In the conventional approach to lens imaging, rays are used to map object points to image points. However, many students have a need to think of the image as a whole. To answer this need, lens imaging is reinterpreted as a superposition of sharp images from different viewpoints. These so-called elemental images are uncovered by covering the lens with a pinhole array. Rays are introduced to connect elemental images. Lens ray diagrams are constructed based on bundles of elemental images. The conventional construction method is included as a special case. The proposed approach proceeds from concrete images to abstract rays.Although the students' holistic approach seems naïve, we can find a kernel of truth in it by treating Kepler's ray drawing as an ambiguous image, see Fig. 1(c): Once we switch our attention to rays that go through a single point on the lens, we see that these rays represent a refracted camera obscura projection, cf. [22]. Thus, each point on the lens produces a whole image. Images from different points on the lens represent different views [22][23][24]. This multi-view approach allows us to take the students' preconceptions seriously: We may consider rays as connections between camera obscura images, as in Fig. 1(c).Accordingly, I will use this multi-view approach to build a bridge between the students' holistic approach and the scientists' point-to-point approach. First, I present experiments that allow students to observe the camera obscura images and their superposition. Then, I will simulate lens imaging as a superposition of multiple views. Afterwards, I introduce rays as connections between the camera obscura images. Finally, I propose a method for constructing lens ray diagrams based on these images.
Observing elemental images and their superpositionEach of our eyes has a lens, so we will start with that. Facing a varied background, hold a pen about 30 cm in front of you. Close one eye. With the other eye, try to get a sharp image of the pen and the background simultaneously. It is impossible: If the pen appears sharp, the background looks blurry, and vice versa [25].