A gradient-index lens with a parabolic variation of refractive index (n) with radial distance (x). The lens focusses light in the same way as a conventional lens.

Gradient-index optics is the branch of optics covering optical effects produced by a gradual variation of the refractive index of a material. The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium

An example of gradient index optics is the common mirage of a pool of water appearing on a road on a hot day. A mirage is a naturally-occurring Optical phenomenon, in which light rays are bent to produce a displaced image of distant objects or the sky The pool is actually an image of the sky, apparently located on the road since light rays are being refracted (bent) from their normal straight path. Refraction is the change in direction of a Wave due to a change in its Speed. This due to the variation of refractive index between the hot, less dense air at the surface of the road, and the denser cool air above it. The variation in temperature (and thus density) of the air causes a gradient in its refractive index, causing it to increase with height. This index gradient causes refraction of light rays (at a shallow angle to the road) from the sky, bending them into eye of the viewer, with their apparent location being the road's surface.

This bending effect is exploited in a gradient-index (GRIN) lens. This is a device with a radially-decreasing refractive index (usually a parabolically shaped index profile). In Mathematics, the parabola (pəˈræbələ from the Greek παραβολή) is a Conic section, the intersection of a right circular A slab of this material acts like a conventional converging lens, but does not need to be shaped like one, simplifying the mounting of the lens. A lens is an optical device with perfect or approximate Axial symmetry which transmits and refracts Light, converging or diverging GRIN lenses are commonly used where many very small lenses are needed to be mounted together, such as in photocopiers and scanners. A photocopier (or copier is a machine that makes Paper copies of documents and other visual images quickly and cheaply Historical precedent Scanners can be considered the successors of early telephotography input devices consisting of a rotating drum with a single Photodetector at

Certain optical fibres (gradient- or graded-index fibres) are also made with a radially-varying refractive index profile; this design strongly reduces the modal dispersion of a multi-mode optical fibre. An optical fiber (or fibre) is a Glass or Plastic fiber that carries Light along its length In Fiber optics, a graded-index or gradient-index fiber is an Optical fiber whose core has a Refractive index that decreases with In Optics, dispersion is the phenomenon in which the Phase velocity of a wave depends on its frequency

The lens of a human eye also uses a radially-decreasing index gradient, as well as its shape, to focus light. The lens is a transparent biconvex structure in the Eye that along with the Cornea, helps to Refract Light to be focused Eyes are organs that detect Light, and send signals along the Optic nerve to the visual areas of the brain

One of the most important advantages of GRIN lenses compared to classical lenses is that the optical surfaces of GRIN lenses are flat. The lens is a transparent biconvex structure in the Eye that along with the Cornea, helps to Refract Light to be focused This fact is very important for creating a good quality joint between lens and, for example, optical fiber.

The most popular production method of the glass-made GRIN lens is ion exchange. Ion exchange is an exchange of Ions between two Electrolytes or between an electrolyte Solution and a complex. For example, a glass sample with Na+ ions could be immersed into liquid melt with Li+ ions. Sodium (ˈsoʊdiəm is an element which has the symbol Na( Latin natrium, from Arabic natrun) atomic number 11 atomic mass 22 Lithium (ˈlɪθiəm is a Chemical element with the symbol Li and Atomic number 3 As a result of diffusion, Na would be partially exchanged with Li, with a larger amount of exchange occurring at the edge. Diffusion is the net movement of particles (typically molecules from an area of high concentration to an area of low concentration by uncoordinated random movement Thus the sample obtains a gradient material structure and a corresponding gradient of the refractive index.

## References

E. W. Marchand, Gradient Index Optics, New York, NY, Academic Press, 1978.

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