We're starting the year in conceptual physics with geometric optics. On the very first day, we'll set up a mirror and a ray box. The class together will measure a bunch of angles of incidence and reflection, and we will together graph θr vs. θi. We'll set up both axes from zero to ninety degrees, and show that we get a straight line. We'll show from the graph that, say, doubling the incident angle also doubles the reflected angle. No slopes, no calculations, just graphical experimental evidence for the law of reflection.
The next week, we'll use the ray box to shoot light into a plastic block. We'll set up the same axes, and this time graph refracted vs. incident angle for light refracting in the block.
Now, in AP physics, we'd make a new graph of sin θi vs. sin θr; the slope of that line would be the index of refraction of the plastic. But this year I'm not teaching AP physics. This is ninth grade conceptual physics. So what are we doing? And why are we doing it?
Well, I will certainly spend about five minutes asking students to predict what the θr vs. θi graph might look like. I'd be happy if anyone recognizes that the data won't ever approach 90 degrees on the refracted angle axis. But prediction is not really the essential issue. My goals for this experiment are:
(1) Establish norms for data collection. This is a simple experiment. I showed my nine-year-old how to do it just once, and he collected data without my help. So there's no reason we shouldn't be able to acquire data quickly, accurately, without asking a bazillion questions. I will go around the class and hurry them along, teaching them not to second-guess data, not to be overly precise... and importantly, to collect data rather than argue with the partner. It's also a good experiment with which to establish the rule that since no one is leaving early or doing work for another class, we might as well take as many data points as humanly possible.
(2) Practice graphing data as it is collected. I recognize that many freshmen will struggle with a skill as simple as graphing data by hand. So I use this straightforward experiment with axes scaled identically on the vertical and horizontal to start practicing. Each partnership will graph data as it is acquired, one graph per group; then I'll show them where they need to collect more data in order to define the shape. When they're done collecting, I'll give them a homework sheet, part of which will ask them to regraph their data on axes that I've prepared. The homework is one graph per person. This way, a partnership can split duties efficiently during lab, but nevertheless everyone will have to physically make a graph.
(3) Make a first stab at interpreting graphs. A novice physics student might think it "stands to reason" that since the angle of incidence vs. reflection was a straight line, the angle of incidence vs. refraction should also be straight. That's not the case. One of the homework questions will ask whether doubling the angle of incidence doubles the angle of refraction as well... just looking at the graph shows that the angle of refraction does not quite double in this case* -- no use of Snell's Law is required at all.
*Okay, for small enough angles, doubling θi does in fact double θr as well. If someone is actually astute enough to point out the small-large angle difference, I'll be pleased, but I'm not expecting that level of analysis.