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?