# Solid Angle

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## solid angle

[′säl·əd ′aŋ·gəl]
(mathematics)
A surface formed by all rays joining a point to a closed curve.

## Solid Angle

a surface formed by rays having a common origin and passing through a closed curve (Figure 1). Sometimes, particularly in Soviet usage, the term “solid angle” is applied to the portion of space bounded by such a surface. Trihedral and polyhedral angles are special cases of solid angles.

Figure 1

A measure of the solid angle subtended at a given point by a surface S is provided by the ratio AIR2. Here, A is the area of the portion of a sphere, with center at the given point, that is cut by a conical surface with vertex at the point and with the perimeter of S as a directrix, and R is the radius of the sphere. Clearly, the measure of a solid angle is an abstract number. For example, the measure of a solid angle that encloses an octant, that is, oneeighth of space, is the number 4π R2/8 R2 = π/2 (Figure 2).

Figure 2

The unit of measure of a solid angle is called the steradian. It is equal to the solid angle subtended at the center of a sphere of unit radius by a portion of the sphere’s surface that is of unit area. The total solid angle about a point is equal to 4π steradians.

References in periodicals archive ?
From the observer point of vue, the geometric etendue of the HUD image can be assessed summarily as the product of the solid angle associated with the accessible Field Of View (FOV) by the transverse dimensions of the Eye Motion Box (EMB).
Electrons orbit the proton about 200 times further out than the muon and so the solid angle of the proton at the electron is much smaller.
Customers should continue to purchase Arnold through their usual Solid Angle channels.
The BUG rating system was proposed due to its ability to evaluate luminaire distributions in the context of the impact of light emitted in the various solid angles of the LCS as they apply to light trespass, skyglow, and glare, and was intended to replace the IES vertical cutoff classification system (for example, full cutoff, noncutoff).
Second, our method of calculating the solid angle for radiation emitted at a point within the chamber is only approximate.
Hence "taken together, the marks on the glass will subtend the same solid angle as the face of the [object] they trace.
h] is the fraction of a metallic object that is contained within the sensor antenna solid angle [[Omega].
Hence, the ratio of the survey spectroscopic area divided by the solid angle of the sphere is as follows:
This has permitted the effective solid angle (omega) of the detector to be increased by several times over what had been achieved with conventional tube-mount detectors.
10 Kempton Some punters will have a downer on David Simcock's six-year-old after he put in a tame display in claiming company atWolverhampton (1m1f) two days ago, but I wouldn't be in a rush to write him off tonight, as there is a solid angle in with him.
with [OMEGA] the solid angle around the point and d[[OMEGA].

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