I teach physics at a community college, and due to the covid-19 epidemic, we're developing a lab kit for our students so that they can do labs at home in the fall. It's challenging but also kind of fun to try to figure out labs that are good educationally and give decent results, while also staying within our budget of $200 per student. For an activity in which the students investigate polarization and Malus's law, I found a technique that gives nice results, which involves photographing an image on an LCD screen and adjusting the orientation of a polaroid film until brightness A on a computer screen, seen through the filter, appears the same as brightness B. To avoid issues with the gamma correction of the screen, I use speckle patterns rather than the monitor's grayscale, and take the photos from far enough so that the pixels aren't resolved. The technique can actually be done without any electronic devices at all (eye instead of camera, printout instead of computer screen), but I got the best results using the photography technique. The vast majority of our students own both a laptop and a smartphone.
When I did the technique myself using a webcam to photograph my LCD monitor, the big issue I ran into was that the webcam's sensitivity was wildly mismatched to the extremely bright monitor. Through the camera, black on the monitor looked indistinguishable from white. I overcame this by screwing together a stack of neutral density filters to make 7 f-stops worth of attenuation, or about a factor of 1/100.
Even with the monitor's hardware controls set to minimum brightness, it was still much too bright without the filters. Although my webcam does allow software control of its brightness, that didn't seem to help enough either.
My question: is there some way to improvise a filter about this dark, either from very cheap materials that I could include in the kit or from household objects that my students would be likely to have? It can be lousy optical quality -- in fact, if it helps to blur out the pixels, that's a plus.
I tried placing one lens of a pair of sunglasses in front of the webcam (which made the webcam look really cool), but that only seemed to give about 1-2 stops of dimming. Looking around the house for colored plastic, most of what I found, like the lids of tupperwares, was either much too transparent or totally opaque. I did notice a jug of olive oil that looked promising, but I didn't want to cut it up.
I tried using a pair of crossed polaroids, and although it was easy to get about the right attenuation, this is unfortunately incompatible with the physics point of the lab -- it adds two more polarizers to the stack, which changes the math.
I did find a commercial product, described as a "gel sheet," that might work. They'll sell you a 21"x24" piece of ND1.2 (4 stops) for $23. This would probably work, with students possibly stacking two pieces to get 8 stops, but would be kind of a hassle to prepare for the kits, because I'd have to cut out 150 pieces for 75 students.
Is there any really simple option that I'm not thinking of, like maybe some substance from the kitchen spread on a piece of plastic, or some other common household item that hasn't occurred to me? Maybe thin onion-skin paper?
[EDIT] I found a couple of things that sort of worked, although they weren't optimal. (1) Put a tiny pinhole in a piece of paper and use it to reduce the camera's aperture. This worked pretty well, giving maybe 5 stops, but I had to position it by hand, and keeping it in position might be hard. (2) I have some poop bags for my dogs that are made of thin, black plastic. A single thickness of this looked like about 10 stops, but the image quality through it was pretty bad.
