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Problem: Plastic Covering One Slit in Double Slit Experiment

  1. Feb 21, 2007 #1
    1. The problem statement, all variables and given/known data

    A very thin sheet of plastic (n = 1.45) covers one slit of a double-slit apparatus illuminated by 570 nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?

    2. Relevant equations

    Constructive Interference:
    d *sin(theta)=m*lamda

    Destructive Interference:
    d *sin(theta)=(m+1/2)*lamda

    lamda_n=lamda/n

    3. The attempt at a solution

    So I'm a TA for a physics class and I'm a little stumped on explaining this problem. The solutions manual says that the phase shift must be an odd multiple of one half. I got that. However, it then proceeds to write down this equation:

    N= t/lamda_n - t/lamda = 1/2

    where t is the thickness of the plastic. Any idea how they got this relation? I would really appreciate an explanation.

    Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 22, 2007 #2
    t = N lambda right.
    What does N represent?

    number of what??
     
  4. Feb 22, 2007 #3
    N equals the phase shift I believe, i.e. 1/2, I'm not exactly sure though
     
  5. Feb 22, 2007 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Well, that expression is the phase difference between the two beams that converge at the center, expressed in terms of wavelengths. (lambda is the wavelength of light in air (or vacuum), where n = 1; lambda_n is the wavelength of light in the plastic, which is lambda/n.) The physical path lengths are the same; the only difference is that one passes through a thickness of plastic (phase shift = t/lamda_n) while the other beam passes through the same thickness of air (phase shift = t/lambda).
     
  6. Feb 22, 2007 #5
    Okay, I get that. But, why is the phase shift = t/lamda? I just don't see that direct correspondence.
     
  7. Feb 22, 2007 #6

    Doc Al

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    Staff: Mentor

    If a lightwave travels from points A to B, do you not agree that the phase of the light at B differs from the phase it had at A? And that the phase shift in moving from A to B can be expressed by the number of wavelengths contained in the distance between A and B? For example, if the distance A-to-B is 1/2 lambda, when the light reaches B it is exactly 180 degrees out of phase compared to its phase when at A?

    Let me know if this makes sense so far.
     
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