1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook