Parallax and telescope focusing in surveying instruments Which combination of statements about parallax and the eyepiece objective focusing is correct for eliminating parallax when sighting a target?

Introduction / Context:
Parallax causes the apparent motion of the image relative to the cross-hairs when the observer's eye moves slightly. Eliminating parallax is essential for precise pointing with levels, theodolites, and total stations, otherwise readings are biased and inconsistent across observers.

Given Data / Assumptions:

• (a) If the image of the object does not form in the plane of the reticle (cross-lines), parallax exists.
• (b) Claim that parallax has nothing to do with the eyepiece.
• (c) Eyepiece focusing is for clear, sharp cross-hairs.

Concept / Approach:

Parallax occurs when the image of the target (formed by the objective) and the reticle are in different planes. To eliminate it, first focus the eyepiece on the cross-hairs (so the eye accommodates at infinity for the reticle), then focus the objective on the target so that its image also lies in the same plane as the reticle. Statement (a) is true; (c) is true; (b) is false because eyepiece adjustment is a key step in parallax elimination.

Step-by-Step Solution:

Verification / Alternative check:

Instrument manuals specify this two-step focusing precisely; observing no relative shift on slight eye movement confirms success.

Why Other Options Are Wrong:

(b) is incorrect; parallax is strongly related to eyepiece focusing. Options claiming all or only one statement are correct do not match the truth pattern.

Common Pitfalls:

Focusing the objective first; leaving slight parallax that varies with observers; assuming spectacle corrections replace eyepiece focusing.

Final Answer:

Only (a) and (c) are correct