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:
- As the power increases the spectrum produced by the filament shifts to a more sensitive region of the photodiode, and
- 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?