Surveying telescopes – cross hairs: Where are the cross hairs (reticle) fitted relative to the objective and the eyepiece so that both the staff image and the cross hairs appear simultaneously sharp?

Introduction / Context:
Sharp coincidence of the cross hairs with the image is crucial for precise sighting in levels and theodolites. This is achieved by placing the reticle at a location where the image formed by the objective and the cross hairs themselves are both at the eyepiece’s focal plane.

Given Data / Assumptions:

• The telescope is a Keplerian type used in surveying instruments.
• The objective forms a real, inverted image of the target at its focal plane.
• The eyepiece magnifies objects located at its focal plane without introducing parallax if the image and cross hairs are coincident.

Concept / Approach:
Place the cross hair diaphragm at the common focal plane of objective and eyepiece. Then, when the objective brings the staff image into that plane and the eyepiece is focused so the reticle is sharp, there is no relative motion (parallax) between image and cross hairs as the eye shifts, ensuring accurate readings.

Step-by-Step Solution:

Verification / Alternative check:
Instrument manuals specify the reticle location at the focal plane to eliminate parallax; any other placement produces observable image drift against the cross hairs when the eye moves.

Why Other Options Are Wrong:

• Inside the objective or arbitrarily in front of the eyepiece, the image and reticle are not coplanar, causing parallax.
• “Center of the telescope” is a vague geometric location, not an optical plane.

Common Pitfalls:
Focusing the objective before the eyepiece; accepting slight parallax; dirty or misaligned reticle causing apparent focus issues.

Final Answer:
At the optical center (focal plane) of the eyepiece, i.e., the common focal plane of objective and eyepiece