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Homework Help: Double Slit Diffraction fringes

  1. Jan 5, 2010 #1
    1. The problem statement, all variables and given/known data

    A parallel beam of mono-chromatic light (500nm) is incident on 2 long narrow slits: slit width is 0.1mm and the distance between slit centres is 0.3mm.

    a) How many bright fringes cover the central diffraction maximum?

    2. Relevant equations

    Condition for constructive interference:
    [tex]\Delta = 2d.cos\theta = 2m(\lambda\div2)[/tex]

    Reduces to:

    [tex]2d=m\lambda[/tex] as [tex] cos\theta=1[/tex] ?


    3. The attempt at a solution

    I get 1200 once I convert both[tex] d [/tex]and [tex]\lambda[/tex] into metres. Is this the right thing to do? I'm not sure this is the amount that cover the central maximum, what does this bit mean?

    - - - Part b)

    1. The problem statement, all variables and given/known data

    Part b) Calculate the angle corresponding to the first diffraction minima

    2. Relevant equations

    [tex]sin\theta= ((2m-1)\lambda)\div2)\div d [/tex]

    3. The attempt at a solution

    Taking m as 1 because it is the first diffraction minima

    Reduces to:

    [tex]\theta = arcsin[ (5\times10^{-7}) / (6\times10^{-4}) ][/tex]

    I get [tex]\theta[/tex] = 0.048 degrees

    is this correct?

    There is part c) but haven't attempted it yet, overall the whole question is allocated 14 marks.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 7, 2010 #2
    we need to find the range of the diffraction central bright band first by using 1st minima condition a sin theta= lambda(m=1 for first minima) and a=slit width
    then we determine the condition for interferance maxima (in the same angular range)by using d sin theta= m lambda where d= distance between two slits,m= 1,2,3...... for the right half.
    dividing these 2 equations , we will get m which will indicate the number of interferance bright bands within the first diffraction band ON ONE SIDE ONLY.
    remember that we still need to add the left half and the central bright interferance band.
    in general , the number of bright bands will be 2m+1.
     
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