Shadow

A shadow is an area where direct light from a light source cannot reach due to obstruction by an object. It occupies all of the space behind an opaque object with light in front of it. The cross section of a shadow is a two-dimensional silhouette, or reverse projection of the object blocking the light.

An astronomical object casts human visible shadows when its apparent magnitude is equal or lower than -4[1]. Currently the only astronomical objects able to produce visible shadows on Earth are the Sun, the Moon and, in the right conditions, the planet Venus.

Variation with time

Shadow lengths change dramatically throughout the day. The length of a shadow cast on the ground is proportional to the cotangent of the sun's elevation angle – its angle θ relative to the horizon. Near sunrise and sunset, when θ=0° and cot(θ) is infinite, shadows can be extremely long. If the sun passes directly overhead, then θ = 90°, cot(θ)=0, and shadows are cast directly underneath objects.

Non-point

For a non-point source of light, the shadow is divided into the umbra and penumbra. The wider the light source, the more blurred the shadow.

If there are multiple light sources there are multiple shadows, with overlapping parts darker, or a combination of colors. For a person or object touching the surface, like a person standing on the ground, or a pole in the ground, these converge at the point of touch.

Shadow propagation speed

The farther the distance from the object blocking the light to the surface of projection, the larger the silhouette (they are considered proportional). Also, if the object is moving, the shadow cast by the object will project an image with dimensions (length) expanding proportionally faster than the object's own length of movement. The increase of size and movement is also true if the distance between the object of interference and the light source are closer. This, however, does not mean the shadow may move faster than light, even when projected at vast distances, such as light years. The loss of light, which projects the shadow, will move towards the surface of projection at light speed.

The projected shadow may appear to have moved faster than the speed of light, but there is no actual physical manifestation moving upon the surface. The misconception is that the edge of a shadow "moves" along a wall, when in actuality the increase of a shadow's length is part of a new projection, which will propagate at the speed of light from the object of interference. Since there is no actual communication between points in a shadow (except for reflection or interference of light, at the speed of light), a shadow that projects over a surface of large distances (light years) cannot give information between those distances with the shadow's edge.[2]

Other notes

A shadow cast by the Earth on the Moon is a lunar eclipse. Conversely, a shadow cast by the Moon on the Earth is a solar eclipse.

On satellite imagery and aerial photographs, taken vertically, tall buildings can be recognized as such by their long shadows (if the photographs are not taken in the tropics around noon), while these also show more of the shape of these buildings.

A shadow shows, apart from distortion, the same image as the silhouette when looking at the object from the sun-side, hence the mirror image of the silhouette seen from the other side.

Shadow as a term is often used for any occlusion, not just those with respect to light. For example, a rain shadow is a dry area, which, with respect to the prevailing wind direction, is beyond a mountain range; the range is "blocking" water from crossing the area. An acoustic shadow can be created by terrain as well that will leave spots that can't easily hear sounds from a distance.

Mythological connotations

An unattended shadow or shade was thought by some cultures to be similar to that of a ghost, a flicker of a life unable to end for some reason.

It is also believed as an alternative construct that shadows are in fact a representation of God's presence around an object; like a halo. Early eastern beliefs also play to this theory. For example, Vishnu (a prominent Hindu god) would appear to help followers by assisting with tasks by lending some of his extra arms to assist the burden of the person.

Quote

The brighter the shining of the spiritualized personality (the Father in the universe, the fragment of potential spirit personality in the individual creature), the greater the shadow cast by the intervening mind upon its material investment. In time, man's body is just as real as mind or spirit, but in death, both mind (identity) and spirit survive while the body does not. A cosmic reality can be nonexistent in personality experience.