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Optics
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====Refractions==== {{Main|Refraction}} [[File:Snells law.svg|class=skin-invert-image|thumb|upright=1.35|Illustration of Snell's Law for the case {{math|''n''<sub>1</sub> < ''n''<sub>2</sub>}}, such as air/water interface]] Refraction occurs when light travels through an area of space that has a changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an [[Interface (chemistry)|interface]] between a uniform medium with index of refraction {{math|''n''{{sub|1}}}} and another medium with index of refraction {{math|''n''{{sub|2}}}}. In such situations, [[Snell's Law]] describes the resulting deflection of the light ray: <math display="block">n_1\sin\theta_1 = n_2\sin\theta_2</math> where {{math|''θ''{{sub|1}}}} and {{math|''θ''{{sub|2}}}} are the angles between the normal (to the interface) and the incident and refracted waves, respectively.{{sfnp|Young|Freedman|2020|p=1109}} The index of refraction of a medium is related to the speed, {{math|''v''}}, of light in that medium by <math display="block">n=c/v,</math> where {{math|''c''}} is the [[speed of light in vacuum]]. Snell's Law can be used to predict the deflection of light rays as they pass through linear media as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. In most materials, the index of refraction varies with the frequency of the light, known as [[dispersion (optics)|dispersion]]. Taking this into account, Snell's Law can be used to predict how a prism will disperse light into a spectrum.{{sfnp|Young|Freedman|2020|p=1116}} The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton. Some media have an index of refraction which varies gradually with position and, therefore, light rays in the medium are curved. This effect is responsible for [[mirage]]s seen on hot days: a change in index of refraction air with height causes light rays to bend, creating the appearance of specular reflections in the distance (as if on the surface of a pool of water). Optical materials with varying indexes of refraction are called gradient-index (GRIN) materials. Such materials are used to make [[gradient-index optics]].<ref>{{cite book |first=E.W. |last=Marchand |title=Gradient Index Optics |location=New York |publisher=Academic Press |year=1978}}</ref> For light rays travelling from a material with a high index of refraction to a material with a low index of refraction, Snell's law predicts that there is no {{math|''θ''{{sub|2}}}} when {{math|''θ''{{sub|1}}}} is large. In this case, no transmission occurs; all the light is reflected. This phenomenon is called [[total internal reflection]] and allows for fibre optics technology. As light travels down an optical fibre, it undergoes total internal reflection allowing for essentially no light to be lost over the length of the cable.{{sfnp|Young|Freedman|2020|pp=1113–1115}} =====Lenses===== {{main|Lens (optics)}} [[File:lens3b.svg|class=skin-invert-image|upright=1.65|thumb|A ray tracing diagram for a converging lens]] A device that produces converging or diverging light rays due to refraction is known as a ''lens''. Lenses are characterized by their [[focal length]]: a converging lens has positive focal length, while a diverging lens has negative focal length. Smaller focal length indicates that the lens has a stronger converging or diverging effect. The focal length of a simple lens in air is given by the [[lensmaker's equation]].{{sfnp|Hecht|2017|p=159}} Ray tracing can be used to show how images are formed by a lens. For a [[thin lens]] in air, the location of the image is given by the simple equation <math display="block">\frac{1}{S_1} + \frac{1}{S_2} = \frac{1}{f} ,</math> where {{math|''S''{{sub|1}}}} is the distance from the object to the lens, {{math|''S''{{sub|2}}}} is the distance from the lens to the image, and {{mvar|f}} is the focal length of the lens. In the [[sign convention]] used here, the object and image distances are positive if the object and image are on opposite sides of the lens.{{sfnp|Hecht|2017|p=165}} [[File:Lens1.svg|class=skin-invert-image|upright=1.65|thumb]] Incoming parallel rays are focused by a converging lens onto a spot one focal length from the lens, on the far side of the lens. This is called the rear focal point of the lens. Rays from an object at a finite distance are focused further from the lens than the focal distance; the closer the object is to the lens, the further the image is from the lens. With diverging lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at a spot one focal length in front of the lens. This is the lens's front focal point. Rays from an object at a finite distance are associated with a virtual image that is closer to the lens than the focal point, and on the same side of the lens as the object. The closer the object is to the lens, the closer the virtual image is to the lens. As with mirrors, upright images produced by a single lens are virtual, while inverted images are real.{{sfnp|Young|Freedman|2020|p=1157}} Lenses suffer from [[optical aberration|aberrations]] that distort images. ''Monochromatic aberrations'' occur because the geometry of the lens does not perfectly direct rays from each object point to a single point on the image, while [[chromatic aberration]] occurs because the index of refraction of the lens varies with the wavelength of the light.{{sfnp|Young|Freedman|2020|p=1143,1163,1175}} [[File:Thin lens images.svg|thumb|none|upright=2.25|Images of black letters in a thin convex lens of focal length {{mvar|f}} are shown in red. Selected rays are shown for letters '''E''', '''I''' and '''K''' in blue, green and orange, respectively. Note that '''E''' (at {{math|2''f''}}) has an equal-size, real and inverted image; '''I''' (at {{mvar|f}}) has its image at infinity; and '''K''' (at {{math|''f''/2}}) has a double-size, virtual and upright image.]]
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