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Homework Help: N-slit Interference/Diffraction

  1. Mar 20, 2006 #1
    Hi, having trouble determining whether my lab book has made an error, or I have.

    Intensity as a function of [tex]\phi[/tex] for 2 slits is given as

    [tex]A^2={A_2}^2\frac{sin^2(\frac{\phi}{2})}{{(\frac{\phi}{2})}^2}cos^2(\frac{\beta}{2})[/tex]

    but then it gives the amplitude for N slits to be

    [tex]A^2={A_N}^2\frac{sin^2(\frac{\phi}{2})}{{(\frac{\phi}{2})}^2}\frac{sin^2(\frac{N\beta}{2})}{sin^2(\frac{\beta}{2})}[/tex]

    However, when I sub in N = 2 for the equation (2), and use the double angle formula to reduce the right fraction in equation (2) I get 4*equation(1) rather than just the equation(1) alone. Am I doing it wrong?

    To be more succinct, isn't [tex]\frac{sin^2(\frac{N\beta}{2})}{sin^2(\frac{\beta}{2})} = 4cos^2(\frac{\beta}{2})[/tex]?
     
    Last edited: Mar 20, 2006
  2. jcsd
  3. Mar 20, 2006 #2

    Doc Al

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    Staff: Mentor

    I don't have my optics references handy, but I don't think you're doing anything wrong.

    I'd say that should be:
    [tex]A^2={A_0}^2\frac{sin^2(\frac{\phi}{2})}{{(\frac{\phi}{2})}^2}\frac{sin^2(\frac{N\beta}{2})}{sin^2(\frac{\beta}{2})}[/tex]

    It makes sense that the peak intensity should be proportional to the number of slits squared.
     
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