Naked Science Forum
Non Life Sciences => Technology => Topic started by: Atomic-S on 12/02/2016 02:30:01
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How does the lumen output of visible light from a standard incandescent bulb vary with voltage applied?
How does the total output, including infrared and ultraviolet, from such a bulb vary with voltage?
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Well, from a basic standpoint, P = V2*R where P is the power of the bulb, V is the voltage applied, and R is the resistance of the bulb (more or less fixed).
The spectrum of the light depends on the temperature of the filament, but for a given bulb, as the voltage is increased, the intensity of the light at every wavelength increases, and the overall average emission gets blue shifted.
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I guess I should have realized that. The total output is simply proportional to the square of the voltage. This assumes of course that resistance is constant, which in actuality it is not because it changes with temperature, and I think is less at lower temperature, so an adjustment for that would be required.
According to https://en.wikipedia.org/wiki/Black-body_radiation, the power per unit area is σT4. But since power is proportional to the square of the voltage (assuming constant resistance), temperature varies as the square root of the voltage. As to how spectrum varies with temperature, Wein's displacement law says that the wavelength of maximum radiance varies inversely with temperature, which is to say, inversely with the square root of the voltage. However, this is not a complete answer because we require not just the wavelength of maximum emission, but the integral of the spectral curve within the visible band, to get the answer for the visible output; and the total power minus that would give the invisible output. This however is starting to become a complicated calculation.
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We also should correct these results, if to be used for analyzing lighting, for the different sensitivity of the eye at different wavelengths, to get an adjusted illumination value for the different spectral distributions. I can see this will not be a simple problem.
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We also should correct these results, if to be used for analyzing lighting, for the different sensitivity of the eye at different wavelengths, to get an adjusted illumination value for the different spectral distributions. I can see this will not be a simple problem.
Yes, like sound level meters are weighted for the response of the ear, light meters for lighting are weighted for the response of the eye.
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I guess I should have realized that. The total output is simply proportional to the square of the voltage. This assumes of course that resistance is constant, which in actuality it is not because it changes with temperature, and I think is less at lower temperature, so an adjustment for that would be required.
According to https://en.wikipedia.org/wiki/Black-body_radiation, the power per unit area is σT4. But since power is proportional to the square of the voltage (assuming constant resistance), temperature varies as the square root of the voltage. As to how spectrum varies with temperature, Wein's displacement law says that the wavelength of maximum radiance varies inversely with temperature, which is to say, inversely with the square root of the voltage. However, this is not a complete answer because we require not just the wavelength of maximum emission, but the integral of the spectral curve within the visible band, to get the answer for the visible output; and the total power minus that would give the invisible output. This however is starting to become a complicated calculation.
It looks like you're on the right track. It is possible to make evermore accurate predictions using evermore complicated models, but perhaps the best approach would be an empirical one. One could procure a variable voltage source, a few different types of bulbs and a light meter (even a spectrometer if your interested in spectral analysis) and spend an afternoon gathering data. Could be a fun project, and not too pricy if you have access to some of the equipment already, or are able to jerry-rig from cheap components.
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Simplest of all, look up the color temperature charts for "photoflood" lamps. These are (or were - I doubt that anyone still uses them) fairly ordinary incandescent bulbs run at higher than normal temperatures, sacrificing life (they rarely ran for more than 2 hours) for color balance, so you could use outdoor film for studio work. I used to run them with a series/parallel switch so I could set up the shot with about 120 volts on each filament (giving a reddish light but adequate shadow geometry) then shoot at 240V to get near-daylight color balance.
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The resistance odf the filament is not fixed- it varies by a factor of about ten as the filament heats up.
[/size]Light output is approximately proportional to V ^ 3.4[/size]Color temperature is approximately proportional to V ^ 0.42fromhttps://en.wikipedia.org/wiki/Incandescent_light_bulb (https://en.wikipedia.org/wiki/Incandescent_light_bulb)