Experimental evidence that brightness depends on power

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 e^x 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.