Gustavo, Contributor posted:Without "at," "look" can have, apart from the physical meaning, a more mental one, similar to "realize."
"Look who's here" does not mean "Look at the person who's here," but "See who's arrived." The same applies to "Look what you've done," being similar to "See what you've done."
In "Look where you're going," "look" is more like "pay attention to."
I agree with Gustavo's observations here. One way to see that the version without the preposition is special is to see that it can only be used in the imperative. The following sentences are ungrammatical or highly nonstandard:
*If you look what you've done, you'll see you've made a mess.
*He looked what he did.
*She will look where she is going.
Each of those examples would be grammatical if "at" were added after "look(ed)," just as related imperative sentences ("Look what you've done," "Look where she is going") are grammatical with or without the preposition.
As Gustavo says, the preposition-less "look" construction (in the imperative) conveys special meanings, not present with the preposition. It often indicates surprise or hortatory meaning, or is purely rhetorical (e.g., "Look who's talking").