In a typical many-many arrangement like this...
Movies Actors Movies_Actors ------ ------ ------------- movie_ID actor_ID FK_movie_ID
In SQL Server, a composite index can be used for a single field search for the first column only. That means you should have an additional, one field index on FK_actor_id if there will be searches on that field without FK_Movie_id in the same query.
FK_actor_id
FK_Movie_id