Every Bible artist would love to know the answer to this question. The simple answer is, 'We don't know!'
I read an historical document in the 70's which was supposed to be a letter from a 'Roman officer' who was present in Jerusalem at the time of the crucifixion. The letter was written in answer to a letter he had received from a roman governor who had asked 'What was Jesus like?' The letter contained a physical description and more, but the authenticity of the document remains in doubt.
In the 50's, The Lord Jesus was often depicted as blond. (see my post 'My favorite Bible artists #1').
The reason for this may have been the influence of movies made at the time.
The portrayal of Jesus by Robert Powell in the Franco Zeffirelli Epic 'Jesus of Nazareth' has greatly influenced the way in which I, (and others) have drawn the Lord Jesus. We live close to the second largest Jewish community in the U.K. So I can vouch for the fact that although there are blond and even redheads among Jewish people, The vast majority have dark hair.
I have heard it suggested recently that the Lord Jesus was 'Black!' I can't see this myself. If this was the case, I believe that scripture would be very clear on it.The only things that we do know from scripture for certain is that He was Jewish, He had a beard and a robe that was woven throughout! (seamless).
For a long time I have illustrated the Lord Jesus with the traditional 'blue & white ' clothing. I am now trying to move towards more authentic colors of the time.
(Amendment added later). Blue and white were authentic colors of the time. What I meant was more earthy colors, like the ones used in 'Jesus of Nazareth'. I wanted to get away from the sanitized image of Jesus that we are used to seeing in many films and children's Bibles.
Some believe that we should not show pictures of Jesus at all. There are Bible pictures available where Jesus is shown as a black silhouette! I've been present at children's meetings where these have been used, and I have to say that most children were puzzled! Bible pictures should be an aid to hold a child's attention during the telling of a Bible story, and shouldn't become an obstacle!
Although we may not know what the Lord Jesus looked like, we do know that He was just like His father! (Hebrews ch1 v3).
In other words, If you want to know what God is like, look at Jesus!
Related posts:
How old were the disciples?
