After a diffraction problem on our recent, I asked students to explain why the bright fringes even occur. The quotes below included diagrams not shown (which made them even strong), but you can get the gist of student explanations from what they have written. These were definitely the strongest in the bunch.

Strong Examples:

“Bright Fringes are caused, because when the laser light passes through the diffraction grating, it can be treated as a wave. The slit is so narrow that the wave spreads out in a circular pattern toward a screen., and all of this happens in multiple locations on the grating. Along the screen, where the wavelengths of light meet correctly–where they’ve traveled a difference of an integer number of wavelengths (meaning the path difference is a whole number of wavelengths), there is constructive interference. At places where the path difference is  m + 1/2 wavelengths, there are dark spots caused by destructive interference. This destructive / constructive interference can happen in multiple places, so you get a pattern of bright and dark fringes.”

“When light passes through the small slits (they sit side-by-side), the light wave spreads out from each slit in circular patterns. All of this happens right on top of each other so that the waves interference with each. It gets kind of crazy. At places where all the waves land in phase–when one crest occurs will all the other crests for example,  the light waves amplify each other to create a bright fringe. Because there are lots of slits in a diffraction grating, these bright fringes occur more and more infrequently the further you go away from the central bright fringe. They are also very thin–constructive interference only happens in a very precise location. What happens more commonly, on the other hand, is that destructive interference occurs. Because of the many wave fronts overlapping from different slits, they are much more likely to be out of phase, thus creating large sections of dark regions between the bright ones.”

“The bright fringes are caused by constructive interference of the light waves. When the waves are in phase, their crests and trough lines up causing constructive interference. This is a wave property of light. As the waves pass through the slits, they diffract away from grating in spherical wave fronts. When waves from one slit have traveled a certain number of wavelengths, they constructively interfere with waves that came from other slits that have traveled “m” number of wavelengths (m being whole number). When all the waves constructively interfere, the amplitudes of the wave is increased dramatically, making intensely bright fringes.”

—–

Slightly weaker ones usually had nothing incorrectly said, but may have had idea of constructive / destructive but not clearly linked to path difference and wavelengths. Or a student might have commented on the importance path difference and wavelength, but not linked to the mechanism of constructive interference clearly.

The weakest ones without incorrect information might just have said, “constructive interference”, or mentioned something vague about wave-like behavior with out details.

The incorrect ones almost almost always mentioned either refraction (I think confusing refraction with diffraction/interference) or mentioned something about how only certainly rays make it through the slit (confusing I think with discussion of a pinhole camera, how rays are blocked from entering the camera).

——

I didn’t, but I’d like to assess these explanations using something similar to PSET (clarity, completeness, correctness), so that simply saying the word, “constructive interference” would might get less credit than a thoughtful attempt to explain using refraction.

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.