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Double Slit, different wavelengths change in X

  1. May 28, 2009 #1
    1. The problem statement, all variables and given/known data

    Two slits are 0.158mm apart. A mixture of red light (wavelength = 665nm) and yellow-green light (wavelength = 565nm) fall onto the slits. A screen is located 2.2m away. Find the distance between the third-order red fringe and the third-order yellow-green fringe.


    2. Relevant equations

    Since they ask for colored fringes, and not dark ones, it must be constructive interference.

    x/L = (m*λ/ d)

    x = 0.000158m
    L = 2.2m
    m = 3 (third order fringe)

    λ of red = 6.65E-7m
    λ of yellow-green = 5.65E-7m

    3. The attempt at a solution

    I did the equation twice, once for each wavelength.

    For red I got x as 2.7E-2m, and for yellow-green i got x as 2.36E-2m.

    The difference between these 2 values is 0.0034mm or 3.4mm.

    The answer however, is supposed to be 28mm. . .


    How was I supposed to do this?
     
  2. jcsd
  3. May 28, 2009 #2
    Here is another question, similar concept.

    Light of wavelengths 480nm and 632nm passes through two slits 0.52mm apart. How far apart are the second-order fringes on a screen 1.6m away?
     
  4. May 28, 2009 #3

    Redbelly98

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    x for red is slightly off. Can you express the answer with one more decimal place of accuracy? I.e., 2.7_ e-2 m.

    You're already in the right ballpark. I disagree with the 28 mm answer, who or what told you that is the answer?
     
  5. May 28, 2009 #4
    The textbook says that in the back.

    Also, the second question I posted has an answer of 7cm, according to the book.
     
  6. May 28, 2009 #5
    I am going to bump this thread, hopefully my question will be answered before my test tomorrow.
     
  7. May 29, 2009 #6

    Redbelly98

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    You have the correct approach, but you had some round-off error in the first problem.

    Both book answers are wrong. For the 1st question, 28 mm is the displacement of the 665 nm, 3rd-order fringe, not the separation of the two colored fringes.

    Not sure where they got 7 cm for the 2nd problem.

    Good luck on the test.
     
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