# Question about transmission of paraboloidal light waves in bi-convex lens

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.