At the Sermon on the Mount, I have always believed that Jesus taught only His disciples (Matt. 4:25-5:2). Or at least that is what I though about chapters five through seven, until I noticed the last two verses of Matthew seven. They indicate that the multitude was astonished at His teaching. You may not think so, but understanding that Jesus was speaking to the nation of Israel, instead of just His twelve disciples, makes a difference as to how one interprets His teaching. If He were speaking only to His disciples, He was telling them they were the light of the world (5:14), but if to the entire multitude, He was saying that Israel was supposed to be a light to the world. That does not seem like a significant difference, but it is. The disciples represented the Church that was to begin following Christ's Ascension. The Gospel of Matthew is written primarily to the Jews. Since the Church will remain "salt" and "light" while it is still here on earth, it is Israel that was in danger of failing to illuminate the world.
I have always been taught that Israel was to be a light unto the nations, but I have not been able to find Scripture to support that. All my resources that address the idea of Israel being a light to the Gentiles give Isaiah 42:6 and 46:9 as references, but both of those are speaking of the Messiah. There are numerous places where the concept is inferred, but it is not stated in those specific terms. An example was Solomon's dedication of the temple in 1 Kings 8:60. So, while I cannot prove Israel is the "light of the world" referred to in Matthew five, I believe it has to be. They had been under Gentile domination for over six hundred years (Babylon, Medo-Persia, Greece, and now Rome); it is easy to see how they would lose faith and cease to be "salt" and "light" to the world.
There is great irony in the fact that God chose the Gentiles to rekindle the fire that was nearly extinguished by isolationism and disgrace. In Romans nine through eleven, Paul teaches us that Israel has been temporarily set aside, and that the Church is being used to provoke Israel to jealousy (Rom. 11:10-11). Today, it is the Church that is to be a light unto Israel!
There is one thing I noticed about the passage in Matthew concerning light. It is not written to individuals, although individuals can each serve as light-bearers; it is an admonishment to the nation as a whole. Notice it does not say you, as individuals, are to stand on a hilltop and shine forth; it is the combined light of unified believers which He describes as "a city" (Matt. 5:14). By the time He prayed what should actually be called the "Lord's Prayer in John seventeen, Jesus had already been rejected by Israel. In just hours, He would be tried, crucified, buried, and raised from the dead according to the Scriptures (1 Cor. 15:3-4). Christ's last recorded prayer, other than those He uttered on the cross, was that Christians would be united so that the world would believe God loved them, and that He sent His Son to prove it (Jn. 17:21-23). It is our unity that is the light. Together, we shine forth with His glorious Gospel. Praise God!