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Homework Help: L'Hopital's rule and Probability

  1. Aug 29, 2009 #1
    The problem statement

    Using the Equation

    P([tex]\theta[/tex])= P1[ [tex]\frac{sin(Nkdsin(\theta)/2)}{sin(kdsin(\theta)/2)}[/tex] ]2

    show that the probability at sin([tex]\theta[/tex])=j[tex]\frac{\lambda}{d}[/tex], where j is an integer, is P([tex]\theta[/tex]=sin-1(j[tex]\lambda[/tex]/d))=N2P1

    Hit: find [tex]\frac{sin(Nkdsin(\theta)/2)}{sin(kdsin(\theta)/2}[/tex] as sin([tex]\theta[/tex]) approaches j([tex]\lambda/d[/tex]) using L' Hopital's rule.

    My problem: I am not sure how to apply L Hopital's rule to this situation. What would be my F(x) and what would be my G(x)?
  2. jcsd
  3. Aug 30, 2009 #2
    This looks like a problem from diffraction theory, but here's a little help. Basically L'Hopital's rule is used when the limit as an equation that can be expressed as a fraction of two equations diverges. L'Hopital's rule says to find the limit of the derivative of the numerator over the derivative of the denominator.
  4. Aug 30, 2009 #3


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    Homework Helper

    Hi Crazy Gnome! :smile:

    Your x can be either θ or sinθ …

    it makes no difference, the result will be the same. :wink:

    (Personally, I'd use θ. :smile:)
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