![]() Despite the implicit promise of his theory, invisibility proved impossible to discover or manufacture from a material that exhibited the behavior that Vesalago had predicted. Vesalago did not explicitly mention invisibility in his paper, but the capability of manipulating light in the ways he described made invisibility a consequence. Without any reflections, a cloaked object would appear invisible since no light would bounce off of it. Moreover, a correctly engineered interface could bend light without any reflections, a phenomenon that was impossible for natural materials. However, Vesalago hypothesized that if the values of the electric permittivity and magnetic permeability were negative, a left hand rule would apply, and it would be possible to bend light at angles much greater than previous interpretations of Snell’s Law allowed. This choice is consistent with the right hand rule, which says that if we use our right hand to rotate the electric field vector into the magnetic field vector, the thumb will point in the direction of the light ray. Maxwell’s equations show that the positive square root is the correct choice, if the electric permittivity and magnetic permeability are both positive. Before Vesalago, scholars assumed that this meant only the positive square root. The index of refraction is the square root of the product of those two numbers. The way the atomic and molecular structure of a medium affects the propagation of light is captured by two numbers: the electric permittivity (amount of resistance a medium supplies when forming electric field) and the magnetic permeability (how well a material can support the forming of a magnetic field). The secret behind this phenomenon lies in mathematics. This feat requires a material with a negative index of refraction. ![]() No known natural materials can perform the opposite phenomenon, that is making something invisible where it should be visible. These natural variations in index of refraction bend light in a way that makes the sky visible in a place where it is normally not seen. Human eyes are not trained to interpret the bending of light, so the image of the sky in the ground is seen instead of the ground itself. By the time the light rays reach human eyes, they have bent so much that they are moving up rather than down. For instance, a mirage is formed when hot air near the ground has a lower index of refraction than cooler air above, causing the light rays coming down from the sky to bend upward as they pass through the hotter air. Variations in the index of refraction lead to incorrect views of objects. The larger the index of refraction, the slower that light travels. Its technical definition is the ratio of the speed of light in a vacuum to the speed of light in the medium. The index of refraction can be thought of as the slowness of the speed of light in the medium. Bending light around what is usually blocked by an object, without reflection, would allow the viewer to see what is behind the object instead of the object itself, thus creating the illusion of invisibility (see Fig. Recent advances in the understanding of this rule allow for the prospect of engineered invisibility. ![]() It is the more complicated law of refraction, however, that describes the bending of light. Lasers and holograms make use of this simple law of reflection. We can use this understanding to direct light along precise paths. ![]() Light reflects from a mirror like a ball bouncing off a wall: the incident and reflected rays make equal angles with the normal line (perpendicular line) to the reflecting surface. When light interacts with an object (a wall, mirror, or even air), it reflects and refracts. It is the wave properties of light that make cloaking possible. This dichotomy is called the wave-particle duality. It travels in straight lines, like an unaccelerated particle yet, it exhibits diffraction patterns as do water and sound waves. Light exhibits the properties of both waves and particles. The nature of light has always been a puzzling concept for physicists. Through the use of mirrors in this figure, the red animal is not visible to the purple animal. Figure 1: Mirrors can be used to create an illusion of invisibility.
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