Why a Resignation Letter? In these digital times, why should we submit a resignation letter, anyway? A paper trail does seem old_fashioned, but in this case, it's a best practice. It makes your intentions clear, as well as the conditions. You're removing any ambiguity about the end of your time there.
Acceptance With Displeasure. It's possible that your boss won't take immediate action like the reaction above__but will make it clear that he or she isn't exactly happy about your resignation. Maybe, for example, she'll mutter a curt, "Thank you for letting me know," followed by two weeks of obvious displeasure or denial that you're leaving__through gruff comments ("You know, you're really leaving us in the lurch") or a refusal to interact with you more than absolutely necessary.