Question
Tue April 19, 2011 By: Anupama Ray

respected ma'am / sir what ia a plain angle and a solid angle ? also explain the diagram .

Expert Reply
Tue April 19, 2011

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other (see "Measuring angles", below). Where there is no possibility of confusion, the term "angle" is used interchangeably for both the geometric configuration itself and for its angular magnitude (which is simply a numerical quantity).

 

The solid angle, ?, 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.

 
Any area on a sphere, totaling the square of its radius and observed from its center, subtends precisely one steradian.The SI units of solid angle are steradian (abbreviated "sr"). 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 4? sr, and the solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2?/3 sr. Solid angles can also be measured in square degrees (1 sr = (180/?)2 square degree) or in fractions of the sphere (i.e., fractional area), 1 sr = 1/4? fractional area.

 

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