Regarding Socrates, there is a problem, known as the "Socratic Problem." Since he never wrote down any of his ideas, all we know about them is hearsay, presented in the writings of others, with Plato, Xenophon. and Aristophanes being the main sources. But which of the statements of Socrates that they present is really an accurate presentation and which are those authors putting their own words and ideas into Socrates' mouth? No one is sure.
With the image of Socrates, we have the same dilemma. What we know for sure from ancient writings is that Socrates was ugly. But while there are many images of him, which one is the most true to life? Again, no one knows. You can see some of them below.
Click the following link to learn more about images of Socrates: http://www.stoa.org/projects/demos/article_portraits?page=12
All images below are in the public domain.
Title: Marble Bust of Socrates
Style: Late Classical
Period: Roman
Collection: Naples, Museo Archaeologico Nazionale
Title: Marble Head of Socrates
Find spot: Rome
Style: Late Classical
Period: Roman Imperial
Region: Latium
Collection: Rome: Museo Nazionale delle Terme
Title: Marble Portrait Bust of Socrates
(Roman copy of an original ca. 330 BCE)
Collection: Vatican
Title: Mosaic of Socrates Among the Seven Sages
Find spot: Baalbek
Collection: Beyrough Museum
Title: Inscribed Herm of Socrates
Style: Late Classical
Period: Roman
Collection: Naples, Museo Archeologico Nazionale
Title: Head of Socrates, Perhaps from a Herm Portrait
Find spot: Athens, Agora
Style: Late Classical
Date: Ca. 150 BCE (Roman copy after an original by Lyssipos, ca. 330 BCE)
Region: Attica
Period: Antoine
Photo: Amy Smith
Title: Head of Socrates
Style; Late Classical
Period: Roman
Collection: Paris, Louvre
Title: Painting of Socrates in a Roman House
Location: Ephesus