multiplying constant should be 100 (not 0), the exact opposite assignment.
Key Concepts for Students
- Anallactic lens is the key enabling technology: This small additional lens element, placed between the objective and the eyepiece, optically repositions the apparent centre of the stadia diaphragm to coincide with the instrument’s vertical axis, eliminating the additive constant entirely.
- Always read which value goes with which constant carefully: Since this question (and similarly worded ones) lists “additive and multiplying” in that specific order, always match your computed/known values to the correct position — reversing the order is a very common careless mistake.
- This connects directly to Q29’s intersect angle calculation: The K = 100, C = 0 combination is exactly the condition assumed when calculating the anallactic telescope’s intersect angle, since C = 0 confirms the telescope qualifies as truly anallactic in the first place.