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The design of tips is of outstanding importance to obtain maximal efficiency in scanning near-field microscopy. As a support towards this optimization, this work presents the computation of the electromagnetic field penetrating into two-dimensional tips. The investigated geometries consist of elongated two-dimensional dielectric slabs (glass) terminated by pointed tips. Distributions of the electric field amplitude inside and outside two-dimensional models of tips are computed and from those solutions, far-field differential cross-sections are obtained.