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Homework Help: Diffraction grating

  1. Jan 26, 2004 #1
    Consider two wavelengths that differ by .6nm and a 1cm diffraction grating that has 105 slits. How great must D (dist. to detector) be in order to resolve these wavelengths from a source containing them at better than ΔY=0.1mm?

    From the intensity equation, I find that a maximum will occur whenever Yd/D=n2λ. So I need (solving for D)
    [tex]D=\frac{d\Delta Y}{2\Delta \lambda}=8.3\textrm{mm}[/tex]. My work seems fine, but my answer seems off the mark. .6nm is a small wavelength difference. I'd expect a large D.
    Verify anyone?
    (d is the dist. between slit, which I take to be 1/105cm)
     
    Last edited: Jan 26, 2004
  2. jcsd
  3. Jan 26, 2004 #2
    I am surprised no one can help me. Has no one ever studied this before?
     
  4. Jan 27, 2004 #3

    Doc Al

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    Staff: Mentor

    Your equation seems fishy since it shows no dependence on the number of slits. The more slits in the grating, the greater the resolving power. (Also, the distance D need not be all that big if there are lots of slits.) Check this out:
    http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/gratres.html
     
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