A year or so ago, Michael Gray emailed me a wonderful quantitative demonstration idea to show that brightness of a bulb depends on power, not voltage. Basically, he used a light probe to measure brightness directly. When he doubled a bulb's voltage, the brightness didn't double -- the brightness reading quadrupled. And that makes sense, since power is V2/R .
I took the light probe approach a bit further the other day. I asked the class to sketch a plot for the brightness reading in the probe as a function of the bulb's voltage. After some discussion, the randomly chosen student sketched a parabola*on the board. Yes -- since a bulb doesn't change its resistance, and since power is V2/R, a power vs. V graph should be quadratic. And since brightness is correlated with power, the power graph should also be quadratic.
* Though he called it, of course, an exponential. What is it with teenagers that any concave up, increasing function is labeled as "exponential?" Have *you* ever seen an ex in any physics B equation, at least since half-lives were taken off the exam a decade ago, and besides that was e-x? Should I stop ranting now?
And so I turned out all lights, held the probe about 10 cm above the bulb, and increased the bulb's voltage at a constant rate (by turning the dial approximately uniformly). As you can see, I was a bit jerky in turning the voltage knob. But the principle was well-verified -- the brightness vs. time graph was clearly curved.