Optics in surveying and engineering drawing: Which statements about the power of a lens and how powers combine for thin lenses in contact are correct?

Introduction / Context:
Lenses appear in many civil and surveying instruments (levels, theodolites, total stations) and also in drafting aids and optical sights. Understanding “power” clarifies how focal length relates to instrument magnification and how compound eyepieces or lens groups behave when combined. This question checks three foundational facts: definition of power, its unit, and how powers add for thin lenses in contact.

Given Data / Assumptions:

• Lenses are thin and coaxial so the “thin lens” approximations apply.
• Focal length f is measured in meters for power calculations.
• When thin lenses are placed in contact, spacing is negligible for first-order power addition.

Concept / Approach:
Lens power P quantifies refracting strength. By definition, P = 1 / f when f is in meters. The SI unit is diopter, written D or m^-1. For thin lenses placed in contact, the equivalent power is the sum of individual powers: P_total = P1 + P2 + …, which is widely used in designing eyepieces and objective–eyepiece combinations in surveying telescopes.

Step-by-Step Solution:

Verification / Alternative check:
Optics texts for engineering instruments adopt diopters for quick mental calculation: for example, a 0.25 m focal length lens has power 4 D. Stacking two 2 D thin lenses gives 4 D total (approximate) when in contact, matching P_total = P1 + P2.

Why Other Options Are Wrong:

• If any one statement were false, modern optical design basics would be contradicted. Since all three are correct, the only complete answer is the inclusive option.

Common Pitfalls:
Using focal length in centimeters when calculating diopters; forgetting that power addition presumes thin lenses in contact (finite separations demand more detailed matrix methods); confusing magnification with power (they are related but not identical).

Final Answer:
All of the above