The Magnetic Shadow Effect

0:01 A friend recently sent me a video where the shadow of a post seemed to grow outwards towards them when their shadow got close to that of the post. Their question for me, what's going on? I had noticed this previously myself and immediately tried to replicate it in a controlled setting. It's a bit trippy. What's weird about this touching shadow phenomenon is that it feels a little like one shadow is a magnet pulling the other one towards it or like there's surface tension. Like you know how when you touch water, it stays stuck up and attached to your finger for a bit when you pull it away from the water. Except shadows don't have surface tension and they aren't magnetic. Before I get to the explanation, here are a few more cool examples where the same phenomenon happens, except instead of shadows, it's out of focus objects in an image. You can literally see this with your own eyes. If you focus on something far away and hold a finger in front of your hand, the hand seems to grow outwards towards the finger. But if I hold my finger

0:46 behind my hand, it's the finger that seems to grow outwards. At first, I wondered if perhaps this phenomenon has something to do with the wave nature of light, defraction, interference, and all that. But it's actually much more straightforward. It's just simple, if slightly counterintuitive, geometry. Here's the thing. This touching shadow phenomenon, which is also called the shadow blister effect, happens when you have a light source shining on two objects that are different distances away from the light. The farther one on its own casts one shadow, and the near one casts another. And when those shadows get close, the near object's shadow blocks the far object's shadow, and the shadows appear to merge. But it gets interesting if the light source isn't a point but has actual size because then the different parts of the light source cast slightly different shadows which overlap and combine to create a blurred shadow. You can see this if I turn on first one light then another then another. Multiple shadows blur together into one blurry shadow.

1:33 The core dark part of a shadow is where light from everywhere on the light source is being blocked. The blurry edge of the shadow is where some parts of the light source are being blocked while others get passed. And the brightness outside the shadow is where all parts of the light source reach without being blocked. The geometry of the touching shadow phenomenon means that as the object nearer the light moves to shade the far object, the first shadows that it intercepts are the ones that land on the inside dark edge of the blur. Then it intercepts shadows farther out and farther out and so on, growing the shadow of the farther object until the shadows fully merge. It's kind of hard to describe in words, but easier to intuitively see in a visualization or with real lights and shadows. The point is that the shadow of the farther away object seems to grow from the inside out until the shadows merge. And this is purely due to the fact that the light source has some area and the objects are at different distances from the light. In particular, the fact that you see

2:19 this effect with shadows outside is due to the fact that the sun is not a point source of light and outdoor shadows are blurry. Another nice way to see why the blisters appear is to replace the farther away object with a pinhole. This makes it obvious that the rays of light get flipped when they pass the object. And I'm showing the rays in different colors just so you can track which one is which. So when a nearer object moves to block the light, the shadow is blocked in reverse. This is the blister on the opposite shadow. Essentially, the same blistering happens with a camera or your eye, except that the effect is due to the size of the lens opening rather than the size of the light source. The rays from a point source of light get focused by a lens down to a point and then diverge again. So, if you put the image sensor or your retina just in front of or behind that point, the image of the point light source becomes spread out into a circle. This is the source of bokeh in a blurry image. When you put another object in between the light

3:04 source and the lens, you block the outermost light rays generating the bokeh circle, which shrinks the bokeh from the opposite side. Well, it looks like the same side, but we have to remember that lenses flip images. So, the image of the blocking object will be up here, and the bokeh shrinks from the opposite side relative to it. Here's what the result looks like for a real blurry image of a point source of light. The net result for an extended blurry object like your hand is that the shrinking of all the combined bokeh of the light shining through between the hand and the finger makes the hand appear to blister outwards towards the finger, but it's really the bokeh that's shrinking. Let's look at an object lit from behind by a grid of point lights. You can see that the bokeh circles around the object appear cropped or cut off on the sides of the circles farthest away from the object and are more cut off the closer they are to the object. As we increase the number of points on the grid, the cutff bokeh overlap and combine to create the illusion that the far object is growing outwards. But

3:51 there's another side to the lens blister effect. So far, we've just been looking at the situation where the image sensor or retina is too close to the lens, which happens when you've focused the lens too far away. If the image sensor is too far from the lens, which happens if you focus the lens too close, then a point source still spreads out into a circular bokeh. But now when you block the light, the bokeh shrinks in the same direction as the blocking, which you can see in this blurry image. In fact, if you put a funny shape in front of the lens, you can see the shape normally in the far bokeh and inverted in the near bokeh. The net result for a normal extended blurry object like a hand is that the shrinking bokeh makes your closer finger seem to blister outwards towards the hand. Except how can the finger be growing? The farther away hand can't do anything to block or affect the light from your finger reaching the lens, it's your finger that's blocking the light. Another demo with colored textbooks reveals the explanation. Even

4:36 though the nearer green textbook appears to blister outwards, the blister has the orange color of the more distant textbook. It's a somewhat bizarre mirage-like vision of the more distant textbook that's revealed by the shrinking bokeh between the books. The near object blisters or grows when you focus too near, while if you focus too far, then the far object blisters. Either way, the blister has the same color you'd see in that location if the background were dark. That light is always reaching the lens. It just normally gets overwhelmed by the bright bokeh of the bright background. Put another way, when blurry fingers overlap against a bright background, there's a blister. But against a dark background, you just see the fingers overlapping more or less normally. And when you focus a lens on the far side of a bright grid, a blurry finger appears to attract the lines. While when you focus on the close side of the grid, the finger appears to repel the lines. But there's

5:22 no repelling or attraction happening. What you see here is explained by the geometry of light rays passing through a lens. In summary, blurry fingers and blurry shadows don't have surface tension and aren't magnetic. It's just that the geometry of shadows and lenses is a little weird. [Music] I want to say a big thank you to everyone who supports Minute Physics on Patreon. It really helps keep things going around here. And everyone else, if you like this video, please consider supporting us at patreon.com/minutphysics. The more Patreon support we have, the fewer sponsorships we have to do. It really helps. Thank you.