Relax your eyes and focus on a faraway object, like a light fixture on a wall. Holding your arms straight out towards the fixture, point your forefingers towards each other and slowly bring them together, while still staying focused on the distant object. Oops! Did you just dismember your fingers and created a floating sausage?

This phenomenon has to do with binocular vision, the ability of the brain to fuse slightly different images into a single one to create depth. In our middle school science studio class this block, we have been exploring how depth cues can be manipulated to trick our eyes into "seeing" impossible objects. For instance, we've drawn Penrose triangles, rectangles, and other polygons as part of our discussion of 3-dimensional illusions. We've examined old View-Master toys, which use stereo vision to recreate depth from two pictures. A student brought in a stereoscope that fuses mathematical line drawings into 3-dimensional objects like an icosahedron, and we have created pseudoscopic images, which alter depth perception in surprising ways by swapping the left and right eye images. The simplicity of the foldable stereoscope prompted our class to design our own, and we will soon have a newly designed set made by the students themselves, using convex lenses and cardstock.

In addition to exploring depth perception, we have continued working on extended projects that we started last block. Some students are building a physical model of a pseudoscope, a device built with plane mirrors that can be used to view everyday objects with reversed depth perception. Several students are delving into strobe photography with a lab-made strobe that we will use in the physics class to study the motion of objects that move extremely quickly, and they have conflated their project with others who are exploring persistence of vision. Another group of students is working hard on building a parabolic reflector, refining their design, and devising a simple mechanism to track the sun. In the process, they are investigating some geometrical aspects of the solar system, and how to change the angular elevation of the mirror.

On the pedagogical front, we have adopted an online forum to discuss the assigned readings, and we have changed the homework assignments to include conceptual questions that stem from class investigations. There has been much activity and humor in the online discussions, and students have been answering each other’s questions, clarifying doubts, and adding their own observations outside of class. The questions on their homework now bear tags that help students make connections to what they have learned before and reflect on their thinking as they ponder a problem. As we move forward, this will help the students understand the context of the questions and their relationship to the class activities, and consolidate overarching physical principles behind the phenomena we are studying.

— Kaushik Basu