# Converging Lenses

Lots of refinement needed, but this overall was a good day:

1. We started with some prompts to qualitiatively explore real images formed with a converging lens. We use optics kits from pasco, which are nice because it’s all magnetic and easy to use. Students found an image with object far away, noting orientation, relative size, relative location, and explored how that changed. Guiding questions helped focus their exploration, including one prompt to find where image and object appear about same size. Student observations went in their notebooks and we discussed key relationships we had seen.

2. Then there was some brief Direct Instruction about Converging Lenses, followed by an example of ray tracing to locate an image (no equations).

3. Students were prompted to use a ray diagram to predict where an image would form with their setup, and then check their prediction.

4. Getting Quantitative. I put up a graph of image distance vs object distance, and included two data points we had seen: one where we had seen the image size equal object size and the one students had predicted using diagrams. Each group was given a data point to think about (object distance), and a sticker. They were asked to discuss where on graph they expect to their data point to end up.

At first our graph looked sort of like a “V”. I prompted groups to find a point that they disagreed with and to explain why they think it’s wrong and where they would move it to and why. We had two lines of reasoning: some based on our qualitative exploration, some based on ray diagrams.

After first round of changes our graphs looked like a line with negative slope, but with one point very clearly not on the line, showing a much more drastic change as the object position got small.

I can’t remember my exact prompt, but goal was to get them thinking about whether we expect the trend to follow a line or not. A big idea emerged:

An object at the focal point can’t create an image, because the Rays come out parallel and will never form a point.

I gave some space to this idea, making sure it was understood, but also helped usher this idea toward infinity/asymptote like ideas. After much discussion, we adjusted our points to reflect the vertical asymptote idea.

5. Each group was then tasked with taking data and adding it to our graph. We took a brief break. Over the break, a few students were debating whether or not a horizontal asymptote existed and whether it was at 0 or focal distance.

6. After break, students recorded the collective data in lab notebooks, and I gave some direct instruction on the Thin Lens Equation. This needs to be done better, with more students exploring graph properties and less me showing. Anyway, we ended up modeling the data and finding a focal length that was within 1 mm of advertised focal length.

7. Students were then given some practice problems with the thin lens equation. If I did this again, I would ask groups to change to a different lens, and use both ray tracing and thin lens equation to predict something. This time probably to predict object location of you want an image to appear somewhere. Or maybe ask them to determine an unknown focal length.

8. I ended the day by working an example with a virtual image (magnifier), both diagramming and using thin lens equation. This led to an introduction to sign conventions. We practiced those conventions with clicker questions.

That was 3 hours full of stuff: exploring phenomena, predicting using ray tracing, predicting and discussing expected data trends, collecting and analyzing data, intro and practice with the thin lens equation, and then clicker questions to crystallize new information.