What does 'opened her eyes' mean here? Was the well of water invisible, like the donkey to Balaam?
Genesis 21:19 (KJV) 19 And God opened her eyes, and she saw a well of water; and she went, and filled the bottle with water, and gave the lad drink.
The Hebrew word rendered in Genesis 21:19 (KJV) as "opened" is paqach (Strong's H6491), which is the same word used to express what happened to the eyes of Adam and Eve when they ate the forbidden fruit and were suddenly aware of things that had previously escaped their notice, e.g. their nakedness. The sense of the word, then, is: to make conspicuous by calling attention to.
So, God didn't magically make a well appear, but simply drew Hagar's attention to the fact that it was there. Given, we are told three times in the narrative: Genesis 16:7-14; Genesis 17:20; and Genesis 21:18; that God had a plan for Ishmael, it is unlikely that He would not have been nudging Hagar's wandering in the wilderness (Genesis 21:14) towards the well.
If we were to measure important characters in the Bible by their encounters with God, then Hagar must be considered important. Twice it is recorded that the "angel of God/the LORD" spoke to her -- the same "angel of the LORD" that spoke to Abraham, preventing him from killing Isaac on Moriah 1. The first occasion was in Genesis 16, when she tried to return to Egypt after having fled from Sarah, and the second is what we have here in Genesis 21, where she is sent into the wilderness by Abraham.
The first time the angel spoke with Hagar, he instructed her: "Return to thy mistress, and submit thyself under her hands.", but on the second occasion, nothing is recorded about God's instructions. Clearly, however, Hagar wasn't abandoned in the wilderness, because we are told that God was with the boy, and that he prospered as an archer in Paran (southeast of Shur). Indeed, we are told later on in the narrative, Genesis 25:18, that Ishmael's descendants lived from Shur to Havilah, i.e the Arabian Peninsula, which Moses and the people of Israel walked the boundary of, some six hundred years later, on their round about way back to the promised land.
1. The Word of Promise Audio Bible uses the actor who reads Jesus' words in the NT, Jim Caviezel, as the voice of the "the angel of LORD".
It was "invisible" to her, but that doesn't mean it was invisible to everyone or that it was actually transparent. Something had to be changed about her specifically for her to see it, and the change came from God.
The text doesn't say that something was changed about the well, but says "God opened her eyes". There are no clues in the text that the well was actually transparent, but it does say something was wrong with her (her eyes were "closed") that required God's intervention (God opened them).
Going off your mention of Balaam, the angel wasn't invisible in some absolute sense because the donkey saw him while Balaam didn't. Again, God had to change something about Balaam himself, not about the angel.
Susan's reference to 2 Kings 6:17 in the comment is also similar. Note how the Lord's army was actually all around the whole time and weren't invisible to everyone (Elisha was already seeing them), but action on God's part was required to initiate the sight.
Luke 24:31 goes a little further, saying "And their eyes were opened, and they recognized him." Jesus wasn't invisible up to that point and they didn't just have their eyes shut (they talked with him as they walked along and even ate with him), but they didn't recognize him. It wasn't until their eyes were "opened" that they recognized him.
So I'm pretty sure it just means God changed Hagar so that she recognized something.
A few themes are interesting through these verses: God's action was required; something was deficient about the people that kept them from recognizing something; the thing they were blind to didn't change, but was actually there the whole time.
I can't help but comment on how this reminds me of how the New Testament describes salvation: people don't recognize that they need to repent of their sin that actually exists against a very real God until God himself changes something about them. Then they are able to see and turn toward the solution (Christ's atonement). Conversely, those who don't see the solution are never able to come to Christ.
the well was never invisible.the problem was with hagar's aptitude towards the problem.all that hagar had was a loaf of bread and a bottle of water in the middle of the desert.so she surely thought that they were going to die.but as soon as the god spoke to her and gave the promise that ismael(the lad) shall be made into a nation her vision towards the problem changed.so as her aptitude changed see saw the well.