Suppose I have an adjunction $\mathcal{C}\overset{R}{\underset{I}\leftrightarrows}\mathcal{D}$, where $R\dashv I$, and $I$ is full and faithful. Now let $F:\mathcal{A}\rightarrow\mathcal{C}$ be any diagram, I then want to prove that if $IF$ has a limit in $\mathcal{D}$, then $F$ has a limit in $\mathcal{C}$.
I suppose I have to start by choosing an arbitrary limit of $IF$ in $\mathcal{D}$ and from that construct a limit of $F$ in $\mathcal{C}$. However, I am not really sure where to go from there.
Any help would be appriciated.