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Visibility in Optics: Integration help

  1. Nov 20, 2008 #1
    In calculating the visibility of an non point source interfernce pattern, you integrate the following:

    dI = (C/w)(cos^2[(ud/gL)(y-y_0)]).dy_0.

    between w/2 and -w/2. C, u, d, g, l , y constants.

    I'm finding this pretty tricky to integrate. Could someone help? Step by step would be really helpful.
  2. jcsd
  3. Nov 20, 2008 #2
    Hi Master J,
    As you have it written (and assuming you mean to say that "L" is a constant), this just amounts to evaluating [tex]\int_{-w/2}^{w/2} A\cos^2{\left(B(y-y_0)\right)} \, dy_0[/tex] for constants y, A and B. Then, using a substitution, this amounts to integrating [tex]\cos^2{x}[/tex]. To do that, use the identity [tex]cos^2{x} = \frac{1}{2}(\cos{2x} +1)[/tex]. Show your work so we know where abouts you're getting stuck.
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