Radiant energy behaves both as waves, with measurable wavelengths and frequencies, and as particles, or as discrete "packages" of energy, called photons for visible light. Light cannot be propagated, transmitted, or received in quantities smaller than 1 photon, and a photon of a particular wavelength contains a discrete amount of radiant energy. Light travels at a constant speed of ~3 x 108 meters per second, or 186,000 miles per second, in a vacuum.
Light is usually measured as photon flux, proportional to the number of photons per second striking the human eye or a light meter. Photon flux is called illuminance, and its engineering units are lux (metric) or footcandles (English);both are linear scales. The human eye is capable of observing an extremely wide range of photon flux, from about 6 photons per second of blue light (about 10-9 lux) to brilliant sunlight reflecting off snow (about 104 lux), a range of nearly 10 trillion to one.
In astronomy, illuminance is measured in visual magnitudes, a logarithmic scale similar to decibels for measuring sound, except that the magnitude scale is inverse, where smaller numbers mean brighter objects. The sun has a visual magnitude of -26.7 (producing an illuminance of 108,000 lux) at the top Earth's atmosphere, while the faintest stars visible to the human eye without optical aid are about magnitude 7.2 (0.000000003 lux). Individual light sources can therefore be measured in terms of the illuminance they produce at the observer's location. Photons leaving the source are subject to the inverse square law for radiant energy. This law states that the energy reaching the observer varies at one over the square of the distance to the source.
Energy = Intensity / (Distance from the observer)2
Therefore, doubling the distance will result in one-quarter the illuminance from the same source. Astronomical objects such as the stars are so far away that their illuminance does not change measurably even as Earth moves around the sun. The planets, however, vary in brightness primarily because of the inverse square law. The sun and moon are also subject to small but measurable variations in apparent brightness because of variations in distance from Earth.
Light sources on Earth, however, such as street lamps, obviously produce much more illuminance as an observer gets closer to them. When outdoor light at night escapes from its intended use, and is observed directly, it creates light trespass, a form of light pollution, especially in a natural landscape like a national park. These bright objects are very noticeable, even at a great distance. For example, a typical streetlamp produces about 5 lux of illuminance immediately beneath it (let's say 5 meters away), in the area intended for its use. If the lamp is unshielded and emits light equally in all directions, an observer on the landscape 100 times more distant (500 meters or ¼ mile) away will be illuminated by the lamp according to the inverse square law:
Energy = 5 lux / 1002 = 0.0005 lux
This seems like a small amount, but the crescent moon produces only 0.01 lux, and the planet Venus at its brightest produces 0.0001 lux of illuminance. Therefore, this single unshielded street lamp seen from 500 meters away would be brighter than any natural object in the night sky other than the moon. Also, a small, bright source of light will impair dark adaptation of the human eye, further restricting the observer's ability to enjoy the natural night environment.