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Homework Help: Double slit and colored wavelength

  1. Nov 17, 2008 #1
    1. The problem statement, all variables and given/known data

    White light spans the wavelength range be-
    tween about 400 nm and 700 nm.
    If white light passes through two slits
    0.656 mm apart and falls on a screen 1.7 m
    from the slits, what is the distance between
    the first-order violet and the first-order red
    fringes?
    Answer in units of mm.

    2. Relevant equations

    sin(theta) = m*lambda / d

    x = L*tan(theta)

    3. The attempt at a solution

    I used the first equation to solve for theta for both red light (lambda = 700 nm) which gave theta = .061139 and violet light (lambda = 400 nm) which gave theta = .034936. I used the second equation to plug in theta and solve for x for each of them. I then subtracted the x value of violet from the x value for red and converted to mm. My final answer was 6.781 mm.
     
  2. jcsd
  3. Nov 17, 2008 #2

    alphysicist

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    Homework Helper

    Hi Kris1120,

    Can you show the steps in how you got 6.781mm? That does not look right to me.
     
  4. Nov 17, 2008 #3
    theta(red) = inverse sin (700 e-9 m / .656 e-3m) = .061139 degrees
    x=tan(.061139)*1.7m = .007818

    theta(violet)= inverse sin (400 e-9 m / .656 e-3 m) = .034936 degrees
    x=tan(.034936)*1.7m = .001037

    .007818 - .001037 = .006781 m = 6.781 mm
     
  5. Nov 17, 2008 #4

    alphysicist

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    Homework Helper

    I'm getting 0.001814 for this. Would you check it again?
     
  6. Nov 17, 2008 #5
    yes! I hate when I do silly things like that! Thank you for correcting me!
     
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