Optics used in surveying telescopes: Which statement set correctly describes the power of a lens and its sign convention and unit?

Introduction / Context:
Surveying instruments such as levels and theodolites use compound lenses. Understanding “power” helps relate focal length to optical strength and ensures correct interpretation when lenses are combined or replaced during maintenance. This question checks the standard definition, sign convention, and unit of lens power used in optics.

Given Data / Assumptions:

• Thin lens approximation is valid for first-order calculations.
• Focal length f is expressed in meters for power calculations.
• Sign convention follows the usual physics/optics practice.

Concept / Approach:
Lens power P is defined as P = 1 / f, with f in meters. Converging lenses (convex) have positive focal lengths and thus positive power; diverging lenses (concave) have negative focal lengths and thus negative power. The SI unit is the diopter (1 diopter = 1 m^-1). These conventions are used when combining thin lenses: P_total ≈ P1 + P2 for lenses in contact.

Step-by-Step Solution:

Verification / Alternative check:
Example: a 0.25 m focal length lens has P = 4 D; a −0.5 m focal length lens has P = −2 D. Combining them in contact gives net ≈ 2 D, validating the definitions and signs.

Why Other Options Are Wrong:

• Any individual statement alone is incomplete; the complete and correct description is captured only by “All of the above.”

Common Pitfalls:
Using centimeters for f while quoting power in diopters; confusing magnification with power; ignoring that real instruments use multi-element designs but the power definition still applies element-wise.

Final Answer:
All of the above