MadSci Network: Physics

Re: Dappled Light

Date: Thu Nov 26 18:45:42 1998
Posted By: William Beaty, Electrical Engineer / Physics explainer / K-6 science textbook content provider
Area of science: Physics
ID: 908673549.Ph

Hi David!

REALLY good question! If I recall correctly, this mystery was first discussed by the ancient greeks. The slots in the leaves aren't round. What ARE those little circles of light? Here's a big clue: when a small cloud drifts across the sun, all those little "dapples" become distorted, and something seems to be moving through each one. Another clue: during a solar eclipse, when the moon is taking a big "bite" out of the sun's disk, all those little dapples each appears to have a bite out of it.

As you have probably guessed by now, those circular dapples are images of the sun. The leaves form tiny holes, and so the tree acts like a "pinhole camera". A whole lot of pinhole cameras, actually. Light from tiny spots on the sun's disk goes through the small irregular holes and slots, then the collection of rays expands again on the other side. When it hits the ground, it forms an image of the sun. Another way to think of it: if our sun was a brilliant pointlike object, like a welding arc, then there would be no "dapples", there would simply be the sharp shadows of the leaves.

As the dapples overlap, how bright can the light become? Well, more and more holes in the leaves will create more and more overlapping dapples, and if you continue making holes, eventually there will be no leaves at all, and the ground will be illuminated by full sunlight. Without the tree, the ground receives one enormous, very bright "dapple" which contains numberless copies of the sun's image, all blurred together.

Is this useful? Yes, because all optical images are formed by "pinhole" geometry. Without a central "fulcrum point" for the crossing light rays, projected images cannot exist. Yes, lenses are important too. Lenses allow us to use very large pinholes, all without making the projected image all blurry. But it's the basic geometry of the pinhole which allows projected images to be created. The romans harnessed this effect by making a small hole in the side of a darkened room. People in the room saw an upside-down image of the outside world projected upon the wall opposite the hole. This "camera obscura" (latin for "room, dark"), was the first camera. Yes, the modern word "camera" is latin for "room" Well, a camera IS a small dark room, with a hole in its side.

Besides being the basis for imaging optics, pinhole optics explains many odd little things in the everyday world. For example, why are shadows on the ground so very sharp if the opaque object is near the ground, but the edges of the shadows are fuzzy whenever the object is far from the ground? Why is the shadow of a crawling bug so sharp, yet the shadow of a flying airplane is totally fuzzed-out? And during sunset, why don't we see the sharp shadows of distant hills racing across the ground? It's because that "fuzz" on the edge of the shadows is composed of overlapped sun images, all lined up along the shadow edges. The edges of opaque objects acts as "half of a pinhole". The greater the distance between the object and its shadow, the larger the sun's disk-image becomes, and so the band of "shadow fuzz" is also larger. The hill-shadows DO rush across the ground at sunset, but because their band of fuzz is so enormous, we only see an increasing darkness and we never see any motion. Look at the shadow of a chain-link fence. The shadow of the top of the fence is fuzzy, while the shadow of the bottom of the fence is not. It's because of pinhole optics and sun-disk images. If the sun was a "dot," all the shadows would be sharp, and in many ways the world would look like a very different place.

Here's a link to an entire website devoted to exploring these ideas: Bob Miller's LIGHT WALK, at the Exploratorium

And from my site, here's a misconception about lenses and ray diagrams which OBSCURES (sorry!) the importance of pinholes in lens-based optics: lens1.html

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