Science of Light
The response of the human eye over the visible light spectrum defines the so-called luminosity function or photopic curve. The peak of this curve is in the yellow-green, at a wavelength of 555 nano-meters (nm). The curve shifts toward the blue under very dark conditions (called scotopic or dark-adapted) because of differences in the chemistry of the rod and cone cells in the human retina. Scotopic vision is more blue-sensitive, but it is perceived as a black-and-white image by the human brain, since the rods do not have a means to differentiate color. While scotopic vision is important in observing the night sky and the landscape at night, light measurement (or photometry) is based upon daytime vision or the photopic curve. Light meters are designed with a filter in the optical system which appears green and mimics the photopic response of the human eye.
The manner in which the human eye-brain combination perceives light is important to the aesthetic appreciation of night sky quality. The eye (and other human sensory devices) natural measures in a logarithmic scale, hence the original stellar magnitude scale was logarithmic. That is, objects are seen relative to each other, so if four objects were seen side by side with an actual brightness of 2, 4, 8, and 16, they would be perceived by the eye as 1, 2, 3, and 4 in brightness. This logarithmic response allows the eye to see faint objects without "bottoming out." Visual contrast, as well, is seen in a non-linear manner. Contrast is also dependent on the angular size of the object.
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.
Atmospheric Scattering and Light Pollution
The sky may also appear luminous at night because of light scattered by the atmosphere. When light passes through any medium other than a vacuum, it is subject to reflection, refraction, diffraction, and absorption. The combined effect of these processes is scattering of the original light beam. The atmosphere includes molecules of gases (such as nitrogen, oxygen, water vapor, and carbon dioxide) and suspended solid particles (such as dust, soot, salts, and chemical precipitates, collectively called aerosols). The amount and type of aerosols present, the amount of moisture in the air, and the altitude above sea level are the primary variables determining the scattering that will occur. Even perfectly clear air at high altitude will scatter light to some degree. Scattering of sunlight by air molecules gives the daytime sky its blue color. We describe the air as "hazy" when there is high water vapor or aerosol content;the deep blue color is replaced with a milky white hue, especially near the sun.