Definition of Solid Angle
A solid angle is a two-dimensional angle in three-dimensional space that subtends a portion of the surface of a sphere. It quantifies how much of a viewer's field of view an object occupies, or how large an object appears from a specific point. Unlike a planar angle measured in radians, which describes a section of a circle, a solid angle describes a section of a sphere's surface.
Unit and Calculation
The SI unit for solid angle is the steradian (sr). One steradian is defined as the solid angle subtended at the center of a sphere by a portion of the surface whose area is equal to the square of the sphere's radius (Area = r²). The formula for a solid angle (Ω) subtended by a surface area (A) on a sphere of radius (r) is typically given by Ω = A/r².
Practical Example
Imagine looking at the moon. The solid angle it subtends at your eye indicates how much of your field of vision the moon covers. While the moon's physical size is vast, its distance from Earth makes its solid angle small. Conversely, a small object held very close to your eye can subtend a large solid angle.
Applications in Science
Solid angles are crucial in various scientific and engineering fields, particularly in optics for describing the light collected by a lens, in astronomy for measuring the apparent size of celestial objects, and in radiation physics to quantify the fraction of radiation emitted into a specific direction. They are fundamental for calculations involving intensity and flux.