I know intransitive verbs are action verbs that have no receiver (or object), such as "She smiled." In the following sentence, "arrived" is the intransitive verb: "Huffing and puffing, we arrived at the classroom door with only seven seconds to spare."
I'm having trouble with this because I can see "door" as the object. "We arrived at the door."
Another example that puzzles me is "My brother laughed at the joke." The intransitive verb is "laughed." I don't understand why "joke" is not the object because that's what was laughed at.
Please help clear up my reasoning.