OMEGA Formula: Integrating to Find the Answer

[yugo9]

I guess people who know can help. I know that the final formula should look like this:

(OMEGA) = 4tan^(-1) [(e)/n(1+e^2+n^2)^(0.5)] , where e=W/L, n=2z/L

I started with D(omega) = dAcos(theta)
p^2

cos (theta) = z/p

then i did a bunch of integration, but i can't get the same final answer. Please someone help. Just need to understand how to do this.

 

[mathman]

This looks like a math question, not physics. It would help if you would explicitly define your terms: W, L, z theta, p. I'll presume OMEGA is solid angle of something. What is the figure you are talking about?

I started with D(omega) = dAcos(theta)
p^2

Above is not clear.