The use of software controlled passive Reconfigurable Intelligent Surface (RIS) in wireless communications has attracted many researchers in recent years. RIS has a certain degree of control over the scattering and reflection characteristics of the electromagnetic waves, compared to the conventional communications in which the received signal is degraded due to the uncontrollable scattering of the transmitted signal and its interaction with the objects in propagating medium. Further, in RIS assisted communications, the phases of the multiple incoming signals can be controlled to enable constructive addition of multiple signals from different channel paths to improve Signal to Noise Ratio (SNR). On the other hand, Non-Orthogonal Multiple Access (NOMA) provides massive connectivity and low latency. The power domain variant NOMA uses superposition coded symbols with different powers for different user symbols. In this paper, a novel RIS assisted downlink NOMA system is proposed by combining the merits of both RIS and NOMA to improve the reliability of the system. Analytical expressions are derived for the Bit Error Rate (BER) performance of the proposed RIS assisted power domain NOMA system. The BER performance of the proposed system is analyzed using the numerical simulation results. It is observed that the proposed system has better performance than the conventional NOMA system.