Barnafoss was really more of a series of rapids on the Hvítá River (not to be confused with the river by the same name responsible for Gullfoss). The river was forced through a narrow rocky chute that apparently once had a natural bridge spanning across it.
The meaning of this waterfall translates into "Children's waterfall", but the signs here indicated that there was a saga describing why it got this name. The saga said that there were two children in the Hraunsás household who were supposed to stay home while the parents went to church for Christmas Mass. When the parents returned from mass, they discovered that the children had disappeared (possibly because the children got bored and decided to go out).
They then followed the children's tracks to this waterfall at the stone natural bridge where the tracks disappeared. The mother concluded that the children must have fallen into the river and drowned. Then, the mother had the arch destroyed in order to ensure no one else faces a similar fate. I've seen some accounts say it was by spell or curse, which induced the bridge's collapse by earthquake. In reality, natural bridges usually collapse over time, and given the powerful erosive forces from the rapidly moving river that undercut whatever was supporting the bridge, that could very well have been the fate of the natural arch here.
We did a little bit of a walk to reach this rapids flanked by lava walls and rocks. Even though the obvious natural bridge had already collapsed, it looked like there was still another one near the level of the river. I'm not sure whether it was the same bridge that had fallen or a different one, but it was intriguing nonetheless. The walk probably takes less than 20-30 minutes round trip.
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