  Let $q$ be a power of a prime $p$. In this paper, we study reversible cyclic
codes of arbitrary length over the ring $ R = \mathbb{F}_q + u \mathbb{F}_q$,
where $u^2=0 mod q$. First, we find a unique set of generators for cyclic codes
over $R$, followed by a classification of reversible cyclic codes with respect
to their generators. Also, under certain conditions, it is shown that dual of
reversible cyclic code is reversible over $\mathbb{Z}_2+u\mathbb{Z}_2$.
Further, to show the importance of these results, some examples of reversible
cyclic codes are provided.
