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Homework Help: The wave nature of light

  1. Jun 1, 2003 #1

    Dx

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    Hello,

    In a double slit experiment the slit seperation is 2.0mm and two wavelengths 750nm and 900nm illuminate the slits. A screen placed 2m from the slits. at what distance from the central maximum on the screen will a bright fringe from one pattern first conincide with a bright fringe from the other?

    my formula?
    d = sin[the] / (m [lamb]

    Is my answer correct 6.0mm

    Thanks!
    Dx :wink:
     
  2. jcsd
  3. Jun 2, 2003 #2
    d=2E-3meters, λ1=750E-9m, λ2=900E-9m, D=2m (D being adjacent leg of right triangle, y1 and y2 being opposite legs, θ being angle between slits.)
    y1 = mλ1D / d = (1)(750E-9m)(2m)/(2E-3)m = 7.5E-4m
    y2 = nλ2D / d = (1)(900E-9m)(2m)/(2E-3)m = 9.0E-4m
    were n=m=1, WHICH THEY're not.
    You can't solve it trigonometrically.
    In order to solve it, you need to equate
    y1=y2=mλ1D/d = nλ2D/d
    Then you just solve for m:
    m = (λ2/λ1)n = 1.2n
    The first instance of this relation being true is if m=6 and n=5
    Now you just solve y1 and y2 above to get...

    y1=y2=0.0045m
     
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