Measurements of light intensity are reported in a somewhat bewildering
array of units, which makes things tough to sort out at first. The
first thing to know is that when dealing with measurements of light
intensity, there are two types of units: photometric units, which are
measures of *visible* light intensity, and radiometric units, which
are measures of the total electromagnetic energy (including those
wavelenghts that the human eye is not sensitive to). "Lux" is a
photometric unit that takes into account the sensitivity of the human
eye to different colors (wavelengths) of light. See
http://www.physlink.com/Education/AskExperts/ae409.cfm.
The total energy emitted by a light source per unit time is measured
in units of power and is called either the "radiant flux "when all
wavelengths are included, or "luminous flux" (sometimes "photometric
flux") if only the human response to the light is considered. Radiant
flux is expressed in units of Watts, while luminous flux is expressed
in units of "lumens". See
http://www.intl-light.com/handbook/flux.html. When talking about the
sun or stars, scientists use the term "luminosity" to refer to the
total radiometric power emitted by the the object. The sun's
luminosity is about 3.9 * 10^26 Watts. Empirically, the masss and
luminosities of stars are correlated, and the luminosity for "typical"
stars (what are called "main sequence" stars) varies as the the mass
raised to a power somewhere between 3 and 4 (usually taken as
luminosity ~ M^3.5). See
http://csep10.phys.utk.edu/astr162/lect/binaries/masslum.html.
Another way to describe the amount of light given off by a source is
in terms of "radiometric intensity" or "luminous (or photometric)
intensity", which is defined as the flux (see above) per unit solid
angle. Intensity, therefore, has units of power per unit solid angle;
Watts/steradian for radiant intensity, or lumens per steradian for
luminous intensity. One lumen per steradian is defined as one
candela. See http://www.intl-light.com/handbook/intens.html. There
are 4*pi steradians in a sphere. See
http://whatis.techtarget.com/definition/0,,sid9_gci528813,00.html for
a description of solid angles a the definition of a steradian.
Typically, a light source (like the sun or a star) emits a constant
amount of energy per unit time (more or less). Now, think of a hollow
sphere with radius R surrounding the light, and centered on the light.
All the energy emitted by the light must pass through the surface of
that sphere. As the sphere gets larger, the surface area of the
sphere also gets larger. In fact, the surface area grows as R^2
(formula for the surface area of a sphere is A = 4*pi*R^2). The
amount of energy per unit area at a given distance, R, from a light
source is then the total power of the source (in Watts or lumens)
divided by the surface area of the sphere with radius R. Obviously,
as one gets further and further from the light source, the energy
emitted by the light must be distributed over larger and larger
surface areas, and the "flux density" decreases as 1/R^2. The
radiometric flux per unit area is called the "irradiance" and is
expressed in units of Watts/meter^2, while the photometric flux per
unit area is called the "illuminance" and is expressed in units of
lumens/meter^2. One lumen per square meter is defined as one "lux".
See http://www.intl-light.com/handbook/irrad.html
Finally, one can report the intensity of a light source in terms of
the flux density per unit solid angle. Radiometric measurements are
given in units of Watts/Meter^2/steradian and this measure is called
the "radiance". Photometric measurements are given in units of
lumens/meter^2/steradian, and this measure is called the "luminance".
Unlike flux density measurements given in terms of irradiance or
illumance, the luminance and radiance of a source are independent of
the distance from the source. See
http://www.intl-light.com/handbook/rad.html. |