Re: Why do shadows seem to merge?

MacKenzie,

there is a simple effect and a complex effect at work here. The simple effect is due to the fact that the sun is not a point source, meaning the sun appears as a disk of light instead of an infinitesmally small point of light. The sun subtends about 1/2 of a degree in the sky instead of zero degrees for a perfect point source. If you trace the rays from the sun you will find that along the edges of an obstruction (your hand, for instance), not all of the suns rays are blocked. The result is a 1/2 degree blur in the edges of shadows. The extent of the blur is 2*d*tan(.5) where d is the distance from your hand to the wall. If your hand is four feet from the wall, the blur would be about 0.84 inches, or a little more than three quarters of an inch. The blur gets larger as your hand moves away from the wall, so the shadow cast by your hand appears to merge with the shadow of your head.

Even if the sun was a point source, a more complex effect known as diffraction also causes a blurring of shadows. Diffraction is not as easy to see, but if you were to observe the shadow cast from a very small light source, like a clear light bulb with a small filament, you would still see a blurry shadow. This cannot be explained with simple geometry as above. The first scientist to write about this observation was Francesco Grimaldi in the 1600s. Grimaldi noted that light didn't didn't always follow a perfectly straight path (deviation of light from rectilinear propagation). Grimaldi called this phenomena "diffractio", which is where the English word diffraction comes from. The theory of diffraction was later formalized by Fraunhofer and Fresnel (the s is silent) in the 1800s. The basic theory of electromagnetic waves (which include radio waves and light) was developed by James Clerk Maxwell in the late 1800s.

It turns out that any wave, be it water waves, sound waves, or light waves, exhibit diffraction. What actually happens is that when a wave encounters an obstacle, a diffraction pattern will be created by the edges of the obstacle. If the light source is of a single wavelength, the shadow would consist of a series of contours around your hand. The spacing between the contours depends on the wavelength of the light and the distance to the wall. The light from the sun is white, so it contains many wavelengths, not just one. Because of this, there are numerous contours representing many different wavelengths. The contours are superimposed on top of each other creating a blur effect. The farther your hand from the wall, the greater the seperation of the contours and the blur that you see. Scientists often use lasers to generate single wavelength light in optics experiments to avoid blurring caused by many wavelengths, but there is nothing that can be done to completely eliminate diffraction.

You can try a simple diffraction experiment at home using water waves. Fill a container with water and wait until the surface is calm. If you carefully poke your finger into the water, you will generate a series of water waves that look like concentric circles. If you place an obstacle in the path of the water waves, you should be able to see the waves almost bend around it. This is diffraction at work. In this case, we are are working with a single wavelength as you can see each distinct wave crest. Of course, the wavelength of water waves is huge (a centimeter or so) when compared to light waves (less that a millionth of a meter), but you get the point.

When we observe diffraction, it tells us that we are working with a wave. It turns out that that even particles, like electrons and protons, exhibit diffraction. This was a very startling discovery in the early part of this century, everyone used to believe that waves and particles were two different animals. Who would have ever expected that a billiard ball was anything like a water wave? It turns out that we actually observe a wave-particle duality, that is, particles can behave like waves and waves can behave like particles. This is not significant in the macroscopic world we live in, but very significant in the sub-microscopic world of atoms. These observations, along with others, led to the development of quantum mechanics. Quantum mechanics is weird and even mind blowing to some. The wavelike nature of particles results in the inability to measure certain parameters, like energy and time or position and momentum with perfect certainty. This is known as the Heisenberg uncertainty principle, which suggests that small particles are really a blur, like your shadow. The great Albert Einstein wasn't particularly fond of some of these conclusions. He remarked that "God does not play dice with the universe", suggesting that we should be able to measure everything in nature with perfect certainty.

Even with the skepticism of many physicists, diffraction along with quantum mechanics has lead to amazing discoveries and developments. The millions of transistors that make up desktop computers and other electronics would not have been possible without it. Diffraction is also used by engineers when designing antennas, because radio waves are basically light waves at a much longer wavelength. Diffraction effects are also taken into account when designing auditoriums or possibly recording studios to improve sound quality. High density semiconductor devices like the Pentium microprocessor are getting very close to diffraction limits, because current fabrication techniques depend on masks that produce shadows on a silicon wafer. Diffraction causes imperfect shadows, so it is becoming more difficult to make denser, faster processors with smaller features.

Just think, that simple merging shadow you see is responsible for so much. You can learn more about diffraction and related effects in any book about optics.