What is the narrator's reaction to the police officers in "The Tell-Tale Heart"?

The narrator of The Tell-Tale Heart has committed murder and has hidden his victim underneath the flooring in his chamber. He seems to think he has gotten away with murder and has finally rid himself of the "vulture eye" that plagued him incessantly.

As he is settling in to the comfort of getting away with the crime, police show up, saying that "a shriek had been heard by a neighbour during the night." The narrator is at first calm, saying he has nothing to fear, and concocts a story about how he himself had screamed in the midst of a nightmare.

The narrator then asks the police to search the house and finishes by bringing out chairs for them to sit and relax. It is at this point that his conscious begins to weigh on him. Suddenly a ringing is heard, faint at first, and then louder. The narrator begins to panic, talking quickly and loudly and then pacing the room.

Then police do not hear the noise, as evidenced by the lines "It grew louder—louder—louder! And still the men chatted pleasantly, and smiled." Reason would conclude that police who came suspecting foul play would be quick to investigate any suspicious noises coming from the this house. But the narrator has lost reason. He works himself into a frenzy, convinced that the men indeed hear the noise (which is just a manifestation of guilt for the crime he has committed) and finally screams his admission of the crime in the closing lines.

In "The Tell-Tale Heart," how does the police visit affect the narrator?

When the police first arrive at the narrator's apartment, he is feeling supremely confident; he is so confident, in fact, that he brings in some chairs for the officers and places them directly over the spot where he's buried the old man's body.  He says, "I was singularly at ease."  However, the longer the officers sit there, the more nervous the narrator gets.  He hears a ringing in his ears that increases in volume until he begins to think that it is not inside his own head but outside.  He talks louder to cover it up.  He describes it as "a low, dull, quick sound -- much such a sound as a watch makes when enveloped in cotton," and this is precisely the way he described the sound he thought was the old man's heartbeat, just before the narrator killed him.  However, the old man is dead, and so the sound must be the narrator's own heartbeat, speeding up from his adrenaline.  The narrator grows suspicious that the officers suspect him of murder, and he eventually confesses.  Although he is calm at first, the presence of the police makes him so nervous that he guiltily confesses, having misinterpreted the sound of his own rapid heartbeat as well as the behavior of the officers who "chatted pleasantly, and smiled." 

Why is the "Tell-Tale Heart" narrator light-hearted when meeting the policeman?

The following excerpt from Edgar Allan Poe's short story "The Tell-Tale Heart" explain why the narrator has "a light heart" when he opens the front door.

I then took up three planks from the flooring of the chamber, and deposited all between the scantlings. I then replaced the boards so cleverly, so cunningly, that no human eye—not even his—could have detected any thing wrong. There was nothing to wash out—no stain of any kind—no blood-spot whatever. I had been too wary for that. A tub had caught all—ha! ha!

When I had made an end of these labors, it was four o'clock—still dark as midnight. As the bell sounded the hour, there came a knocking at the street door. I went down to open it with a light heart,—for what had I now to fear?

The murderer has taken great pains to hide the body. He would have been successful in committing the perfect crime if he had not given himself away. In another short story, "The Imp of the Perverse," Poe identifies what he calls a natural human tendency to do exactly the wrong thing just out of perversity. The narrator of "The Tell-Tale Heart" allows his imagination to get away from him. He begins to think the policemen are playing mind games with him, because he can hear the heart beating so loudly and they act as if they hear nothing unusual. Finally the narrator breaks down and confesses. 

Poe probably included the statement, "I went down to open it with a light heart," because he wanted to stress that the narrator was not in the least conscious of his heart beating--but evidently what he was hearing during his interview with the policemen could only have been his own heart. He was much more anxious than he admitted to himself. Our bodies often give us away when we are trying out best to appear calm and poised. There were no such things as lie detectors in Poe's day, but a modern lie detector would have easily exposed the guilt of the nervous narrator of "The Tell-Tale Heart."

Why does the narrator in "The Tell-Tale Heart" have a "light heart"?

Toward the end of the story, after the narrator has killed, dismembered, and hidden the body of the old man in order to rid himself of the "vulture eye," he hears a knocking at his door. Though it is only four o'clock in the morning, the narrator says, "I went down to open it with a light heart, -- for what had I now to fear?" The implication, then, is that the narrator has a light heart because he has no fear of being caught. He has already taken "wise precautions" to be sure that the body will not be discovered and that no blood was left to stain the floors (he'd thought to use a tub to catch it all when he took the old man's body apart). He feels that he has no reason to fear anyone who might be knocking at his door at this hour because he has been so careful, so meticulous, and that he has committed the perfect crime.