Basic Radiometry & Geometry – Solid angle facts Which of the following statements about radians, solid angle, and its unit are correct?

Introduction / Context:
Remote sensing and geodesy rely on angular measures. Plane angles (radians) and solid angles (steradians) appear in sensor instantaneous field of view (IFOV), radiance definitions, and calibration geometry. Understanding these basics prevents unit and interpretation errors.

Given Data / Assumptions:

• Definition of radian in plane geometry.
• Definition of solid angle at the centre of a sphere.
• Mathematical form of a solid angle Ω.
• SI units for angles.

Concept / Approach:
Check each statement against standard definitions: π rad = 180°; Ω is the conical spread from an area A on a sphere of radius r; Ω = A / r^2; SI unit is steradian, symbol sr.

Step-by-Step Solution:
Confirm plane-angle relation: π rad = 180°.Interpret “cone subtended by area” as the geometric definition of solid angle Ω.Use Ω = A / r^2 to connect area and radius.Recall SI unit: steradian (sr).

Verification / Alternative check:
On a unit sphere (r = 1), Ω = A; thus steradians numerically equal area on the unit sphere, ensuring consistency with Ω's definition.

Why Other Options Are Wrong:

• a–d are all correct, so the combined correct choice is “All of these”.

Common Pitfalls:
Using degrees for calculations requiring radians, or confusing planar angle (rad) with solid angle (sr), leads to scaling mistakes.

Final Answer:
All of these