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Homework Help: Diffraction grating question

  1. Jan 19, 2009 #1
    1. The problem statement, all variables and given/known data
    Monochromatic light shines on the surface of a diffraction grating with 5.3x10^3 lines/cm. The first order maximum is observed at an angle of 17 (degrees). Find the wavelength.

    a) 420nm c) 530nm
    b) 520nm d) 550nm


    2. Relevant equations
    d(sin [tex]\Theta[/tex])=m[tex]\lambda[/tex]

    d= 5.3x10^lines/cm=5.3x10^3 lines/m

    [tex]\Theta[/tex]=17

    m (the order maximum)= 1
    3. The attempt at a solution
    I rearranged the problem so it looked like this: [tex]\lambda[/tex]=(d[tex]\Theta[/tex])/m

    Since m=1, I dropped it and only worked with the numerator.

    The distance between the slits is 1/53 metres so the full equation looks like this: (1/53)(sin17)= [tex]\lambda[/tex]

    (1/53)(.29)=[tex]\lambda[/tex]
    .0054716981=[tex]\lambda[/tex]

    Just by looking at this answer its easy to see its wrong, but why? I followed the equation, so whats up? Any help would be appreciated.
     
  2. jcsd
  3. Jan 19, 2009 #2
    d is not 1/5.3 it is 1/5.3 times 10 to the power of 6.
     
  4. Jan 20, 2009 #3
    So my work was correct but i just needed that 10^6? thanks for the help
     
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