# Non-linear relationship between power supplied and perceived brightness in a filament lamp?

I was expecting the relationship between these two to be linear, but after conducting an experiment my data fits almost exactly on the curve, $y = 2800.2 x^{2.0173}$, where $y$ is the brightness in Lux and $x$ is the power supplied in Watts.

Is this due to some property of filament lamps which I have missed, or is my data simply inaccurate?

• This is probably because your filiment lamps are non-ohmic (meaning that voltage and current are not proportional, the fact used to correlate power and brightness). In general, most lightbulbs are non-ohmic resistors. – Cicero May 27 '15 at 23:02
• How did you measure perceived brightness? If you used the visible spectrum, the increasing temperature as the power goes up will shift more of the output into the visible. If you measure total output over the whole spectrum, the relationship should be linear. – Ross Millikan May 28 '15 at 4:22
• @RossMillikan Thankyou! I used a photometer, which I believe only measured light emitted in the visible spectrum, so that may well be why my readings turned out non liniear. – user3129805 May 28 '15 at 14:01
• @Cicero perhaps I'm missing something, but it appears to me that the non-ohmic nature of the filament would in fact mean that the resistance is increasing as power increases, meaning that my graph's gradient should have been decreasing rather than increasing as power supplied went up – user3129805 May 28 '15 at 14:17
• The increasing resistance should not be a problem if you truly measure power in. It takes more voltage to push a given current, but power in should equal light out as long as you measure all the radiation. – Ross Millikan May 28 '15 at 15:14