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The question is as follows:

Show that a paraboloidal wave centered at $z_1$ is converted by a lens of focal length $f$ into a paraboloidal wave centered about $z_2$, where $\frac1{z1} + \frac1{z2} = \frac 1f$, the imaging equation.

I have tried using the definition of complex amplitude transmittance for this kind of lens, so I can multiply it by a paraboloidal wave under the Fresnel approximation, with the idea of obtaining a new paraboloidal wave in the other side, but I'm not sure how to get the center of the wave at the right of the lens.


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