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Confused on diffraction grating question

  1. Mar 21, 2009 #1
    1. The problem statement, all variables and given/known data

    a) Exactly 4 bright fringes are seen on either side of the central maximum when a diffraction grating is illuminated with yellow-green light of a wavelength of 570 nm. What is the maximum number of lines/meter for the grating?


    2. Relevant equations

    sin(theta) = m(wavelength) / d

    so solving for d = m(wavelength) / sin(theta)


    3. The attempt at a solution

    I want to find the max number of lines/ meter for the grating
    so d= ? m/line
    m = 0 because the question says central maximum
    wavelength is given to you and in meters it is 570*10^-9 m

    ***what i dont understand is how do you find the angle Theta? Does it have to do with the "4 bright fringes" part of the question? And does that mean m=4?

    because after finding the angle Theta i would be able to solve for d = m(wavelength) / sin(theta) and get an answer. Then I would do 1/answer to get the final answer in lines/m.
     
  2. jcsd
  3. Mar 21, 2009 #2

    Redbelly98

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    Yes! Also, what is the largest angle you could have?

    Yes, that's the idea.
     
  4. Mar 21, 2009 #3
    so m = 4? or m = 0? and is the largest angle you can have 180 degrees? im still very confused on this question....
     
  5. Mar 21, 2009 #4

    Redbelly98

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    m = 4 for the fourth fringe from the the central maximum.

    PF_diffraction-grating_2009-03-21.gif

    Hope this picture shows you what is going on. The m=4 diffracted beams are shown in green. How large can the angle θ be, and still have that m=4 beam (the green beam to the left) be visible?
     
  6. Mar 21, 2009 #5

    rl.bhat

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    Yes. In that 8 bright fringes are there. All of them are equally spaced. So what will be the angular separation of the first bright fringe from the central fringe?
     
  7. Mar 21, 2009 #6
    is the angle 90? so then sin of 90 = 1?
     
  8. Mar 21, 2009 #7

    Redbelly98

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    Yes. Now you can do what you said before:
     
  9. Mar 21, 2009 #8
    thank you so much!! =]
     
  10. Mar 22, 2009 #9
    I have the same problem but I can not understand the communication between the two of you. M=4 correct? but why would the angle be 90 and not 45?
     
  11. Mar 23, 2009 #10

    Redbelly98

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    Welcome to PF :smile:

    Yes, M=4.

    In the figure in post #4: We're talking about the angle between the central, vertical green ray and either of the other green rays. Is it not clear that angle could be more than 45? (It's roughly 80 in the figure).
     
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