Symbol Analysis
A mirror can only show us what is already there. In lines 11-12, Demeter says there won't be any curses on Hades, because it's a curse enough for him to have to face the reflection of his soul in the mirror. While you can't exactly see your soul, Demeter knows that, when Hades sees himself, he'll be tormented by what he's done, and that's punishment enough. A mirror therefore serves as a symbol of having to face our mistakes and the resulting mess they cause.