Analogue of radians on spheres. A sphere has solid angle $4\pi$ comparing to the $2\pi$ radian for a circle.
Questions tagged [solid-angle]
124 questions
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Is there a reason why a differential solid angle is represented by a cone?
Just wondering... is there a geometric reason why a differential solid angle is usually represented by a cone? I cannot see that given the formula
$$
d\Omega = \sin \theta \, d\theta \, d\phi
$$
I cannot see that.
user8469759
- 5,285
1
vote
1 answer
Solid angle definition - can it be seen shown using an image?
How do we show on a picture that a solid angle equals to this equation i found on a Wikipedia:
\begin{align}
\Omega =\!\!\!\int\limits_{\vartheta =0}^{\pi}\int\limits_{\varphi=0}^{2\pi}\underbrace{\sin\vartheta\, \textrm{d}\vartheta\,…
71GA
- 841
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vote
2 answers
How to find out the solid angle subtended by a tetrahedron at its vertex?
Given that the angles between the consecutive lateral edges AB, AC & AD meeting at the vertex A of a tetrahedron ABCD are $ α, β, γ$ (as shown in the diagram below). Is there any set-formula to find out the solid angle subtended by the tetrahedron…
Harish Chandra Rajpoot
- 37,450
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0 answers
What is the solid angle substended by a point on some closed surface?
I'm trying to find out the solid angle subtended over the entirety of some closed surface S by some point P located on the surface. For a point within the surface, the answer is of course 4$\pi$, but I'm trying to get the result if that point were…
0
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0 answers
Fraction of Solid Angle
I wonder which way is the correct way to calculate a specific fraction of a solid angle.
I divided a hemisphere into a number of solid angles by using weights of gauss quadrature in the zenith direction ($W_j$) and in the azimuthal direction…
Elad
- 1
0
votes
1 answer
Orienting a solid angle
I'm working on a project in which I need to somehow define oriented solid angle in Cartesian coordinate system, similar to how "regular" oriented angle is defined. And well, I have no idea how to do it. I thought about some plane with one point…
Proki
- 3