Introduction: Refraction: Seeing Is Not Believing
Almost everyone has noticed that things in glasses of water look different from how they look in air. And you've seen things in bathtubs.
But few of us have taken a close look at things that stick out of a fishtank, especially from multiple perspectives.
Have a look at the video at teachingandlearninglabs.com[1]. An action figure is placed in a plastic tank. The tank is turned, so you can see it from multiple perspectives. Then, it's filled with water, and the tank is turned again. What do you think will happen?
[1] I would have embedded the video here, but I don't have an account at a video-hosting site that instructables links to.[back]
Supplies
- A clear container ("the tank") able to hold water that has flat, vertical sides (I used a display case you can find most craft/hobby stores. You could use a fish tank, a food storage tub, etc.)
- Optional: If you want to rotate it easily, put it on a turntable or lazy susan
- Water (or any other clear liquid)
- Something to put in the tank partly under water, part above the water
Action figures are especially nice. In fact, this instructible was inspired in part by images like Physics is Phun, Infinity pools mess with my head, and a headless polar bear. I wanted something easier to make (and put away) but still captured the sense of a severed head.
Step 1: Make It
- Put Your Object in the Tank.
- Fill the Tank. Make sure part of the object is out of the water.
- Have Your Eyes or Camera at the Level of the Water. This tends to produce the most surprising and dramatic images - but play around. You can see some surprising effects from other directions. Looking down into the water can make things seem squashed and distorted; from below, you see internal reflections from the surface of the water.
- Have Fun!
Even knowing how this works and after designing something that would produce this effect, seeing things seemingly break apart and move around still seems somehow magical. Keep that sense of wonder, and kindle it in others.
Step 2: Understand It
How Does This Work?
Sure, it's cool to see new things; but it's even better to use those things as an opportunity to learn how the world works.
After all, how can your head be on a stick? How can you have a stick for a head?
It all has to do with refraction[2] - which is a technical way of saying that light changes direction when it passes from one material to another material. It's also a clear example of the fact that trigonometry is useful for describing nature, even in situations that have nothing to do with circles or triangles.
Just the Concepts
If you want a conceptual understanding of how this works, you need to make some observations about light bending when it goes from water to air.[3] (If you want to measure exactly how much, you need Snell's Law.)
Any time light passes from one material to another material, it changes direction.
As shown in another video at teachingandlearninglabs.com[5], when light comes "face-on" to a surface, it keeps going straight.[4] But when it arrives at an angle, it takes a sudden turn at the boundary between the two materials. And the path of the light is always closer to "face-on" to the boundary when it's in water than when it's in air.
This allows us to understand overhead views of the same situation. Light from Han's head travels straight to the camera, since it's going through air the whole way. But light from Han's neck bends when it goes from water to air - so his head and neck can't line up.
Snell's Law
Getting an even better understanding requires some math - Snell's Law.
Snel's Law? Snell's Law? You may find different sources insisting on one spelling or the other. It's actually named after Willebrord Snellius, who derived it in 1621. It's been around a long time.[6]
If you observe the bending for a lot of different transparent materials (air, water, glass, plastic, etc.), you find that the amount of bending is different for different materials - it's a characteristic of each material. Scientists call this characteristic the "index of refraction" and use the letter n when using it in equations. And, since it's useful to have a reference, the index of refraction of air is defined to be 1[7] (since multiplying or dividing by 1 doesn't change any number in any way). Finally, the index of refraction of every other material is greater than 1.
When calculating the interactions of light with a surface (whether reflection or refraction), scientists measure angles from the "normal line". In the context of math, science, and engineering, the word "normal" usually means "perpendicular"[8].
If you measure carefully, you find, for light traveling from any material (typically called "material 1") to any other material (typically called "material 2")
n1 sinθ1 = n2 sinθ2
where n1 and n2 are the index of refraction of the two materials, and θ1 and θ2 are the angles the light makes from the normal line, in each of those materials.
Think about how the sine function works: when θ = 0, sinθ = 0. As θ gets bigger, sinθ gets bigger. (We only consider from zero to 90°, since a ray can't be more than 90° from the normal line - that's the definition of "normal".)
nair ≈ 1.00 and nwater ≈ 1.33. So, sinθair must be greater than sinθwater[9]. That means that a ray in water that was headed straight toward your eye will bend away from the normal line[10] (and toward the surface) when it passes into the air - so you don't actually see that ray. Instead, you actually see a ray that was originally closer to the normal line.
Using these equations, you can calculate exactly how much of an offset there should be for any real-world situation. Or, you could design a ray-tracing program to create realistic refractions - but that could make things (like the photos and videos above) that people might not believe!
Step 3: Footnotes
[1] I would have embedded the video here, but I don't have an account at a video-hosting site that instructables links to.[back]
[2] From "re-" ("back") and "frangere" ("to break"). A beam of light seems "broken" at the boundary between materials. Try remembering "fracture" if you have "refraction" as a vocabulary word on a test.[back]
[3] The camera was able to "see" Han because light from the room bounced off of him, traveled through the water and/or air, and got to the camera. The camera does not shoot out rays of light (and neither do your eyes). (See Can We Believe Our Eyes?, starting around 11:15.)[back]
[4] Actually, some light also gets reflected. How much gets reflected depends, in part, on the material the light starts in, the material the light goes into, and how far from "face-on" the light is at the boundary. There are equations for that too - which good ray-tracing software use to create realistic scenes. See the discussion at The Physics Classroom.[back]
[5] I would have embedded the video here, but I don't have an account at a video-hosting site that instructables links to.[back]
[6] A lot longer than that. It was also described by Ibn Sahl in 984, Thomas Harriot in 1602, René Descartes in 1637, and likely others we don't know about - each probably independent of the others.[back]
[7] The index of refraction of air is really 1.0003 while the index of refraction of vacuum (absolute nothingness) is exactly 1 (that is, 1.000000000000...). The difference is hard to notice for the types of demonstrations shown here, but it can become important: smaller differences lead to dramatic mirages, for example.[back]
[8]From the Latin norma for "carpenter's square" which carpenters use to make sure things are perpendicular. Never call it the "natural line" or "usual line" - it has a totally different meaning. I teach my students to build an autocorrect function into their brains: "normal" → "perpendicular".[back]
[9] (except when θ = 0, when they're both equal to zero) [back]
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