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Homework Help: Parabolic Waves

  1. Mar 3, 2010 #1
    1. The problem statement, all variables and given/known data

    Show that a paraboloidal wave centered at the point P1 (x,y, z1) is converted by a biconvex lens of focal length f into a paraboloidal wave centered about P2 where 1/z1 + 1/z2 = 1/f.

    2. Relevant equations

    3. The attempt at a solution
    if U1(r) = A0/(z-z1) exp(-jk(z-z1)) exp(-jk(x^2 + y^2)/(2(z-z1))

    Now I also know that the transmittance thru a thin lens is given by
    t(x,y) = h_0 exp( jk (x^2+y^2)/2f) where h_0 = exp(-jnk*thickness)

    So I would think that U2(r) = t(x,y) * U1(r)
    Unfortunately, if I multiply the two together I don't really get anything that I would find useful.

    My question is - how do I get z1 and z2 so that I can show that I am satisfying the imaging equation?
  2. jcsd
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