Lerner Physics

I got a little ahead of myself today, but I think it'll all work out okay in the end.

The question my guest blogger was so interested in was what would happen if you only had half a mirror. Would it still work as a mirror? Would you still get an image? I wanted them to see it in real life, but I know it works better with lenses.

So, after we got through some of the refraction homework, we went back into lab, to look at what happens when you cover parts of a lens. They were shocked. A great picture of before and after is shown above.

While we were in lab, we graphed 1/di vs. 1/do for a converging lens. This might have been too much. We hadn't even gone over all of refraction yet. But the graph was so nice, and we were already in lab, and it seemed to make sense at the time.

Hopefully we can make sense of all of it tomorrow. We'll see.

Below is written by a student. I took a personal day. I'm so proud that they debated the answer!

Today's test was a little longer than expected. By the time everyone had finished, there was only twenty minutes left of class to begin whiteboarding. For the first three questions, the class reached a general consensus, using object distance and focal distance to solve for image distance and height. Things took a turn for the last question, as I'm guessing you predicted. We entered little schools of debate, motioning and scribbling to figure out what image, if any, would arise from reflection off of half a concave lens. Yet, as we reached the pinnacle of the debate, we were kicked out by the substitute and left with a number of literal and figurative question marks swimming around the question. We are hoping for some answers (okay not answers, more like insight) on Monday.

We didn't start today with whiteboarding. Usually we do. I wonder, is it a bad idea to start with whiteboarding so often? Is it a good way to make sure we're all on the same page? 

We started instead with a lab. We used the three pin method not to find out how reflection works but what happens when the light enters a new medium. We found the relationship between the angle of incidence and the angle of refraction. It wasn't linear, and it doesn't make sense to square an angle in radians, so we tried some mathematical transformations that make sense for angles.

I'm off tomorrow, so one of my students has promised to be the guest blogger tomorrow. They have a test and some whiteboarding to do. I won't be there to supervise the whiteboards; I'm excited to see how it turns out.

We started today with the six cases of curved mirrors—five for concave mirrors and one for convex mirrors. We learned about the principal rays of light to find where the image will form. Of course, any time I draw mirror diagrams, I have to pull out the concave and convex mirrors. They make weird images!

For the first time of my teaching career, I did a geometric proof of the mirror equation. It looked familiar, but I don't think I saw it since the 1990s. Why did I never do it before? It's so cool. The students who loved geometry loved that proof.

As you can tell, it was a lot of me in the front of the room. I felt it. It was needed and useful, but I remembered why I don't like lecturing.

How long does a plane mirror need to be so you can see your whole body? Where is your image located? We experimented with that today. I realize I should by more long plane mirrors so more people are willing to try it out.

We also looked, in detail, about how light would bounce off a curved mirror. There seemed to be a focal point, where the parallel rays of light would all converge. But what about objects that are not infinitely far away? It was off to lab to collect some data.

We got great data, but then finding a function to model the object distance and the image distance was difficult. I need to find a better way than just guess-and-check until I have to show them the quite-complicated fit.

How do you know light travels in a line? We looked through camera obscuras and drew pictures to understand how the light makes the images we saw. Then we practiced a bit before we moved on to our first test of the ray model of light—reflection. We learned the three-pin method for finding a ray of light that goes through three pins, hitting the mirror at the second pin. We came up with a very simple law for reflection.

We finished standing waves today, for the most part. I had students gone to a concert, and I knew some of the pictures would be difficult to draw, so we did a lot of working in groups today. We also explained the results to our sound lab, and our results came out pretty darn close to what we expected.

When I went around the room today, trying to get a sense of where we were as a class, some students really liked this unit. Students told me that they liked how it applied to music, liked how it seemed to make sense, and liked that they could be successful with it. A few students didn't like the unit, but that came from the fact that it didn't feel like the rest of physics. Well, physics contains lots of different models. You're just going to like the beauty of some models more than others.

How does the Doppler effect work when the source is accelerating? We couldn't really explain it, so I made the Desmos animation above.

We also talked about standing waves. But we found music more interesting. It's so interesting to see octaves and resonance and frequency all interrelated.

What happens when wave pulses go from one medium to another? What happens at the boundary? It took many trials, and this video, to get everyone in class on the same page.

We also talked about what happened when two waves of very similar frequencies occur at the same point in space. Thanks again, Desmos:

We also talked about what happens to the frequency of a wave when the source of the wave is moving relative to the observer.

Last, we started talking about what happens to a wave that is confined to a fixed space. It seemed that, with the bounce at the end, you could get constant constructive interference. Cool!

So, what happens when a wave hits a boundary? We went to lab and saw that pretty quickly.

What happens when two waves overlap? That was more difficult. We went to lab, but we couldn't really see it that well. We had to go to simulations to understand what was going on.

I made an answer key for one of the practice sheets I found in the Modeling materials. I won't post the answer key, for obvious reasons, but I've never made an animated answer key before:

Desmos can be so cool sometimes.