Rethinking Refraction

2000

In computer graphics, it is often an advantage to calculate refractions directly, especially when the application is time-critical or when line graphics have to be displayed. We specify efficient formulas and parametric equations for the refraction on straight lines and planes. Furthermore, we develop a general theory of refractions, with reflections as a special case. In the plane case, all refracted rays are normal to a characteristic conic section. We investigate the relation of this conic section and the diacaustic curve. Using this, we can deduce properties of reciprocal refraction and a virtual object transformation that makes it possible to produce 2D-refraction images with additional depth information. In the three-dimensional case, we investigate the counter image of a straight line. It is a very special ruled surface of order four. This yields results on the order of the refrax of algebraic curves and on the shading of refracted polygons. Finally, we provide a formula for the diacaustic of a circle.

It is generally accepted that mirage is formed when temperature of the ground surface, in a flat area like desert, is higher than the temperatures of the over ground air layers. In this case, light emerging from a distant object makes total internal reflection in the air layers and forms the image of the object that is called mirage. Our investigation on mirage formation in desert indicates that there is no meaningful relation between mirage formation and temperature change over the ground. In addition, we show that, the interference of the lights reflected from different air layers destroys the coherency of the image forming light. This happens because the temperature change occurs in an interval larger than a wavelength. In the second part of the report we demonstrate theoretically and experimentally that flat rough surfaces behave like mirrors at very large incident angles. We show that there is a threshold incident angle for observation of image in a rough surface that depends on the surface roughness and light wavelength. The shortest distance between observer and the image is determined by the threshold incident angle. Mirage is such an image. Image formation is studied in rough sheet glass surfaces that prepared by grinding with powders of different sizes.

CERN European Organization for Nuclear Research - Zenodo, 2022

Light Science, 2019

In general, when light encounters the boundary between two media, a part of the light is reflected and part is transmitted into the second medium. The ray that enters the second medium usually experiences a change in direction. This bending of light is called refraction. In this chapter we will introduce a law that governs the path of the refracted light in the second medium. An understanding of how light behaves when passing from one medium to another is of importance for it is central to the operation of optical devices such as eyeglasses, cameras, microscopes, and telescopes, and is the basis for understanding the functioning of the human eye and the formation of rainbows and mirages. The most obvious result of the phenomenon of refraction is the bending of light when it passes from one medium to another (Fig. .1a). When a light ray goes from air to glass, for example, it is slowed down and bent toward the normal. When it leaves the glass, it is bent away from the normal. If the two boundaries of the glass are parallel (as in a thick pane of window glass), the angle of deviation (bending) in both cases is the same, so the ray emerges traveling parallel to its original path, as shown in Fig. .1a, b. This is a good thing, of course, or else the world would appear to be pretty distorted when viewed through a window! Note that if the ray had traveled the shortest distance between A and D, it would have taken the straight-line path AD, shown as a dashed line. However, to get from A to D in the shortest time, it is advantageous to follow path ABCD, which reduces the time spent in the slow medium. (This is like driving a few miles out of your way in order to travel part of the distance on an expressway, which may reduce your total travel time.) The principle of least time, in fact, predicts that light will always choose the path of least time. This powerful principle, formulated by French physicist Pierre de Fermat in 1657, can also be used to arrive at the law of reflection h i = h r (see Chap. 3).

2015

Optics scholars did not only discover optical phenomena and laws governing them. Some of them also invented impressive optical systems and instruments or offered us techniques to juggle with optical signals and rays. One typical example of the impressive optical systems is the camera obscura invented by Ibn Al-Haytham. For techniques enabling us to easily handle optical rays, one can mention Young's method to handle rays put into play by refraction. Nine centuries before him, Ibn Sahl proposed an elegant method to manipulate refraction related rays. These three examples will be handled in this paper, together with a historical overview inviting the reader to be in the context of this fascinating works.

European Journal of Physics, 1997

Incoherent averaging over orientations of refracted beams of rays can generate a 'fake caustic', namely an intensity pattern with a geometrical singularity identical to that of a caustic produced by focusing of a family of rays (i.e. its envelope). However, the diffraction at a fake caustic is very different from the Airy fringes near a genuine caustic. We calculate this unusual type of diffraction and demonstrate its existence experimentally with a rotating prism. Zusammenfassung. Inkoherente Mittelungüber die Orientierungen von gebrochenen Strahlenbündeln kann eine 'falsche Kaustik' erzeugen, nämlich ein Intensitätsmuster mit einer geometrischen Singularität identisch zu der einer Kaustik, die durch Fokusierung einer Familie von Strahlen (d.h. ihre Einhuellende) hervorgebracht wurde. Die Beugung in einer falschen Kaustik aber ist sehr verschieden von den Airy Streifen nahe einer echten Kaustik. Wir berechnen diesen ungewöhnlichen Typ einer Beugung und zeigen ihre Existenz experimentell mit einem rotierenden Prisma.

The British Journal for the Philosophy of …, 2011

Camera Graeca: Photographs, Narratives, Materialities, 2015