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Diffraction grating, angular with of the intensity peaks to the first maximum

  1. Apr 19, 2012 #1

    Leb

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    1. The problem statement, all variables and given/known data
    A diffraction grating is ruled with 500 lines/mm and
    is 1 mm in width. Calculate the angular width of
    the intensity peaks to the first minimum in the
    Fraunhofer diffraction pattern of this grating, when
    illuminated with light of λ = 600 nm.


    2. Relevant equations

    n- order, d separation of slits
    nλ = dsinθ

    Single slit function ψ(θ)=Aa sinc (kθa/2) (not sure if relevant)
    A-amplitude,
    a -width of the slit
    k = 2π/λ
    b = 1mm the width of the
    3. The attempt at a solution
    TBH, I am not really sure what do they mean by angular width ( I assume θ). But I was not sure how to attempt this problem. I was thinking of convolving f(x) = ...+ δ(x+ 2d)+δ(x+d)+δ(x)+δ(x-d)+δ(x-2d)+... [the infinite array of slits of negligible width] with g(x) = (from -b/2 to b/2)∫dx [the width of the grating] and then looking for zeros of intensity, from which I can tell the θ. Does this sound correct ?
     
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