Optics of telescopes – defining magnification in surveying instruments The ratio of the angle subtended at the eye by the virtual image to the angle subtended by the object itself is known as the telescope’s:

Introduction / Context:
Surveying telescopes are optical systems used to sight distant targets with precision. Several performance metrics characterize their behavior, including magnification, resolving power, field of view, and image brightness. This question focuses on the formal definition of magnification as perceived by the observer’s eye when viewing the virtual image formed by the instrument.

Given Data / Assumptions:

• The telescope forms a virtual image at or near infinity for comfortable viewing.
• Angles are small, and paraxial approximations hold.
• The observer compares angular sizes, not linear sizes at the object plane.

Concept / Approach:

Angular magnification M is defined as M = θ_image / θ_object, where θ denotes the angle subtended at the eye. A higher magnification makes the target appear larger angularly, improving fine pointing and reading of cross-hairs on the staff or target. This definition distinguishes magnification from resolving power (ability to separate closely spaced details), field of view (angular width of the observable scene), and brightness (related to aperture and exit pupil).

Step-by-Step Solution:

Verification / Alternative check:

Optics references consistently define angular magnification this way; instrument datasheets list “magnification” as a unitless ratio (e.g., 30×), confirming the concept.

Why Other Options Are Wrong:

Resolving power: linked to aperture and wavelength; not a simple angular size ratio.

Field of view: total angular extent observable, typically decreases as magnification increases.

Brightness: influenced by exit pupil and coatings; not defined by the angular ratio.

Common Pitfalls:

Equating high magnification with better resolution without considering diffraction and stability; overlooking that excessive magnification narrows field and reduces brightness.

Final Answer:

Magnification