Parallax test in levelling: When viewing through a level telescope and shifting the eye slightly causes relative movement between the staff image and the cross-hairs, the instrument condition is best described as what?

Introduction / Context:

Parallax is a focusing error that introduces reading bias in levelling and angle measurements. It occurs when the real image formed by the objective lens does not coincide with the plane of the cross-hair diaphragm. Detecting and removing parallax is part of standard instrument setup before taking observations.

Given Data / Assumptions:

• The observer slightly shifts the eye laterally while looking through the telescope.
• A relative motion between the staff image and the cross hairs is observed.
• Standard optical layout: objective → cross-hair diaphragm → eye-piece.

Concept / Approach:

If the target image and cross hairs lie in different planes, moving the eye changes the line of sight through the eye-piece, making the cross hairs appear to slide over the image (or vice versa). This is parallax. The cure is two-step focusing: first focus the eye-piece sharply on the cross hairs, then focus the objective until the target image snaps into the same plane, confirmed when no relative motion is seen upon eye movement.

Step-by-Step Solution:

Verification / Alternative check:

Repeat the test at a different staff distance to ensure the condition persists; minor residual parallax at extreme distances may require small refocusing.

Why Other Options Are Wrong:

• Correctly focussed / free from parallax: contradict the observed relative movement.
• Not correctly focussed: true in effect, but the technically precise description is that the instrument ‘‘has parallax’’; eliminating parallax achieves correct focus.

Common Pitfalls:

• Focusing the objective before the eye-piece; always focus the eye-piece first to set the reticle plane.

Final Answer:

said to have parallax