Island logicians and a public eye-colour remark

Fifty perfect logicians live on an island, each with blue or brown eyes; suppose $k\ge1$ of them have blue eyes. Nobody may learn their own eye colour directly, and anyone who deduces that their own eyes are blue must leave that night. Everyone sees everyone else. What happens while nothing is said, and what happens after a visitor announces to all of them that at least one islander has blue eyes?

Before: nothing. After: all $k$ blue-eyed islanders leave together on night $k$. For $k\ge2$ everyone already knows someone has blue eyes, but it is not common knowledge. After the announcement, induction applies: a blue-eyed person sees $k-1$ others, expects them to leave on night $k-1$, and when they do not, concludes they are also blue.