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In traditional optics education, shadows are often regarded as a mere triviality, namely as silhouettes of obstacles to the propagation of light. However, by examining a series of shadow phenomena from an embedded perspective, we challenge this view and demonstrate how in general both the shape of object and light source have significant impact on...
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... transformations of shadow images can be discovered in everyday life [13,14]. Figure 5 shows a bouncing ping-pong ball illuminated from above by a rod light. Whenever the ball's distance from the ground increases, its shadow stretches in a direction determined by the orientation of the rod light: the shadow becomes the dark image of the latter. ...
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... This pinhole projects a pinhole image of the lighting situation onto the second semi-transparent screen. The pinhole image then displays what is visible from the respective pinhole position while moving the first screen through the caustic body [19]. Within the strongly illuminated region (figure 8(a)), three images are perceived (figure 11, positions 1-5), while outside this region only one image is visible (position 6). ...
... than gives the eye caustic. (19) yields intricate yet analytical mathematical expressions. For the particular case of R = 7.5 cm and n = 1.54, figure 16 shows the caustic curves for different values of the eye distance a. ...
... When interpreting the caustic as a light caustic, we substitute a with object distance g. If we set j = π/2, (19) gives the caustic focus coordinate as (5). ...
Lens phenomena, such as caustics, image distortions, and the formation of multiple images, are commonly observed in various refracting geometries, including raindrops, drinking glasses, and transparent vases. In this study, we investigate the ball lens as a representative example to showcase the capabilities of Berry’s eye caustic as an optical tool. Unlike the conventional paraxial approximation, the eye caustic enables a comprehensive understanding of image transformations throughout the entire optical space. Through experimental exploration, we establish the relationship between the eye caustic and traditional light caustics. Furthermore, we provide mathematical expressions to describe both the caustic and the image transformations that occur when viewing objects through the ball lens. This approach could be of interest for optics education, as it addresses two fundamental challenges in image formation: overcoming the limitations of the paraxial approximation and recognizing the essential role of the observer in comprehending lens phenomena.
The inverse-square decay law of illuminance of a point light source with distance is a common notion of basic optics theory, which is readily demonstrated to be a direct consequence of the propagation of spherical wave fronts with centre at the light source. It is far less common to address the experimental verification of this law and, even less, to study the illuminance decay with distance of extended light sources, which represent somehow an unknown topic. We propose a scientific experiment where the light sensor of a smartphone is used to collect illuminance data as a function of the source-to-sensor distance and orientation. Through this procedure, students can realize the limit of validity of the inverse-square law and determine the luminance flux of the chosen point-like light source (e.g. the white LED flashlight of a smartphone). More interestingly, when dealing with extended sources (e.g. the LCD of a laptop displaying a white image) subtle characteristics of the decay trend emerge, particularly for distances lower that the source size. A detailed analysis of these characteristics is presented though a process allowing student engagement in a real scientific investigation, envisaging steps of data acquisition through experimental measurements, model construction on the basis of the observed patterns, and finally model testing. We provide a guided formulation for the general modelling of planar emitters, starting from the theoretical treatment of Lambertian sources. In this way, students are able to quantify the luminous emission also for extended sources and their deviation from a Lambertian behaviour.
We introduce an approach for three-dimensional full-colour non-line-of-sight imaging with an ordinary camera that relies on a complementary combination of a new measurement acquisition strategy, scene representation model, and tailored reconstruction method. From an ordinary photograph of a matte line-of-sight surface illuminated by the hidden scene, our approach reconstructs a three-dimensional image of the scene hidden behind an occluding structure by exploiting two orthogonal edges of the structure for transverse resolution along azimuth and elevation angles and an information orthogonal scene representation for accurate range resolution. Prior demonstrations beyond two-dimensional reconstructions used expensive, specialized optical systems to gather information about the hidden scene. Here, we achieve accurate three-dimensional imaging using inexpensive, and ubiquitous hardware, without requiring a calibration image. Thus, our system may find use in indoor situations like reconnaissance and search-and-rescue.
