Have you ever sat on the bottom of a swimming pool and pondered your watery ceiling? Most of the surface is a sheet of light blue, and you can’t see through it, even though the water is clear. But right above you, there’s a round window of transparency.
And here’s the awesome thing: Through this ring you get a fish-eye view that shows you not just the sky, but stuff around the side of the pool, like trees or people sipping mai tais on the pool deck. This cool effect is caused by the optical properties of water, and it has a name: Snell’s window.
You can see this even if you don’t spend much time underwater. Perhaps, like me, you prefer to watch spearfishing videos on YouTube. Here is a beautiful example of Snell’s window from the channel YBS Youngbloods (the link takes you right to the 15-second segment of interest).
One curious thing to notice there: As the diver (Brodie) and the camera person descend, the window seems to stay the same size. So what, you ask? Well, think about it: If you filmed a window in your home as you backed away from it, it would appear to get smaller.
In fact, Snell’s window is getting bigger—see how the diver on the surface fills less and less of it? But unlike a window or anything else on dry land, its angular size, as perceived by your eye, stays the same as the distance increases.
Mysteries of the deep! There’s some beautiful physics behind all this, so let’s investigate, shall we?
Refraction and Snell’s Law
Since light is an electromagnetic wave, it doesn’t need a medium to “wave in” (unlike sound). That means it can travel through empty space—as sunlight does, luckily for us. Since light travels at a speed of 3 x 108 meters per second, this trip from the sun to Earth takes about eight minutes.
But something happens when the light enters a transparent medium like our atmosphere: It slows down. Air slows it by just 0.029 percent, but when light enters water it loses around 25 percent of its speed. It’s just like how you slow down when you run from the beach into the ocean, because water is denser than air.
This speed differential varies for different media, and it is described by its index of refraction (n), which is the ratio of the speed of light in a vacuum to the speed in a particular material. The higher the index of refraction, the slower light travels in that medium. In air, n = 1.00027. In water, n = 1.333. In glass, n = 1.5
But here’s the thing: Changing speed also causes the direction of the light to change. That’s actually what we mean by “refraction.” You see it when you look at a straw in a glass of water: The part of the straw underwater doesn’t match up with the part above. Why? The bending of light off the underwater portion causes you to see it somewhere that it’s not.
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