Solid angle by placing one disk on a cylinder

[Shams]

Hello,

I am trying to find an analytical expression to determine the solid angle subtended by a disk source onto the face of the cylinder. I will appreciate if someone can provide me directions.

I am aware how to calculate solid angle by a point source to cylinder's face ( omega = 2*pi(1-cos(theta) ). In my case I have a source of radius 0.3 cm at 5 cm away from a cylinder with radius 2.5 cm. The source is on the cylinder axis.

Anyone has any idea of the right expression?

 

[kuruman]

Hi Shams and welcome to PF.

Is this like an extended disk-shaped radioactive source in front of a counter? Since you have the solution for a point source, consider the extended source as a collection of point sources. Assuming uniform distribution of source activity, find the contribution to the flux from a source of strength $dS = S\frac{dA'}{\pi R^2}$ located at polar coordinates $[r',\phi']$ ($dA=r'dr'd\phi'$). Note that the source is off the axis of the cylinder so you need to modify the solution you already have. I hope it does not involve elliptic integrals. Anyway, once you have that answer, then you will need to integrate over the primed source coordinates.