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Name: Matthew T.
Status: student
Age: 18
Location: N/A
Country: N/A
Date: 2001-2002

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.

Tim Mooney


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 source.

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 = f.

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, is:

Vince Calder


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
Physics Instructor
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 the bulb.

Greg Bradburn

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