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shaf777
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Homework Statement
I have an equation to solve. See the attach pichture.
I(r,φ,λ) = I0.sin(2πr/R).sin2(φ).(1/λ)
where
I0 , R are constants
r,φ are cylindrical coordinates
0≤r≤R/2 : the cut is laterally limited
λa ≤ λ ≤ λb : the beam contains a limited frequency spektrum
where the shortcut for integration:
∫sin2(ax) dx = x/2 - 1/4a .sin(2ax)
∫x. sin(ax) dx = (sin(ax)/a2) - (x.cos(ax)/a)
The qustions are to find the total power/Intensity of the light beam, that was produced by λ.
Homework Equations
The Attempt at a Solution
I want to integrate the above equation to get the power or intensity of the beam, but I am stuck.
∫I(r, φ, λ) dλ = ∫ I0 sin(2πr/R).sin2(φ).(1/λ) dλ
= sin(2πr/R).sin2(φ) ∫ (1/λ) dλ
= sin(2πr/R).sin2(φ) . ln|λ| + C
Is my answer correct? Because I did not even use the given Integration shortcut.
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