Phenomenon: How to Stretch a Shadow

"I hope I have helped to raise the profile of science and to show that physics is not a mystery, but can be understood by ordinary people."

Stephen Hawking

October 21, 2017 by S. Alex Martin

The most fundamental truth about science is that, to use it, you need to ask one question. That may be why science is so beautiful. Its entire practice relies on our own curiosity. ​ You might have read that first sentence one of two ways. Did you read it as a statement? "To use science, you need to ask one question." Or did you read it as a prelude to me providing a question? "Okay, what is the question I need to ask?" ​ If you reacted the second way, you're already thinking like a scientist. And that's a good thing, because this entire essay stems from me asking one, single question: "Why?" ​ I look for phenomena in everything. Refracting light, sound waves, streams of dry sand blowing over a beach. Even on the tennis court in my apartment complex, there are these strange, dirty streaks along the fence-line that, oddly enough, look like iron filings dusted over magnetic field lines -- and I have no idea what these streaks are, or how they were formed. Every time I play tennis there, I stare at them, and a bunch of questions bounce around in my head: "What are they? What formed them? How did they form?" All of those questions boil down to a single question: "Why?" More explicitly, "Why do these streaks exist and look like magnetic field lines?" ​ Several months ago, at my old workplace in Pennsylvania, the sun was shining in through the window, casting long shadows over the ground. I'm not sure what possessed me to do so, but I took a piece of paper and placed it in the sunlight, then moved its shadow toward another shadow on the ground. Before the shadows touched, however, something fascinating occurred: the two shadows stretched toward each other. ​ I pulled the shadow away, then brought it closer again. Just like before, the two shadows bent toward each other. It wasn't a trick of the eyes: I called over my coworker, and she witnessed it, too. I proceeded to show this phenomenon to everyone I worked with, and we all saw the exact same thing: the two shadows, when brought close together, would bend, warp, and pull toward each other. Every time, I asked the same question: "Why are the shadows bending toward each other?"

In this series of images, you can see how as the shadow of my finger approaches the shadow of a window frame in Starbucks, the two shadows appear to stretch toward each other. ​ I looked absolutely ridiculous as I filmed this experiment in public, but hey, the things you do for science.

Naturally, I began constructing my own conclusions, and the one that made the most sense was this: when the gap between the two objects became small enough, it acted like a slit and caused the light to diffract, much like diffraction you would see in the double slit experiment. I had solved the mystery. ​ But...I was troubled. What had I proven? Nothing. I came up with an answer, accepted it, and didn't conduct another shadow experiment with any other variables. In fact, it would take me another several weeks to try bending shadows again -- and when I did, I discovered my conclusion was, in fact, wrong. ​ If closing the gap between the objects created a slit that diffracted light and bent the shadows toward each other, it should work at any distance. I put the paper next the post casting the shadow, and the shadows bent toward each other. Then I put the paper near the ground, slid it close to the shadow of the pole...and the shadows didn't stretch toward each other. The horizontal distance between the objects, I discovered, was not the primary cause of the phenomenon I was witnessing. ​ I tried this again and again. When the paper (and other objects I tried this experiment with) was casting a shadow from a distance, that is, several feet from where I was standing, the shadows stretched toward each other. When I brought the paper within a few inches of its shadow, the two shadows didn't stretch toward each other. Therefore, something about the distance to the shadows was causing them to stretch toward each other. ​ Coincidentally enough, I made this observation right before the total solar eclipse of August 21, 2017 (for which I traveled to Oregon to witness!) It helped that I did so, because talk about light and shadows dominated the internet. One certain property about light and shadows stuck out, the fact that all shadows have three distinct regions: the umbra, the dark, more central region where most light is blocked; the penumbra, the border of a shadow, the grayer region where diffuse light reaches, making it lighter than the umbra; the antumbra, the region that mirrors the cone of the umbra, where the light source comes back into view and grows larger as you move away, and is the reason for annular eclipses (admittedly, I was not even aware of this term until writing this article! You learn something every day).

It clicked: somehow, this was the answer. I just needed to figure out why it was the answer, why the penumbras of two shadows made it look like the shadows were stretching toward each other. ​ If you've ever turned on two or more lights located on different sides of a room, you've probably noticed that objects cast multiple shadows. The closer an object is to a single light source, its shadow grows darker in one direction, while the other shadows cast by other light sources fade away. However, if you overlap the fainter

shadows of two objects, the region of overlap becomes darker, if not completely black. Simply put, two overlapping shadows create a darker shadow in their region of overlap.

Left: an object with multiple light sources will project multiple penumbras. The penumbra nearest either source will appear dimmer than the other.

Right: overlapping penumbras will create a darker umbra.

All objects project an umbra and penumbra and antumbra, but the size (and, in the case of the antumbra, the existence) of each region depends on how far the shadow is projected. In the experiments at my work, the stretching effect was most distinct when the shadow of the paper was projected on the floor several feet away, and seemed to not work at all when the paper was inches from the floor. I also discovered that the more rounded/uneven the objects, the greater the effect was. The penumbra of any object is larger at a distance, because there is more area for more diffuse light to reach. The penumbra is almost nonexistent when the object is close to the surface, because almost no diffuse light can get inside the shadow region. ​ All of these observations led me to the following conclusion: the stretching effect is caused by the two penumbras overlapping one another: that of the pole, and that of the paper. The greater the projection distance, the greater the observed effect. I also discovered that the more uneven/bumpy either object is, the more profound the effect, likely because they have uneven penumbras that overlap unevenly. ​ Knowing all of this, let's take a closer look at it in action!

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Watch the video of this phenomenon (16 seconds)

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