Jesus was well known on account of the miracles he performed. Then why was it necessary for Judas to identify Jesus when they came to arrest him?

That’s a good point–Jesus was well-known on account of the miracles he worked. Why would Judas need to identify who he was? Let’s think about the circumstances of Jesus’ public life.

First of all, consider that while Jesus was well-known among certain groups of people (namely, the Jewish people of his day), that didn’t necessarily mean that the soldiers who went to arrest him would have known about him. All four Gospels attest that the mob sent to arrest Jesus came from the chief priests and elders of the people. They might have known about Jesus, but Jesus tended to associate more with the poor and the outcasts than with the elite.

Furthermore, Jesus was arrested near Jerusalem. Geographically, most of Jesus’ ministry was far away from Jerusalem, in Galilee (a region which was way out in the country). He did visit the city periodically for brief spans of time, but for the most part he was not in Jerusalem during his public life.

So if these people never saw Jesus in person, then it would definitely be necessary for Judas to point him out to the soldiers. And even if they had heard about Jesus, they might not have known what he looked like. Remember also–Jesus was with a few of his disciples when he was arrested. Imagine if the soldiers went out and grabbed Peter by mistake!