Telescope optics—image location: For proper focusing and zero parallax, where must the real image formed by the objective lens lie with respect to the diaphragm of cross-hairs?

Introduction / Context:

Eliminating parallax is essential for precise sighting. Parallax occurs when the image of the target and the cross-hair plane do not coincide; moving the eye then causes apparent relative motion between the two. Understanding where the objective's image must be formed ensures correct focusing procedure in levels and theodolites.

Given Data / Assumptions:

• Standard Keplerian telescope with objective, cross-hair diaphragm, and eye-piece.
• Cross hairs are fixed at the focal plane of the eye-piece once initially focused.
• Observer can adjust both the eye-piece (for the reticle) and the objective (for the target image).

Concept / Approach:

First, focus the eye-piece until the cross hairs appear sharp—this places the cross-hair plane at the eye-piece focal plane. Then focus the objective so that the real image of the target is formed exactly in the plane of the cross hairs. Only then will both the target image and the cross hairs be conjugate to the eye, eliminating parallax.

Step-by-Step Solution:

Verification / Alternative check:

If parallax persists, repeat steps because either the eye-piece was not correctly set or the objective focus is off.

Why Other Options Are Wrong:

• At the centre or optical centre are meaningless locations for image formation.
• Anywhere inside or slightly in front produces parallax and reading errors.

Common Pitfalls:

• Focusing the objective before the eye-piece; always focus the eye-piece first.

Final Answer:

in the plane of cross hairs