Name: Matthew T.
I have recently performed an experiment measuring the lux
of a 12 volt, 36 watt, axial tungsten filament lamp with respect to
distance and found a rather strange result. Instead of the expect curve
of 1/R squared over the first 6 cm the lux actually increased before
following the expected path. I have ruled out error and my best theory
is that the opposite side of the bulb from the one I was measuring was
acting as a concave mirror thus creating a focal point. I would be
grateful if you could offer your opinion on the matter.
I like your theory. That 1/R^2 business presumes a point source, and
you have to get well away before this bulb is going to start looking
like a point source.
Lamps are often designed with specific applications in mind. It is quite
possible that the one you are using has a back-reflecting surface by design,
i.e., it reflects backward-going photons in the forward direction. Or the
glass enclosing the filament has focusing ability (as in spot lighting lamps).
If a lens or mirror is involved in your lamp, the 1/R^2 relation will not
apply. Also, if the filament is large, the 1/R^2 will not be accurate unless
one moves sufficiently, say 5 to 10 times the filament size, away from the
You can find out what is going on by measuring the spatial distribution of
flux at a few values of R. Specifications of a particular commercial lamp can
also be obtained from the manufacturer.
Ali Khounsary, Ph.D.
Advanced Photon Source
Argonne National Laboratory
I appreciate your surprise! What has happened to the laws of optics? Your
explanation may well be true, and there is a way to test it. If you estimate
the radius of curvature (R) of the lamp's rear surface, assuming it is
spherical and concave, you can easily calculate the focal length (f): R/2 =
You can then make a "ray diagram" to see if light from the filament
reflected of the rear of the bulb would come to a focus where you see the
light's maximum intensity. If you get really fancy you may have to make a
thin lens correction for the light passing through the front surface of the
bulb too, but I think it won't be necessary. There are many web-sites, and
texts on optics that can walk you through the calculation. One for example,
Your evaluation is a very much possible. Another option is the detector
itself. The detector may have a maximum reading. As the lux approached
this maximum, the detector reading "levels off". Until you were 6 cm away,
it is possible that the detector was receiving too much light. One more
possibility is the length of the filament vs the size of your detector. If
the detector is much smaller than the bulb filament, or if the detector can
only receive light from one direction, the detector may not have been able
to see the entire light until about 6cm away.
One way to test these theories is by adjusting the setup. If turning down
the voltage on the bulb, reducing the lux, moves the peak of the curve
closer to the bulb, it is likely that the detector has a maximum. If
rotating the bulb to make the filament "look shorter" to the detector moves
the peak closer without affecting longer-distance data, it is probable that
the entire filament was not seen. If such a move does affect longer-distance
data, reflection is the more likely culprit.
Dr. Ken Mellendorf
Illinois Central College
We do not have an explanation of your setup but your explanation sounds
reasonable. You did not indicate how much it increased in the first 6
cm. You could get as much as 7 or 8% reflected at the bulb envelope.
Have you looked at the radius of curvature to see if the focal length
is reasonable? Have you tried measuring the Lux above the bulb?
Presumably you wouldn't have the reflections focusing from the base of
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Update: June 2012