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Name: Jesse
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Question:
This concerns a bizarre optical phenomenon I witnessed when I was a teenager, about ten years ago. It was about midnight, and the moon was setting over Lake Superior; the water was fairly calm and the sky was clear. The moon's reflection on the waves made the familiar upside-down "V" shape, but the V didn't point at the moon, but 10-15 degrees to the right! It looked like this (hope the ASCII diagram works): C _____________________________ /\ / \ / \ I've never heard of *anything* like this, and I think I have a pretty decent layman's understanding of optics. I could dismiss it as a dream or false memory, but my dad remembers it too. How could this be possible?



Replies:
Thanks for the question. I think the effect you described was the result of waves on the surface of the lake, moving either diagonally towards you and to the left, or away from you and to the right.

To explain why, let me create some names. For each point on the surface of the water, imagine a line pointing perpendicular to the surface, called the normal. By and large, the normal will point upwards, but because of the waves, it will also point a little to one side or another. The crucial part is that, for waves as I described above, when the normal points slightly towards you, it must also point slightly towards the left. (To verify this, try making some imitation "waves" on a duvet cover.) From each point of the surface, also draw a line to the moon (moonline) and to your eyes (eyeline). Then the rules of optics tell us that you will see a reflection of the moon at all places on the surface that
(1) you can see
(2) the moon can "see"
(3) the normal lies in the plane defined by the moonline and eyeline, and bisects the angle between them

For a reflection to happen very far out on the lake, the eyeline is closer to horizontal than the moonline, so condition (3) requires the normal to point towards you a little. But, because of the way the waves are arranged, this means that it will also point a little to the left. So, the place where the reflection happens has to be a little to the right. The farther out the reflection happens, the farther to the right is has to be. This explains the pattern you saw.

Douglas Stanford



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