1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    tiny-tim

    User Avatar
    Science Advisor
    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:)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: L'Hopital's rule and Probability
  1. Feynman rules (Replies: 7)

  2. Hunds rule (Replies: 1)

  3. Feynman Rules (Replies: 8)

  4. Hund's rule (Replies: 4)

Loading...