Understanding Solid Angle & Calculating Half-Angle in a Cone

[Hoofbeat]

Hi, could someone explain to me the concept and calculation of Solid Angle? I don't think we've actually covered it in our Vector Calculus lectures and I have a question to do on it! Tried searching on the web, but not much information and I really don't understand it.

Also, my question is:
"Calculate the Solid Angle of a cone of half-angle 'alpha'".
What is the half-angle in a cone?

 

[dextercioby]

A transversal section through a cone,if done as to contain the axis reveals a triangle.My gues is that in your case,the triangle is isosceles...The 2 rightangle triangle (congruent) each has an angle $\alpha$...So the total angle is $2\alpha$...Use the definition of the solid angle and compute it.

Daniel.

 

[Claude Bile]

A 2D angle in radians is given by s/r (Where s is the arc length subtended by the angle).

Solid Angles are the 3D equivalent and have (dimensionless) units of steraidians. The Solid Angle is the area projected by the solid angle on a sphere of radius r, divided by r squared.

$$SA=A/r^2$$

The Solid Angle of an isotropic source, for example would therefore be

$$4\pi r^2/r^2 = 4\pi$$

and a hemisphere would be

$$2\pi$$

and so on...

Claude.