"12 Again Jesus spoke to them, saying, “I am the light of the world. Whoever follows me will not walk in darkness, but will have the light of life.” 13 So the Pharisees said to him, “You are bearing witness about yourself; your testimony is not true.” 14 Jesus answered, “Even if I do bear witness about myself, my testimony is true, for I know where I came from and where I am going, but you do not know where I come from or where I am going. 15 You judge according to the flesh; I judge no one. 16 Yet even if I do judge, my judgement is true, for it is not I alone who judge, but I and the Father who sent me. 17 In your Law it is written that the testimony of two people is true.18 I am the one who bears witness about myself, and the Father who sent me bears witness about me.” 19 They said to him therefore, “Where is your Father?” Jesus answered, “You know neither me nor my Father. If you knew me, you would know my Father also.” 20 These words he spoke in the treasury, as he taught in the temple; but no one arrested him, because his hour had not yet come."
John 8:12-20
It is very difficult not to associate the wonderful words in 12 with the story of the woman in 1-11. They fit it so beautifully, for Jesus had been light to her in her darkness. There may also be a backward reference to the incident with Nicodemus in 7:50ff. Here was a man who had been walking in darkness but was now gradually emerging into the light, and perhaps Jesus was thinking to encourage him in his spiritual progress, exhorting him to follow Him. But surely its first reference is to the Feast of Tabernacles and the illumination of the temple courts during the festival symbolising the pillar of cloud and fire in Israel's wilderness journeyings. Jesus is claiming to be the reality of which that was the mere symbol. This, of course, is a Messianic claim (cf Isaiah 42:6, 49:6), and the Jews clearly see the implication of His words as being Messianic. The 'I am' would probably carry much deeper significance for them than it does for us. And it is the authority with which He speaks that they question and challenge (13). It may be that they are quoting Jesus' own words at Him here. He had already said in 5:31, 'If I bear witness of Myself, my witness is not true'. But if so, this is a shallow and superficial understanding of Jesus' words, betraying a basic lack of appreciation of Who He is. There is no contradiction. Indeed, He goes on to say that His authority, and the truth of His witness, reside in the fact that He knows whence He has come and whither He goes. On this ground - His eternal Sonship - He claims the right to be heard and believed (14). There is something important here. On the one hand, there is, ultimately, no mere rational proof of our Lord's authority; and on the other hand, once a man perceives His deity and divinity, there is no further question of the authority of His words. This means, we do not prove Christ, but believe in Him.