Ferdinand asks Bosola how the Duchess is holding up in her imprisonment.
Bosola's kind of impressed, actually. She's understandably sad, but he finds her calm and majestic acceptance of her situation to be really noble.
As directed by Ferdinand, Bosola tells the Duchess that Ferdinand regrets saying he'd never see her again, and wants to make up with her in the dead of night.
Bosola tells her that Ferdinand wants it to be totally dark when he reconciles with her, so all of the torches are removed.
Ferdinand comes in, and instead of reconciling the first thing he does is make a crack about the Duchess's supposedly illegitimate children.
He says he's come to make peace with her, though, and tells her that he's holding out his hand for her to kiss.
Okay, brace yourselves, because this is gross: it's actually the severed hand of a dead man.
The Duchess, not being able to see a thing, kisses the hand, and remarks that Ferdinand must be coming down with something for his hand to be so cold.
Ferdinand leaves, and the lights are brought back in, suddenly, and the Duchess recoils, realizing what Ferdinand's done.
That's not all, though; as the lights come on Bosola presents the Duchess with the dead bodies of Antonio and her children, and tells her that the dead hand she just kissed was Antonio's.
You thought the Duchess was in a glum mood before? She goes from her whole "noble acceptance" thing to professing that, at this point, she has absolutely no wish to live.
She and Bosola go back and forth for a little while, with the main takeaway being that the Duchess is really, really done with life by now. She just wants to die, sooner rather than later, if Bosola can manage it.
She and Cariola leave, and Ferdinand, who's been watching the entire time, is pleased as punch with the results his spectacle has wrought.
Spectacle? Yep—apparently, those bodies we just saw were made of wax; Ferdinand planned the entire thing to psychologically torture the Duchess (in his own words, to "bring her to despair" (4.1.113)). Hint: if you've been wondering if Ferdinand is a Real Bad Guy, this should tip you off.
At this point, even Bosola's having some issues with what's going down. He asks Ferdinand to stop messing with the Duchess, and to give her some recourse to mourn for her supposedly dead family.
Ferdinand could care less about Bosola's newly discovered sense of pity, and tells Bosola he's going to need him to do some more stuff for him.
First up: Bosola's got to round up a posse of madmen from the local insane asylum and bring them in front of the Duchess.
Bosola's not pleased, but Ferdinand closes the scene by telling him that he's going to have him go after Antonio as well.