1. She looked at the person on the table.(When the person is on the table, 'on the table' is an adjective phrase.)

Question

2. She looked at the person on the table.(When she is on the table, 'on the table' is an adverbial phrase.) (How can we distinguish the two situation? According to the situation, the part of speech of 'on the table' is different.)

Answer 1

Both sentences mean the same. The person is on the table -- so the phrase is an adjective phrase.

However, -- the same phrase is an adverb phrase in this sentence.

She left the book on the table.

Answer 2

A prepositional phrase usually is right after the word it modifies.