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Photons Moving Through a Single Slit (Uncertainty)

  1. Apr 18, 2013 #1
    1. The problem statement, all variables and given/known data
    The diagram is attached. Photons are being beamed with momentum [itex]\rho_{0}[/itex] and mass [itex]m[/itex] at a slit of width A

    Estimate the uncertainty [itex]\Delta p_{y}[/itex] emerging from A
    Sketch spot size at B as a function of slit width using the uncertainty principle
    Determine minimum spot size expected at B as a function of L and the deBroigle wavelegth [itex]\lambda_{0}[/itex]


    2. Relevant equations
    [itex]\Delta p_{y}\Delta_{y}=\frac{\hbar}{2}[/itex]
    [itex]\lambda=\frac{h}{p}[/itex]


    3. The attempt at a solution
    My attempt for part one is shown in image two. I achieved an answer of [itex]\frac{h}{\Delta y}[/itex]. [itex]\Delta y[/itex] is represented by [itex]a[/itex] in image one
    Part two wants spot size as a function of width of slit - I found it as a function instead of L but I believe the sketch is relatively accurate. I'm not sure how to give it in the form it wants
    Part three just throws me for a loop and I really don't have any idea

    Thank you as always!
     

    Attached Files:

  2. jcsd
  3. Apr 18, 2013 #2

    mfb

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    Staff: Mentor

    For part 2, don't neglect the width of the slit - if the slit is very large, this is relevant. As a practical example, you do not expect a beam spot of some micrometers if the slit has a width of one meter (like a window). In addition, I think you should express theta in terms of the width of the slit and the wavelength.

    If you fix that part, part 3 will make sense.
     
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