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Diffraction Grating, Maxima, finding slit seperation

  1. Dec 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Light of wavelength 680 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin θ = 0.2 and sin θ = 0.3, respectively. The fourth-order maxima are missing.

    (b) What is the smallest slit width this grating can have?


    2. Relevant equations


    3. The attempt at a solution
    What equations relate slit width to angle theta?
     
    Last edited: Dec 3, 2009
  2. jcsd
  3. Dec 3, 2009 #2
    The diffraction orders do not have to be 1 and 2. Actually they are not.
    You don't need to assume their values. The information that the maxima are adjacent is enough. With your notation, that means m2=m1+1.
    You can find both d and m1,m2 from the equations (with the above condition).
     
  4. Dec 3, 2009 #3
    Yes, I had tried that, but it gave me values that I thought were too far from the correct answer (which I knew the value of). I've looked at all the numbers more closely, and it's just rounding preferences, is all the matter.

    Thanks.
     
  5. Dec 3, 2009 #4
    I edited the first post, to make it about the second part of the problem, for which I cannot think of any equations.
     
  6. Dec 4, 2009 #5
    There is nothing about rounding. The diffraction orders are 1 and 2 (in the first part).
    The same equation will give the minimum size of the slit. The condition is that you have only the maxima with orders 0 to 3 and nothing at 4.
    That means that the sin(theta) will have to be l>= 1 for order 4.
     
  7. Dec 4, 2009 #6
    There is nothing about rounding. The diffraction orders are 2 and 3 (in the first part).
    The same equation will give the minimum size of the slit. The condition is that you have only the maxima with orders 0 to 3 and nothing at 4.
    That means that the sin(theta) will have to be l>= 1 for order 4.
     
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