Merriam-Webster defines a handkerchief as:
1 : a small usually square piece of cloth used for usually personal purposes (as blowing the nose) or as a clothing accessory
Othelle see’s the handkerchief he gave to Desdemona as much more than a simple clothing accessory. He sees it as defining of their love. In telling her the story of the handkerchief and it’s magic powers, he seems to be implying that if she were to lose it, he would stop loving her as the Egyptian charmer warned his mother that his father would stop loving her if she lost it. He is of course trying to scare her because he believes her to be cheating on him with Cassio.
The fact that he is threatening her here is only reinforced later when he says that his father gave the handkerchief to his mother.
1 year ago