In Chapter 1, when Alice first goes through the looking glass, she realizes that the living chess pieces cannot see or hear her. This leads to a sense of dramatic irony as Alice picks up the White King with an "invisible hand":
She said afterwards that she had never seen in all her life such a face as the King made, when he found himself held in the air by an invisible hand, and being dusted: he was far too much astonished to cry out, but his eyes and his mouth went on getting larger and larger, and rounder and rounder, till her hand shook so with laughing that she nearly let him drop upon the floor.
Whereas Alice and the reader both know exactly what is going on, the King does not understand how he is being held in the air and dusted off. His astonishment distorts his face into such an outlandish expression that Alice is moved to shaking laughter. This shaking must be somewhat horrifying to the King, which makes it all the more funny to Alice.
Alice's laughter at the idea that she is an "invisible hand" manipulating the world the chess pieces inhabit suggests that she finds it delightfully silly that she, a little girl, can have such a dramatic effect on the King. Alice goes through her life largely being ignored by adults, so to suddenly be this powerful is new and a bit absurd to her.
In Chapter 5, Alice finds herself rowing through water with the Sheep. The Sheep uses a sarcastic idiom, "complimenting" Alice on "catching a crab," which leads to dramatic irony:
“That was a nice crab you caught!” she remarked, as Alice got back into her place, very much relieved to find herself still in the boat.
“Was it? I didn’t see it,” said Alice, peeping cautiously over the side of the boat into the dark water. “I wish it hadn’t let go—I should so like a little crab to take home with me!” But the Sheep only laughed scornfully, and went on with her knitting.
What Alice doesn't realize is that "catching a crab" is a rowing term that refers to messing up a stroke of the oar by keeping it underwater too long. This is exactly what Alice has just done: she lost control of the oar and could not pull it out of the water. It ended up hitting her in the chin and knocking her over in the boat. Alice believes that the Sheep is telling her she caught a literal crustacean. Because she does not understand the rowing idiom, she fails to understand that the Sheep is making fun of her bad rowing form.
On the one hand, Alice appears naive because of her misunderstanding. A more savvy and socially graceful person would understand that they were the butt of the Sheep's joke. At the same time, Alice has been thrown into a ridiculous situation without any preparation. The Sheep's expectation that she know how to row and that she be familiar with the idiomatic language of rowing is just as laughable as Alice's naivety. This entire situation represents the process of growing up and making one's way in the adult world. Life, Carroll suggests, is a series of ridiculous and unexpected situations in which the world has ridiculous expectations of our competence and know-how.
