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Homework Help: Diffraction grating angular separation

  1. Sep 10, 2011 #1
    1. The problem statement, all variables and given/known data
    Light consisting of two nearly equal wavelengths L and L+dL, where dL << L, is incident on a diffraction grating. The slit separation of the grating is D. Show that the angular seperation of these two wavelengths in the m'th order is dTheta = dL / ((D/m)2+L2)0.5


    2. Relevant equations

    D sin(Theta) = mL (m=0,+-1, +-2,...)

    3. The attempt at a solution

    D sin(Theta1)=m(L+dL)
    D sin(Theta2)=m(L)
    dTheta = sin(Theta1)-sin(Theta2) = (m/D)(L+dL-L) = (m/D)dL= dL/(D/m)
    This answer doesn't match the formular I need to proof: dTheta = dL / ((D/m)2+L2)0.5
     
  2. jcsd
  3. Sep 10, 2011 #2

    wukunlin

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    Gold Member

    highlighted part is incorrect
     
  4. Sep 10, 2011 #3
    Thanks for the response.
    For small angle, sin(Theta) is very close to Theta (in radian).
     
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