= Solution
An ideal focusing lens maps propagation angle to position in its back <focal plane>, with $z\simeq f\theta$ for paraxial <light rays>. The two-slit relative <phase> remains $2\pi s\sin\theta/\lambda$, so the focal-plane interference pattern has the same form with propagation distance replaced by <focal length>:
$$
\boxed{I_f(z)=I_{\max,f}\cos^2\left(\frac{\pi sz}{\lambda f}\right),\qquad\Delta z_f=\frac{\lambda f}{s}}.
$$
The new peak intensity $I_{\max,f}$ accounts for focusing and need not equal the earlier screen peak. The lens forms the angular Fraunhofer pattern at a finite focal-plane distance, so a long free propagation distance is no longer needed to obtain that angular pattern. The displayed position formula assumes the same narrow-slit and paraxial approximations.
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