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Homework Help: Fraunhofer intensity pattern

  1. Mar 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Derive the equation describing the Fraunhofer intensity pattern from a single
    slit of width b centered at the origin. Then show that the same intensity pattern is obtained for a slit that is not centred at the origin (i.e assume the slit edges are at x = a - b/2 and x = a + b/2). Is this physically reasonable? Discuss briefly.

    3. The attempt at a solution
    Suppose the coordinates of P are (X, Y, Z), and the coordinates of a point Q on the aperture are (x, y,z) where z = 0.
    If the distance QP is d then.
    Now chuck that in
    to obtain

    now, how would i attempt the second part of the question?
    would my d² = (X - (x+a))² + (Y-y)² + (Z-z)²
    and L² = (x-a)² + Y² + Z² ??

    meaning d² = L²[1 + (2ax + x² + y²)/L² - (2xX+2yY)/L²]
    so d ~= L[1 - (2xX + 2yY)/L²] like earlier?

    or am i doing it completely wrong?

    Thank you all for your input.
  2. jcsd
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