What is the definition of an object of a preposition?
The object of a preposition is the word or phrase that the
preposition immediately refers to.
For example, in the sentence:
Mary hid under the table.
"under" is a preposition, and "the table" is its object.
The object usually comes straight after the preposition, but
sometimes it appears before. Compare these two sentences:
In whose name shall I book the table?
Whose name shall I book the table in?
In both sentences, "in" is a preposition, and "whose name" is
the object of that preposition.