How does diffraction make a tree's shadow blurry?
Category: Earth Science Published: July 2, 2014
Diffraction is not what makes a tree's shadow blurry. The shadows of trees, buildings, and other outdoor objects are made blurry by the fact that the sun is an extended light source. Although diffraction can make shadows blurry, for human-sized objects at visible wavelengths of light, the diffraction of light is small.
Look closely at the shadow of a tree cast on the grass, your hand cast on the sidewalk, or a fence cast on a distant wall. Each shadow has the general shape of the object casting the shadow, but the edges of the shadows are not crisp. Rather, the edges of the shadow are blurry or fuzzy. The farther away the shadow is from the object creating the shadow, the more blurry the shadow becomes. For instance, move your hand away from its shadow on the sidewalk, and the shadow becomes more of a blob. If light traveled only in perfectly straight lines and there were only point sources of light, all shadows would be perfectly crisp because the light would reach a spot and then not reach a spot right next to it. There are therefore two effects that blur out shadows: 1) light does not travel only in straight lines, but can bend around corners ("diffraction"), and 2) light does not come only from point sources.
The sun is not a point source of light. Rather, the sun has an extended shape with a finite width. Light generated by the sun emanates from different points in space along the sun's surface. This concept can be better understood by looking at the diagram below. Light from one side of the sun can reach the areas that are shadowed from the light of the other side of the sun. Similarly, light from the other side of the sun can reach the areas that are shadowed from other light rays. Light from an extended object is able to penetrate the shadow region because the light comes from different points along the sun. If the shadowing object is close enough to the surface on which the shadow is cast (e.g. the ground), there is an area of shadow where no light from the sun can reach. This inner, darker region of the shadow is called the "umbra". (The word "umbra" comes from Latin and means "shade". It is also the root of the word "umbrella", which shades you from sunlight or rain. This connection between the two words can help you remember what "umbra" means.) The outer, lighter region of the shadow is the area where some of the sunlight is able to reach, making the shadow lighter. This lighter part of the shadow is called the "penumbra". (The word "penumbra" comes from Latin roots which mean "almost shadow", similar to how the word "peninsula" comes from roots which mean "almost island".) As you go towards the outer regions of the penumbra, more and more light of the sun is able to reach the ground, and the shadow grows lighter and lighter. Every object illuminated by the sun can cast a shadow with an umbra and a penumbra just like astronomical objects can.
Interestingly, if a light source is more extended in one direction than the other, then the shadows associated with this light source will be more blurry in one direction than the other. For instance, look closely at the shadow of your hand in a room at night with only a single, long, fluorescent light bulb turned on. Holding your hand in one direction, the tips of your fingers in the shadow will be sharp while the sides of your fingers will be blurry. Now rotate your hand ninety degrees, and the finger tips will become blurry while the finger sides become sharp. Similarly, the sun can also cause this effect. Right before sunset, the sun's light is squashed into a flattened disc by atmospheric refraction. The light from the sun near sunset therefore acts like it came from a light source that is more extended in the horizontal direction than in the vertical direction. Looking closely at the shadow of your hand near sunset, you can see that it is more blurry in the horizontal direction than the vertical, proving that the blurry nature of everyday shadows is caused by the sun being an extended source.
Diffraction can also cause shadows to be blurry, but the effect is more rare in everyday life (stated more carefully: diffraction itself is common in everyday life, but diffraction causing the blurriness of shadow edges is less common). Diffraction is a wave effect where waves are able to bend around the corners of obstructions. First of all, diffraction is a weak effect that depends on the wavelengt of light. The wavelength of visible light is on the order of hundreds of nanometers. As a result, simple edge diffraction, such as would make shadow edges blurry, happens on a very small scale. Diffraction effects can be amplified if very small structures are used, such as diffraction gratings or fog droplets. But at that point, you are not really producing shadows anymore, but are producing complex diffraction patterns. As far as shadows go, the diffraction effects of everyday objects on visible light are largely too weak to notice. Secondly, diffraction is a coherent effect that typically requires a nearly monochromatic beam such as a laser beam in order to become significant. Sunlight contains many colors that all diffract differently, so that the net effect, as far as shadows are concerned, is that the diffraction effects wash each other out.