In The Lord of the Rings we can see that when Frodo wears the ring he becomes invisible. Same is the case for Bilbo. Also in entire Hobbit movie Bilbo became invisible whenever he wore the ring. But in the beginning of LOTR we can see Sauron wearing that ring and be still visible to all the elves and men.
Why is Sauron still visible after wearing that ring? Is there any reference/reason of that mentioned in the book which is not mentioned in the movie?