MadSci Network: Physics
Query:

Re: Converting lumens to candlepower

Date: Tue Apr 10 15:43:32 2001
Posted By: Adrian Popa, Director Emeritus, Hughes Research Laboratories
Area of science: Physics
ID: 986426234.Ph
Message:


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 see adds for million CP spotlights). Also, atmospheric losses are not considered in the
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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