The motivation of this paper is to study the formation of a sheath in plasma contaminated with additional negative ions. Sheath formation has been analysed through the solution of the Sagdeev potential equation derived in a plasma by using the pseudopotential method. Because of the negative ions, it has been shown that the sheath formation, in contrast to that in a simple plasma, faces difficulties. A potential barrier from which modes are reflected is introduced and the potential variation beyond it is complex which, in turn, shows new findings. It is also revealed that the potential variation should be estimated in the plasma sheath in the presence of low as well as high negative-ion concentrations. The levitation of a dust grain into the sheath and its characteristic behaviour have also been investigated. Furthermore, the dust size in the ideal plasma sheath along with the causes of formation of the dust atmosphere have been studied.