What do the Puritan magistrates hope to accomplish with this punishment? (The punishment for Hester Prynne of Adultery)

Due to the fact that there is no proof that Hester's husband is still alive, and therefore she could technically be a widow, coupled with her young, beautiful appearance, the magistrates feel that "branding" her with the scarlet letter is adequate punishment. Hester will be reminded daily of her sin, as she is never to take of the letter in public. It also serves as a public notice, everyone she comes into contact with, will see her sin. Knowing she will be humiliated every day(or so they think) seems just punishment.