what is meant by solid angle?

Answer 1

A solid angle is the three dimensional equivalent of an angle in two dimension. We say that an angle inside a circle subtends a certain amount of arc. Expanding this idea, a cone inside of a sphere is a solid angle that subtends a certain amount of the spherical surface. The unit of measure for a solid angle is a steradian. And just as a radian is defined as the angle subtending an arc equal in length to the radius of a circle, a steradian is the solid angle that subtends an area equal to the square of the radius. Thus, a circle has an angle of 2*pi because the circumference of a circle is 2*pi*r, and so a sphere has a solid angle of 4*pi because the surface area of a sphere is 4*pi*r^2. Solid angle is usually represented in formulae as a capital omega (which looks like a horseshore), and the abbreviation for steradians is sr.

Answer 2

Solid Angle Definition

Answer 3

let me explain u in simple words

have u ever seen a cone the angle at the centre is known as soli anngle

to calculate solid angle
let consider a area S on a sphere the angle substanded by this area at the centre is solid angle the formula is S/r^2 where r is the radius of sphere
by this formula u can calculate that whole sphere substend a solid angle of 4pie at the centre

Answer 4

Solid Angle

The angle that, seen from the center of a sphere, includes a given area on the surface of that sphere.The solid angle, Ω, that an object subtends at a point is a measure of how big that object appears to an observer at that point. The solid angle is proportional to the surface area, S, of a projection of that object onto a sphere centered at that point, divided by the square of the sphere's radius, R. (Symbolically, Ω = k S/R², where k is the proportionality constant.) .The shape of the area doesn't matter at all. Any shape on the surface of the sphere that holds the same area will define a solid angle of the same size.Standard unit of a solid angle is the Steradian (sr).

A solid angle is related to the surface area of a sphere in the same way an ordinary angle is related to the circumference of a circle.

If the proportionality constant is chosen to be 1, the units of solid angle will be the SI steradian (abbreviated sr). Thus the solid angle of a sphere measured at its center is 4π sr, and the solid angle subtended at the center of a cube by one of its sides is one-sixth of that, or 2π/3 sr. Solid angles can also be measured (for k = (180/π)²) in square degrees or (for k = 1/4π) in fractions of the sphere (i.e., 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:

1. To obtain the solid angle in steradians, multiply the fractional area by 4π.
2. To obtain the solid angle in square degrees, multiply the fractional area by 4π × (180/π)², which is equal to 12960

HENCE WE can say

"One steradian (sr) is the solid angle that, having its vertex in the center of a sphere, cuts off an area on the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere."

It is used in radiometry and photometry.

Answer 5

It is the opposite of liquid angle. Liquid angle is used in the manufacture of milks and shakes. It is about 360 degress centigrade which is like a circle. So Solid angle is the opposite of circle which is a cone.

Answer 6

A normal bulb spreads light out in all three dimensions. But Imagine a spotlight beam spreading out light over a much narrower range. The difference is the bulb spreads light out over a much bigger 'solid angle' than the spotlight. It's like taking the idea of an a normal angle (in 2D) and extending it to 3D. Useful designing light and sound systems, where the energy is 'spreading out' as in the above examples. See link.

Answer 7

The solid angle, Ω, that an object subtends at a point is a measure of how big that object appears to an observer at that point. For instance, a small object nearby could subtend the same solid angle as a large object far away. The solid angle is proportional to the surface area, S, of a projection of that object onto a sphere centered at that point, divided by the square of the sphere's radius, R. (Symbolically, Ω = k S/R², where k is the proportionality constant.) A solid angle is related to the surface area of a sphere in the same way an ordinary angle is related to the circumference of a circle.

If the proportionality constant is chosen to be 1, the units of solid angle will be the SI steradian (abbreviated sr). Thus the solid angle of a sphere measured at its center is 4π sr, and the solid angle subtended at the center of a cube by one of its sides is one-sixth of that, or 2π/3 sr. Solid angles can also be measured (for k = (180/π)²) in square degrees or (for k = 1/4π) in fractions of the sphere (i.e., 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:

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

[edit] Practical applications

* Defining luminous intensity and luminance
* Calculating spherical excess E of a spherical triangle
* The calculation of potentials by using the Boundary Element Method (BEM)
* Evaluating the size of ligands in metal complexes, see ligand cone angle.

Answer 8

a solid angle is when we consider an angle in three dimension way instead in a two dimension way eg.edge of a solid prism is a solid angle

Answer 9

An angle formed by three or more planes intersecting at a common point..

Answer 10

awesome