What is Polonius' plan in II,ii?
In Act II scene 2, Polonius is convinced that Hamlet's love of Ophelia is the cause of his distress. He knows that he has told his daughter to return his gifts and to stay away from him. He produces notes from Hamlet to his daughter to Gertrude and Claudius. Gertrude is hopes Ophelia is the cause (she wouldn't want it to be her hasty marriage after her husband's death).
Polonius, to prove his hypothesis, proposes that Claudius and Gertrude arrange themselves so that they can eavesdrop on a conversation between Ophelia and Hamlet. Polonius believes that once they see his interactions with her, they too will be convinced Hamlet's unrequited love of Ophelia is the cause.
POLONIUS: At such a time I'll loose my daughter to him.
Be you and I behind an arras then;(175)
Mark the encounter. If he love her not,
And he not from his reason fall'n thereon
Let me be no assistant for a state,
But keep a farm and carters.