Today I did a quick experiment where I measured the light intensity of a small incandescent bulb for a range of voltages (0 to 31V). I also measured the current. I expected to see the light intensity increase linearly with the power but what I found was much closer to a direct variation between intensity and power squared.

As the power increases, the temperature of the filament increases and the range of wavelengths it produces shifts from all infrared to a mix including shorter and shorter wavelengths of visible light. The light sensor uses a Hamamatsu S1133 silicon photodiode which approximately the same spectral response as the human eye. (Chart attached below.)

A assume what's going on is:

  1. As the power increases the spectrum produced by the filament shifts to a more sensitive region of the photodiode, and
  2. As the power increases more radiation is produced at any given wavelength.

Is it just a coincidence that these two effects combine to produce a pretty linear $I$ vs $P^2$ graph or is there something else going on?

parabolic looking graph of Illumination vs. power

fairly linear looking graph of illumination vs power squared

spectral response graph of S1133 silicon photodiode

  • $\begingroup$ I vote for coincidence. I like your two explanation points, and would also throw in other modes of dissipating heat from the filament, like conduction and convection within the bulb. $\endgroup$ – Duncan Harris Apr 5 at 2:58

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