The diagram to the right shows a mirror. On the diagram, draw a dotted line representing the normal to the mirror's surface. Justify your answer.
Conceptual physics covered ray optics as the first topic of the year, back in September. We then moved on to waves, and to circuits. Part of the reason for this sequence was because these are easier topics than the typical kinematics and forces opening gambits. I want freshmen to adjust to boarding school life a good bit before I hit them with the hard stuff. But the more important reason for this sequence is that it's not sequential at all.
Kinematics and forces are self-referential. It's important to internalize a definition of acceleration, which is used in every context imaginable. Many force problems require kinematics to solve fully, and vice versa. Then in whatever topic is next -- usually either energy or momentum -- it's assumed that students are comfortable with forces and motion.
This approach works fine with my seniors, because they usually are in fact reasonably comfortable with forces and motion by the time I move on; and because even the slower students have enough background that they can become comfortable. Seeing forces and motion in new contexts provides extra practice and encouragement to review previously-discussed physics.
Freshmen, though, can be absent mentally for much of our first trimester. It's not that they don't want to do well -- just the sheer overwhelming nature of life without mom and suddenly with 400 siblings, coupled with the rate at which they're growing physically and mentally, can mean they don't remember information day to day, or even minute to minute. At the senior level, I'm assuming a level of personal organization, daily focus, and self-driven practice that freshmen can simply not fathom.
We just gave our first cumulative trimester exam. Some did great; some did terrible. My point here is, how they did this trimester doesn't matter that much to the students' overall success in the course. When we move on to kinematics after Thanksgiving, it won't make any difference at all whether they remember whether light bends toward or away from normal. I don't HAVE to go over the exam, I don't have to review anything; we can move on to new and different stuff, knowing that everyone can understand it in isolation from the first trimester. Then I can sprinkle some review in over the course of the next six months in preparation for the final exam in June.
The question at the top of today's post shows one of the "justify your answer" questions on the trimester exam. We've learned that the "normal" is "an imaginary line perpendicular to a mirror's surface," and we've extended that definition in the context of refraction across a boundary between materials. This question requires the student to recognize that the normal is not perpendicular to the bottom of the page, but rather to the optical instrument in question; the justification just requires some statement of the definition of normal.
So why do I ask this question on the exam? Because it is the ONLY question I can think of that is truly cumulative with other topics we will be teaching this year... when we get to "normal forces," we'll have seen the word before; and we'll even have seen an explicit situation when the normal is at an angle to the vertical.