What is a Solid Angle?

Question

What is a Solid angle.How do we measure a solid angle? How is it different from a plane angle and how do we construct a solid angle

Answer 1

The solid angle is a three dimensional angle subtended by an object (two dimensional or three dimensional) at a certain point in the space. It merely depends on the relative distance of the object & its configuration with respect to the given point in the space. Solid angle subtended by a straight line or a point is always zero.

Solid angle is a dimensionless quantity which is usually measured in SI unit Ste-radian (in brief "sr"). It is usually denoted by symbol '$\Omega$' or '$\omega$'

Solid angle is obtained as a solid (three dimensional) cone with cvertex at the given point when all the points of the object are joined to the given point in the space such that this cone completely & exactly encloses (engulfs) (2-D or 3-D) object. While a plane angle is obtained as the radial segment (of a circle without arc) which encloses (engulfs) a single linear dimension of the object.

Solid angle is constructed in three dimensional space just by joining all the points of the (2-D or 3-D) object to the given point. This results in a solid cone with vertex at the given point. This cone is called cone of vision. The nature of the cone of vision depends on the surface profile of the given object with respect to the point (eye of the observer). It is right circular for an object appearing circular to the observer's eye at the point O. (See first figure above) While it is skew for all the objects appearing non-circular to the observer's eye at the point O (See second figure above)

Answer 2

Imagine a 45 degree angle drawn on paper. Two lines opening up in a triangular shape right? Well that's a two dimensional angle. It obviously has height and width because it's drawn on paper. A solid angle is very similar. It is simply a three dimensional angle. This means it has height and width just like a regular angle but also has depth. What can this look like? It could be a cone. Or a pyramid. The tips of cones and pyramids have an angle of opening just like regular angles. That right there would be a solid angle. My favorite example of what solid angles are that I like to use are the outward opening angles formed by the beam of a flashlight!

Answer 3

A solid angle is an angle in three-dimensional space. While you can think of a planar angle as the portion a pair of rays cuts out from a unit circle centered at their common point of origin, a solid angle is the area a cone (or a possibily infinite union of cones) cuts out from a unit sphere centered at the apex of that cone. The pair of rays in the plane is therefore the planar analogon to that cone.