Let $D$ be a nonprincipal $\kappa$-complete ultrafilter on $\kappa$. The following are equivalent:
(i) $D$ in normal
(ii) In the ultrapower $Ult_D(V)$, $\kappa=[d]$ where $d$ is the diagonal function.
My question is: how do we know what is $\kappa$ in $Ult_D(V)$?