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Greetings:
Reference: F. A. Jenkins and H. E. White,
Fundamentals of Optics,
McGraw-Hill, 1950
Your question goes to the heart of why we need international
standards. Back in
the middle ages the size of the kings foot was how long a foot was
resulting in
every kingdom having a different unit of length. If something valuable
was
measured by length, such as cloth, then it was best to have a king
with a small
foot. The same is true for other archaic units of measure such as
candlepower and
candles. The wax, wick, size parameters can all be different and each
candle would
give a different answer. Also the temperature of the candle flame and
color
(wavelength distribution) are related key parameters that determine
how bright
candles are. When electric light bulbs were invented in the late 1800s
they rated
the brightness relative to candles just as steam engine manufacturers
rated there
engines in horse power. As you well know there also are many different
sized
horses. So what is a horse power? Thus an international system of
standard units
came into being to have everyone measure things using the same
standard units.
The standards that you are seeking are part of the science of
photometry. These
standards have metric and English units making it difficult for
students to
understand all of the different names. Just as the here in the U.S.A.
we are still
using yards instead of meters. The bottom line is that the world (at
least the world
of science and engineering) has given up on using candle power and
candles and
that currently the candela replaces the old candle. The candela is the
luminous
intensity, in a given direction, of a source that emits monochromatic
radiation of
frequency 540 x 10^12 hertz (a green laser) and that has a radiant
intensity in that
direction of 1/683 watt per steradian. References about the history
and how we
currently measure one candle power ( luminous intensity) today are
based on the
work of the National Institute for Standards and Technology (NIST)
http://www.physics.nist.gov/cuu/Units/index.html http://
www.physics.nist.gov/cuu/Units/index.html
Your question asks about white light sources and in that case the
candle power,
the candle and the candela are all equal to one lumen per
steradian.
There are 4 times Pi steradians in a sphere. If you are not familiar
with working
with steradians as solid angles we can convert the standard to square
degrees.
There are 41,252.96 square degrees in a sphere. Divided by 4 times Pi
that gives
3,282.81 square degrees per steradian. Thus a candle power (CP) =
one
lumen per
3,282.81 square degrees or inversely , 304.6 x 10^-6 (0.0003046)lumen
per
square degree per candlepower. As you can see a one CP is a very
weak
light
source.
Because a flashlight or spotlight is an extended light source (the
diameter of the
reflector or lens) not a point source, it is possible, but difficult
to calculate your
answer. However, experimental measurements will probably give a better
answer.
All that you need to know are the number of square degrees that the
flashlights
illuminate at a distance of 12 feet and 60 feet from the light source.
If the beam
spots are round (a cone of light) then you can measure the diameter of
the beam in
degrees from the light source and calculate the number of square
degrees from Pi
times the diameter (in degrees) squared divided by 4.
To calculate the CP at each location first calculate the number of
lumens from the
flashlight
divided by the number of square degrees in the spot. This gives the
number of
lumens per square degree. Then divide by divide by 304.6 x 10^-6
(0.0003046)
lumens per
square degree per candle power to give the total candle power.
The problem with this measurement or the aperture calculation is that
the light
flux in the spot or in the aperture of the flashlight is not uniform
across the beam
diameter. So which beam diameter do you use? My flashlight has a 30
inch (12 degrees)
diameter beam at 12 feet with a 10 inch diameter (4 degrees) bright
spot
(the filament)in the center.
Using your 125 lumens and the 4 degree hot spot cone angle (113 square
degrees)from my
flashlight optics gives 32,567 CP. The 12 degree cone angle (12.6
square degrees)results in
3691 CP.
However, not
all of the lumens are in the hot spot. If you could measure the number of
lumens in the
hot spot then
you could calculate a more accurate value for CP. I wonder which spot
diameter
spotlight manufacturers use?(probably the greatest CP, that is why we
calculations. As you can see from my example a number for CP is subject
wide variability while
the number of lumens in a beam is much more accurate.
Best regards, Your Mad Scientist
Adrian Popa
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