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sr is the unit, steradian, sr = rad 2. Because the surface area A of a sphere is 4πr 2, the definition implies that a sphere subtends 4π steradians (≈ 12.56637 sr) at its centre, or that a steradian subtends 1/4π ≈ 0.07958 of a sphere. By the same argument, the maximum solid angle that can be subtended at any point is 4π sr.
The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A /2 and r = 1 . The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2 θ , is the area of a spherical cap on a unit sphere
Radiant intensity is used to characterize the emission of radiation by an antenna: [2], = (), where E e is the irradiance of the antenna;; r is the distance from the antenna.; Unlike power density, radiant intensity does not depend on distance: because radiant intensity is defined as the power through a solid angle, the decreasing power density over distance due to the inverse-square law is ...
watt per steradian per square metre per hertz W⋅sr −1 ⋅m −2 ⋅Hz −1: M⋅T −2: Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr −1 ⋅m −2 ⋅nm −1. This is a directional quantity. This is sometimes also confusingly called "spectral intensity". L e,Ω,λ [nb 7]
The SI unit of spectral radiance in frequency is the watt per steradian per square metre per hertz (W·sr −1 ·m −2 ·Hz −1) and that of spectral radiance in wavelength is the watt per steradian per square metre per metre (W·sr −1 ·m −3)—commonly the watt per steradian per square metre per nanometre (W·sr −1 ·m −2 ·nm −1).
Analogous to one degree being equal to π / 180 radians, a square degree is equal to ( π / 180 ) 2 steradians (sr), or about 1 / 3283 sr or about 3.046 × 10 −4 sr. The whole sphere has a solid angle of 4 π sr which is approximately 41 253 deg 2 :
One flick corresponds to a spectral radiance of 1 watt per steradian per square centimeter of surface per micrometer of span in wavelength (W·sr −1 ·cm −2 ·μm −1). This is equivalent to 10 10 watts per steradian per cubic meter (W·sr −1 ·m −3). In practice, spectral radiance is typically measured in microflicks (10 −6 flicks). [1]
If a lamp has a 1 lumen bulb and the optics of the lamp are set up to focus the light evenly into a 1 steradian beam, then the beam would have a luminous intensity of 1 candela. If the optics were changed to concentrate the beam into 1/2 steradian then the source would have a luminous intensity of 2 candela.