Optics of surveying telescopes: The resolving power of a telescope used in theodolites, total stations, or levels primarily depends on which factor? Choose the most appropriate determinant.

Introduction / Context:
Resolving power is the ability of an optical system to distinguish two closely spaced objects. In surveying, this affects the clarity of staff graduations, distant targets, and fine alignment marks. Knowing what governs resolution helps in selecting and maintaining instruments for precise angular and distance observations.

Given Data / Assumptions:

• Typical visible-light observations with standard field telescopes.
• Atmospheric seeing and heat shimmer are moderate.
• Lenses are well-corrected and properly focused.

Concept / Approach:
According to the Rayleigh-style criterion, the angular resolution is proportional to wavelength / objective diameter. Thus, the larger the objective lens (object glass), the finer the detail that can be resolved. Eyepiece design magnifies the image but does not improve fundamental resolution, which is set by the entrance pupil (objective) of the telescope. The observer’s eye pupil can limit perceived brightness and comfort but does not change the optical system’s intrinsic resolving power.

Step-by-Step Solution:

Verification / Alternative check:
Compare two theodolites: a 45 mm objective versus a 30 mm objective under identical conditions. The larger objective resolves finer target details despite using the same eyepiece magnification.

Why Other Options Are Wrong:

• Aperture (generic) may be interpreted broadly; the precise determinant is the objective’s diameter.
• Observer’s eye pupil affects brightness and depth of field perception but not the telescope’s diffraction limit.
• All of the above is incorrect because only the objective diameter defines fundamental resolving power.

Common Pitfalls:
Confusing magnification with resolution; turning up magnification on a small objective simply yields a larger, blurrier image.

Final Answer:
The diameter of the object glass (objective lens)