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Young's Double-slit Experiment

  1. Apr 8, 2015 #1
    1. The problem statement, all variables and given/known data
    In a KhanAcademy video, light of wavelength 700nm shines through a double-slit whose holes are spaced 1300nm
    apart. If a screen is placed 3m away from the double-slit, what will be the distance from the central bright spot on the screen to the next bright spot?
    https://www.khanacademy.org/test-pr...agnetic /v/youngs-double-slit-problem-solving
    2. Relevant equations
    per KhanAcademy: d*sinθ = m*λ

    per what I think: Y = R*m*λ / d

    d = distance between the 2 slits
    m = whether it's the 1st, 2nd, 3rd bright band
    Y = distance from central bright
    R = distance from double-slit to screen

    3. The attempt at a solution
    per KhanAcademy and using d*sinθ = m*λ

    d*sinθ = m*λ
    1300nm*sinθ = 1*700nm
    sinθ = 700nm / 1300nm
    θ = 32.6°

    then use this to find Y
    tanθ = Y / X
    Y = tanθ*X
    Y= tan(32.6°)*3m
    Y= 0.64*3
    Y= 1.92m


    per what I think and using Y = R*m*λ / d

    Y = R*m*λ / d
    Y = 3m*1*700nm / 1300nm
    Y = 1.62m

    (nanometers were converted to meters. I just did it this way to save space when typing it here)

    My Question: Which equation should I use? Why am I getting different answers?
     
  2. jcsd
  3. Apr 8, 2015 #2

    andrevdh

    User Avatar
    Homework Helper

    The second formula is the small angle approximation:
    then sin(θ) ≅ θ in radians and θ ≅ Y/R
     
    Last edited: Apr 8, 2015
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