Final answer:
Plato, a student of Socrates, wrote about his vision of a perfectly governed society, envisioning philosopher-kings as the ideal rulers in The Republic.
Step-by-step explanation:
The philosopher who was a student of Socrates and wrote about his vision of a perfectly governed society following Sparta's conquest of Athens is Plato. In The Republic, Plato envisions a society ruled by philosopher-kings, who would lead with wisdom and justice, educated from childhood specifically for this role. Plato's ideas were heavily influenced by his mentor Socrates, as well as by sophists and other pre-Socratic philosophies, leading him to create a complete philosophical system. Aristotle, Plato's most famous student, founded his own school but had different views on the role of the senses and the empirical world in gaining knowledge.