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Solid angle is expressed in terms of
Radians / meter
Radians
Steredians
Degree
Steredians
A solid angle is a two-dimensional angle in three-dimensional space that an object subtends at a point. Its SI unit is the steradian (sr), which measures the ratio of the surface area of a spherical cap to the square of the sphere's radius.
A solid angle is a two-dimensional angle in three-dimensional space that an object subtends at a point. Its SI unit is the steradian (sr), which measures the ratio of the surface area of a spherical cap to the square of the sphere's radius.
╬й=r2AтАЛ тАФ Fundamental definition of solid angle
╬йtotalтАЛ=r24╧Аr2тАЛ=4╧А┬аsr тАФ Total solid angle for a sphere
The solid angle (╬й) is defined as the area (A) of a portion of a spherical surface divided by the square of the radius (r2) of the sphere. If the surface area A is equal to r2, the solid angle subtended is exactly one steradian. Mathematically, the total solid angle subtended by a sphere at its center is 4╧А steradians.
The steradian is a dimensionless unit because it is the ratio of two areas.
Solid angle is fundamental to calculating luminous intensity (I) where I=d╬йd╬жтАЛ.
A radian is the unit for plane angles, while a steradian is for solid angles.
Simplifies 3D illumination calculations
Essential for defining Luminous Intensity and Luminance
Calculating total luminous flux from a light source
Radiation intensity measurement in physics
Geometrical modeling in optical engineering
One steradian is the solid angle subtended at the center of a sphere of radius r by a portion of the surface having an area r2.
Option B (Radians) is incorrect as it is the unit for plane angles. Option D (Degree) is also a unit of plane angle measurement.
C is correct тАФ Solid angle is a measure of the amount of the field of view covered by an object in 3D space, and its SI unit is the steradian.
Always distinguish between plane angle (radians, 2D) and solid angle (steradians, 3D). In lighting design, remember that 1┬аlumen=1┬аcandela├Ч1┬аsteradian.