The main purpose of providing an anallactic lens in a tacheometer is to:

Detailed Explanation: The Purpose of the Anallactic Lens

The anallactic lens, referenced several times earlier in this set (Q29, Q53), is a specific optical component with one precise, well-defined design purpose. This question isolates exactly what that purpose is.

Why eliminating the additive constant is the purpose:
An anallactic lens is an additional convex lens fitted inside the telescope, between the objective and the eyepiece (or diaphragm), at a carefully calculated fixed position. Its function is to optically shift the effective centre of the diverging rays so that it coincides exactly with the instrument's vertical axis, eliminating the small fixed offset distance (f + d) that would otherwise need to be added in the tacheometric distance formula. With an anallactic lens correctly fitted, the additive constant C becomes zero, simplifying the distance formula to the clean form D = KS, with no correction term needed at all (matching the ideal constants given in Q53).

Why the Other Options Are Wrong

A — Increase magnification: While adding any lens element technically affects the optical path, the anallactic lens's specific design purpose in tacheometry is not magnification enhancement — that is a separate optical design consideration unrelated to this lens's role.

C — Make the multiplying constant zero: A multiplying constant of zero would make the entire distance formula collapse to D = C (a fixed value regardless of staff intercept), which would be useless for tacheometry — the anallactic lens's purpose is the opposite: keeping K at a useful value like 100 while eliminating C.

D — Eliminate parallax: Parallax elimination (Q41) is achieved through proper eyepiece and objective focusing during temporary adjustment, an entirely separate procedure from the anallactic lens's specific optical-constant function.

Key Concepts for Students

• Anallactic lens → C = 0, not K = 0: This single fact, paired with Q53's "0 and 100" answer, fully captures what an anallactic lens achieves — it never targets the multiplying constant.
• "Anallactic" literally means "non-changing": The term reflects that the ratio of staff intercept to distance becomes effectively constant (and the additive offset vanishes) regardless of how far the telescope's focusing adjustment shifts internally as distance to the target varies.
• Most modern internally-focusing tacheometers are anallactic by design: Unlike older externally-focusing telescopes (which inherently have a non-zero d, and hence non-zero C, as in Q7, Q8, Q32), modern internal-focusing designs with a built-in anallactic lens largely eliminate this additive constant concern from everyday field calculations.