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Double Slit Diffraction Problem

  1. Nov 13, 2014 #1
    I had this problem on my exam and I was pretty sure i knew what to do but it couldn't come up with the right answers.
    I diagrammed the problem and showed the way i tried to solve it in blue. Can someone tell me where i went wrong?
    W6xA170.png

    Basically i found the length the of the first maximum off the center. i used Pythagorean's theorem to find D2. Then subtracted the two distances to find the difference. I then took the arctan of that distance divided by D1.
     
  2. jcsd
  3. Nov 13, 2014 #2

    Simon Bridge

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    You way over-thought the problem.
    Start from the physics: what is the condition that makes a maximum?
     
  4. Nov 13, 2014 #3
    the center of a maximum is complete constructive interference from two rays of light?
     
  5. Nov 13, 2014 #4

    Simon Bridge

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    ... good - so what is the condition for constructive interference in terms of the path lengths?
     
  6. Nov 13, 2014 #5
    wouldn't it be the wavelength plus by any integer being multiplied by the wavelength?
     
  7. Nov 13, 2014 #6

    Simon Bridge

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    Almost: the path difference has to be a whole number of wavelengths for constructive interference.
    This makes the central maximum the zeroth maximum ... with the 1st and second etc on either side of it.

    Lets say D is the perpendicular distance from the slits to the screen - as it is in your diagram.
    If D>>d, the path difference between the zeroth maximum and the nth maximum is ##D_n-D=d\sin\theta_n##
    You've seen a formula like that before.
     
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