Modeling Reflection and the Full-length Mirror

Having done quite well as a whole on our shadows, eclipses, and phases assessment before spring break, the physics classes moved on to another light-related topic: reflection.

First task:
     "Here's a ball.  Use it to construct a model of how light changes direction when it reflects off of a surface."

There was some very interesting work here, once everyone stopped considering the "boring case" (dropping the ball vertically onto a horizontal surface).  The biggest challenge was (as is frequently the case) experimental design.  There was lots of ball bouncing in vertical planes to begin with.  This is murderously hard to measure (looking at the angles before an after the bounces), and does that whole parabola thing that we don't really see light do!

Once everyone (literally) got rolling, things went quickly, and the law of reflection was quickly discovered.

We did a quickie whiteboard meeting all together - when everyone quickly came to the same conclusion, presenting it to each other is more than a little repetitive - where we came up with a single conclusion for the class.  I also mentioned that we might want to look at the angle between the normal and the ray, rather than the angle between the surface and the ray, because we'll deal with curved surfaces later, making the surface angle a little harder to measure, and because of this other thing that... well, you'll just need it later, so maybe get used to using this angle instead of the other.

As groups finished early, I put them on the hunt of limitations in our model: what does light do that the ball doesn't? ...what does the ball do that light doesn't?  Just like every other model, this one's an approximation - it gets some things quite well, but you need to be really aware of the things that it doesn't represent/predict well.

It was a great list:

• Light doesn't slow down when it reflects like the ball does
• Light can sometimes be absorbed by the surface, unlike the ball
• Light isn't usually noticeably affected by gravity (good little chat about black holes, gravitational lensing, etc.), unlike the ball
• Light isn't subject to friction/spin effects

We moved on to a challenge/lab next:

     "How long does a mirror need to be in order to be a full-length mirror?"

This was a great opportunity to define the problem, narrowing it down to make it doable, but keeping it broad enough to be useful, considering which assumptions were reasonable, etc.  It was also a chance to talk about doing a pilot experiment.  We had narrowed the task down to considering two variables: the person's height and his/her distance from the mirror.

 

At this point, we could go all crazy taking tons of data and then try to model it.  Instead, we discussed how, in real research, there's a cost to taking data which can be quite high.  For us, the cost is time.  Everybody remembered how much data they took when trying to determine the effect of amplitude on oscillator period, and we talked about how we could've saved that time by just taking a few data points that were well spread-out over the range of possible data, noticed that there wasn't an effect, and moved on.  The kids went off in groups, armed with small mirrors (they had to determine how to use these to determine how long the mirror would be for any given situation) and tasked with doing pilot studies on these two variables.  Some groups came to conclusions, and will refine their methods and take more comprehensive data on the variable(s) that matter, and other groups aren't quite there yet - we'll finish up next time.