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Homework Help: Intensity from a multi slit grating

  1. Jan 29, 2006 #1
    The intensity from a multi slit grating with 2N+1 slites is given by:

    [tex]I(Y)=\frac{M^2}{2R^2} \frac{sin^2 \left[(2N+1) \frac{x}{2}\right]}{sin^2 \left[\frac{x}{2}\right]}[/tex]

    where [tex]x=\frac{2 \pi Y d}{D \lambda}[/tex]

    I am to show how to find the limiting case of just two slites and show that in this limit the formula is exactly the same as:

    [tex]I(Y)=\frac{2M^2}{D^2} cos^2 \left(\frac {\pi d sin\theta}{\lambda}\right)[/tex]

    so what I did:

    [tex]I(Y)=\frac{M^2}{2R^2} \frac{sin^2 \left[(2N+1) \frac{x}{2}\right]}{sin^2 \left[\frac{x}{2}\right]}[/tex]

    [tex]=\frac{M^2}{2R^2} \frac{sin^2 \left[ \frac{2 \pi \lambda d}{D \lambda} \right]}{sin^2 \left[\frac{\pi \lambda d}{D \lambda} \right]}[/tex]


    I could turn this into cos/cos but I dont know how to get it into cos(sin) any ideas?
     
  2. jcsd
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