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Diffraction maxima

  1. Apr 12, 2015 #1
    1. The problem statement, all variables and given/known data
    A single slit diffracts laser light of wavelength 650 nm onto a screen 2.00 m away. The distance between the two first-order maxima on either side of the central peak is 2.05 mm. How wide is the slit?

    2. Relevant equations
    a=width of slit
    y=distance from central max to specific spot
    L=distance of screen from the slit
    λ=wavelength of light
    sinΘ≈Θ=y/L
    minima occurs at: a*sinΘ=mλ
    (found on internet) approximation of maxima occurs at: a*sinΘ=(m+.5)λ

    3. The attempt at a solution
    L=2m
    λ=650*10^-9m
    each maxima is the same distance from the central maxima so if the distance between the 2 first order maxima is .00205m then
    y=.001025m

    a*(.001025/2)=(1.5)(650*10^-9)
    I found answer to be 0.001902m (wrong)

    just in case I decided to try and see using the minima formula a*(.001025/2)=(650*10^-9)
    answer :0.001268m (wrong)

    any assistance would be great.
     
  2. jcsd
  3. Apr 12, 2015 #2
    The maximum of the sinc function is not at m+0.5 . It's close, but not exactly.
     
  4. Apr 12, 2015 #3
    what equation should I use then?
     
  5. Apr 12, 2015 #4

    BvU

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    You differentiate the intensity expression...
     
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