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Homework Help: Single-slit diffraction diffraction pattern

  1. Feb 25, 2012 #1
    1. The problem statement, all variables and given/known data
    A single slit forms a diffraction pattern with monochromatic light. The 6th minimum of the
    pattern occurs at an angle of 23° from the central maximum. The number of bright bands on
    either side of the central band is closest to:
    A) 16 B) 13 C) 14 D) 15 E) 17


    2. Relevant equations
    asin(theta)=mlambda


    3. The attempt at a solution
    Honestly I have no idea how to do this. Using the data given, I can only set up one equation with 2 unknowns, which is impossible to solve. On top of that I am unable to deduce a relationship between maxima and minima in a single-slit diffraction. I hope someone would throw me some light on this, thanks!
     
  2. jcsd
  3. Feb 25, 2012 #2

    PeterO

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    Homework Helper

    There is a formula governing the angle to each minimum which is something like

    sin θ = (n) λ/W

    where is the wavelength of light, and W is the width of the slit, and n is a count of the number of the minimum - so would be 6 here; for the 6th minimum.

    Your formula looks like a transformation of that to W sin θ = (n)λ

    Anyhow, once you have established the value of λ/W, you can work out the maximum value of (n) - since the sinθ has a maximum value of 1.
     
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