Abstract: In this talk we demonstrate how to approximate $1d$ Schrodinger operators with a $\delta$-potential by the Neumann Laplacian on a narrow waveguide-like domain. Namely, we consider the domain consisting of a straight narrow strip and a small protuberance with "room-and-passage" geometry. We show that in the limit when perpendicular size of the strip tends to zero and the protuberance is appropriated scaled the Neumann Laplacian on this domain converges in (a kind of) norm resolvent sense to the above singular Schrodinger operator. The estimates on the rate of this convergence are also derived. As an application we proof the Hausdorff convergence of spectra. This is a joint work with Olaf Post (Trier).