Final answer:
The object of the preposition in "the headmaster of the academy" is "the academy". This prepositional phrase functions to provide additional information about the relationship between the headmaster and the academy. In sentences, it's important to use the objective case for pronouns acting as objects, such as 'whom' in related constructions.
Step-by-step explanation:
The object of the preposition in the phrase "the headmaster of the academy" is "the academy". The term prepositional phrase typically includes both the preposition and its object, which together express a relationship between the object and another word in the sentence. In this case, "of" is the preposition, and "the academy" is the noun phrase serving as its object. Such phrases can function as adverbials, modifying a verb, an adjective, or another adverb in a sentence, providing additional details such as location, direction, time, or condition.
Furthermore, when constructing sentences, it's important to use the objective case for pronouns that act as objects. For example, in sentences like "I don't know whom to ask", "whom" is used because it is the object of the verb "ask". Similarly, "To whom should I give the extra concert tickets?" uses "whom" since it is the object of the preposition "to".
Sometimes a prepositional phrase may act as a subject complement, which follows a linking verb and names or describes the subject as in "The meeting is on the first floor." The prepositional phrase "on the first floor" acts as a subject complement, completing the meaning by telling us more about the meeting's location.