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Homework Help: Single slit diffraction

  1. Dec 9, 2007 #1
    1. The problem statement, all variables and given/known data

    Interesting Problem...

    monochromatic light of wavelength [tex]\lambda[/tex] falls on a slit and is transmitted as

    t=1 for 0<x<(d/2)
    t=-1 for (-d/2)<x<0
    t=0 otherwise...

    Define [tex]\ w [/tex]=[tex]\ k(d/2) [/tex][tex]\sin[/tex][tex]\theta[/tex]...[most possibly,if I can exactly remember...]

    Now what should be the dependence on w of Intensity [tex]\I(\theta)[/tex]?

    It was a multiple choice question and a number of options were given...

    (A) [tex]\frac{sin^2 \omega}{\omega^2}[/tex]

    (B) [tex]\frac{sin^2 \frac{\omega}{2}}{\omega^2}[/tex]

    (C) [tex]\frac{cos^2 \omega}{\omega^2}[/tex]

    (D) [tex]\frac{sin\omega}{\omega}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    (B) seems plausible to me as it considers w/2...Note that in this particular problem,the phasor amplitudes are different about the centre.If you take the geometrical point of view,the phasor vectors will be a bit different than they are shown normally.
    [I do not know which classical book uses the geometrical phasor derivation...I saw it in Resnick Halliday Krane's fifth volume.]
  2. jcsd
  3. Dec 9, 2007 #2


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    Homework Helper
    Gold Member

    What is 't'? I'm not familiar with this notation.
  4. Dec 9, 2007 #3
    t is transmission co-efficient
  5. Dec 9, 2007 #4

    Doc Al

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    Staff: Mentor

    Answer (B) is correct.
  6. Dec 9, 2007 #5

    Any better argument?
  7. Dec 9, 2007 #6

    Doc Al

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    Staff: Mentor

    Last edited by a moderator: Apr 23, 2017
  8. Dec 9, 2007 #7
    Exactly,I was talking of this derivation.
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