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Fringes from Different Interfering Wavelengths

  1. Apr 3, 2014 #1
    1. The problem statement, all variables and given/known data

    The questions is...
    Coherent light with wavelength 597nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is a distance of 4.84 mm from the center of the central bright fringe.

    For what wavelength of light will the first-order dark fringe (the first dark fringe next to a central maximum) be observed at this same point on the screen?



    But I am doing something wrong because I keep getting an incorrect answer.
    Any help would be appreciated! Thank you!

    2. Relevant equations

    dsinθ=mλ --constructive interference
    dsinθ=(m+1/2)λ --destructive interference
    λ/d=x/L

    3. The attempt at a solution

    I think that I should use the equation for constructive interference: dsinθ=mλ
    And I am pretty sure you can use the approximation that sinθ≈tanθ
    But doing this, and looking at the triangle, I am getting confused as to where to put the values. I think that "m" would be 1, but I am not sure if that is correct.

    I also tried using the third equation: (597E-3)*(3E6)/(4.84E3)=370, but this answer is not correct either.
     
  2. jcsd
  3. Apr 3, 2014 #2
    Use the constructive interference formula to find d and then use the destructive interference formula to find the new wavelength. There are two separate experiments here.
     
  4. Apr 4, 2014 #3
    equation you are using is of DIFFRACTION. I think you should use the one of interference , ie,
    ß=λD/d ; ß=fringe width , λ=wavelength,D-distance to screen,d-distance b/w slits.
     
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