1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to find the center of a paraboloidal wave

  1. Mar 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that the paraboloidal wave centered at the point z1 is converted by a lens of focal length f into a paraboloidal wave centered about z2 where 1/z1+1/z2 =1/f


    2. Relevant equations
    Equation of paraboloidal wave and transmittance through a thin lens.


    3. The attempt at a solution
    I multiplied the paraboloidal wave and the transmittance through the thin lens and I got
    U(r)=Aexp(-jnkd)exp[jk([itex]\frac{x^2+y^2}{2f}[/itex]-z)]
    But how do I continue to show that this paraboloidal wave is centered at f?
     
  2. jcsd
  3. Mar 12, 2012 #2
    It looks like your lens is located at z=0; the parabolic wave centered at z is basically a spherical wave centered at z1 where z1 is faraway from the lens, i.e., z1^2>>x^2+y^2, so that the wavefront at the lens ~ exp[ik(x^2+y^2)/(2z1)]. (Taylor expansion of the phase ikR where R^2=x^2+y^2+z^2) Now multiply by the lens phase exp[ik(x^2+y^2)/(2f)] and figure out where the center is. Double check the sign conventions since I haven't done these for years.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook