On topology over R[x]

Question

Take $R$ a topological ring. Suppose for example that $R$ is equipped with the $I$-adic topology for a certain ideal $I$. Take $R[x]$ the ring of polynomials with coefficients in $R$ and variable $x$. I was looking for a natural topology on $R[x]$ induced by the topology on $R$. I was thinking for example to take the set $$ R[x]I^n$$ for $n \in \mathbb{N}$ as fundamental system of neighborhood of the origin. The idea is take the ideal generated by $I^n$. Is it right? If yes, is this natural? If not, is there another one?