Perhaps this should be moved to the math forum, but I've never quite been able to understand solid angles. For example, in terms of thermal radiation and the planck distribution (black bodies), we can show that the energy flux denisty [itex]J_u[/itex] (the rate of energy emission per unit area) is equal to(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

J_u = \frac{cU({\tau})}{V} * \frac{1}{4}

[/tex]

Where [itex]U({\tau})[/itex] is the total energy in the cavity.The geometrical factor [itex]\frac{1}{4}[/itex] can be derived by solving the following problem:

Show that the spectral desntiy of the radiant energy flux that arrives in the solid angle [itex]d\Omega[/itex] is [itex]cu_{\omega}\cos\theta{\cdot}\frac{d\Omega}{4\pi}[/itex] where [itex]\theta[/itex] is the angle the normal to the unit area makes with the incident ray, and [itex]u_\omega[/itex] is the energy density per unit frequency range. The sum of this quantity over all incident rays is [itex]\frac{1}{4}cu_\omega[/itex].

Now, my understanding is that the solid angle is a projection of your object (in this case a small hole, or perhaps the beam emerging from the hole) onto a sphere of radius 1. I just really have no idea of what's going on, can anyone point me in the right direction?

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# Solid Angle Woes

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