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Diffraction Grating, calculating rulings/mm from spectrum

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Assume that the limits of the visible spectrum are arbitrarily chosen as 430 and 680 nm. Calculate the number of rulings per millimeter of a grating that will spread the first-order spectrum through an angle of 20.0 degrees.


    2. Relevant equations
    (y is lambda)
    dsinø = my (maxima)



    3. The attempt at a solution
    So, the first-order spectrum of white light has a line (maxima) the lowest wavelength and another line at the highest wavelength - right?

    And for the first-order spectrum would have a m of 1, right?

    If this is true, then,
    dsin(ø1) = 430
    dsin(ø2) = 680

    And, ø2 - ø1 = 20 degrees

    And
    ø1 = arcsin(430/d)
    ø2 = arcsin(680/d)

    But, I want to find out d. How can I extract d from these equations?

    Or, alternatively, do I not understand what's going on?
     
  2. jcsd
  3. Dec 6, 2009 #2

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper

    You have the right approach, but we can't solve for d explicitly; a numerical approach is needed here. What value of d results in ø1 and ø2 that are 20 degrees apart?
    If you can set this up in a spreadsheet, it won't take very long to find d that gives the required 20 degree spread.
     
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