Kelvin = Color temperature is a characteristic of visible light. The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of comparable hue to that light source. The temperature is conventionally stated in units of absolute temperature, kelvin (K).Higher color temperatures (5,000 K or more) are called cool colors (blueish white); lower color temperatures (2,700–3,000 K) are called warm colors (yellowish white through red).
Photosynthetically active radiation, often abbreviated PAR, designates the spectral range (wave band) of solar radiation from 400 to 700 nanometers that photosynthetic organisms are able to use in the process of photosynthesis. This spectral region corresponds more or less with the range of light visible to the human eye.
OK so kelvien and PAR are measurements of visible light…
The visible spectrum is the portion of the electromagnetic spectrum that is visible to (can be detected by) the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nanometers
Nanometers
280 nm — near ultraviolet wavelength
380–420 nm — wavelength of violet light
420–440 nm — wavelength of indigo light
440–500 nm — wavelength of blue light
500–520 nm — wavelength of cyan light
520–565 nm — wavelength of green light
565–590 nm — wavelength of yellow light
590–625 nm — wavelength of orange light
625–740 nm — wavelength of red light
700–1400 nm — Wavelength of near-infrared radiation
Phosphors are transition metal compounds or rare earth compounds of various types. The most common uses of phosphors are in CRT displays and fluorescent lights. Phosphor layers provide most of the light produced by fluorescent lamps, and are also used to improve the balance of light produced by metal halide lamps. Various neon signs use phosphor layers to produce different colors of light.
What does this all mean… Well the lights we buy that have labels telling us the Color temperature in Kelvin are selling to people that want to know the color of visible light the bulb produces and nothing more. Because we know that a Phosphor layer can be added to a bulb to change the Color temperature the (light we see) we can't know if a light bulb produces the right wavelengths of light with high enough intensity to make are corals grow fat and happy.
So you go and find out the PAR spectrum of your light bulb how do you know if the coral you keep will do well under this bulb any way? Well I really don’t know, but nether do most of the people that wright reef books. Most just assume that the light that can be measured at the depth the animal is found in the ocean is the light the animal needs. Well that’s good enough for me.
By knowing how deep the coral is found and the spectrum of light in Nanometers found at that depth we can determine if a given light bulb will be good to use. By knowing the PAR spectrum of a light bulb you will know the intensity of each color in the spectrum of the bulb.
