explain solid angle in detail ?

love singh, 13 years ago

Grade:

1 Answers

suryakanth AskiitiansExpert-IITB

105 Points

13 years ago

Dear singh,

The solid angle, Ω, is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large that object appears to an observer looking from that point. A small object nearby may subtend the same solid angle as a larger object farther away (for example, the small/near Moon can totally eclipse the large/remote Sun because, as observed from a point on the Earth, both objects fill almost exactly the same amount of sky). An object's solid angle is equal to the area of the segment of unit sphere (centered at the vertex of the angle) restricted by the object (this definition works in any dimension, including 1D and 2D). A solid angle equals the area of a segment of unit sphere in the same way a planar angle equals the length of an arc of unit circle.

Steradian

The units of solid angle can be called steradian (abbreviated "sr") according to SI. From the point of view of mathematics and physics solid angle is dimensionless and has no units, thus "sr" might be skipped in scientific texts. The solid angle of a sphere measured from a point in its interior is 4π sr, and the solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2π/3 sr. Solid angles can also be measured in square degrees (1 sr = (180/π)² square degree) or in fractions of the sphere (i.e., fractional area), 1 sr = 1/4π fractional area.

One way to determine the fractional area subtended by a spherical surface is to divide the area of that surface by the entire surface area of the sphere. The fractional area can then be converted to steradian or square degree measurements by the following formulae:

To obtain the solid angle in steradians, multiply the fractional area by 4π.
To obtain the solid angle in square degrees, multiply the fractional area by 4π × (180/π)², which is equal to 129600/π.

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