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We present theory of dc Josephson effect in contacts between Fe-based andspin-singlet $s$-wave superconductors. The method is based on the calculationof temperature Green's function in the junction within the tight-binding model.We calculate the phase dependencies of the Josephson current for differentorientations of the junction relative to the crystallographic axes of Fe-basedsuperconductor. Further, we consider the dependence of the Josephson current onthe thickness of an insulating layer and on temperature. Experimental data forPbIn/Ba$_{1-x}$K$_{x}$(FeAs)$_2$ point-contact Josephson junctions areconsistent with theoretical predictions for $s_{\pm}$ symmetry of an orderparameter in this material. The proposed method can be further applied tocalculations of the dc Josephson current in contacts with other newunconventional multiorbital superconductors, such as $Sr_2RuO_4$ andsuperconducting topological insulator $Cu_xBi_2Se_3$.

The Josephson current in Fe-based superconducting junctions: theory and experiment