Light & Optics

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lectromagnetic waves arises as a consequence of two effects : (1)A changing magnetic field which produces

an electric field , (2)A changing electric field which produces a magnetic field, which for example means that if a current passing through a wire changes with time then the wire emits Electromagnetic Waves.

ESo Generally, Electromagnetic waves are generated by accelerating electric charges and the radiation consists of oscillating electric and magnetic fields which are at right angel to each other and at right angel to the direction of wave propagation.

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These Electromagnetic waves travels in vacuum with a definite speed which is equal to the speed of light (C=3×108 m / s)

Since Electromagnetic waves travel in vacuum with a definite speed (c), then these waves must have a frequency (f) and a wavelength (λ).

So consequently Electromagnetic waves were divided into many types of rays and waves where each type has a definite range of wavelength and frequency this classification was named Electromagnetic Spectrum.Here is a simplified classification of the Electromagnetic Spectrum according to their frequency and wavelength:

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So visible light is a sort of Electromagnetic waves with a wavelength that ranges between 400nm – 700nm, IT can also be defined as the electromagnetic spectrum that is detected by the human eye.Early ideas about light propagation: Before the 17th century, scientists believed that there was no such thing as the "speed of light". They thought that light could travel any distance in no time at all. Later, several attempts were made to measure that speed.

In 1667, Galileo is often credited with being the first scientist to try to determine the speed of light. His method was quite simple. He and an assistant each had lamps which could be

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covered and uncovered at will. Galileo would uncover his lamp, and as soon as his assistant saw the light he would uncover his. By measuring the elapsed time until Galileo saw his assistant's light and knowing how far apart the lamps were, Galileo reasoned he should be able to determine the speed of the light. His conclusion: "If not instantaneous, it is extraordinarily rapid". Most likely he used a water clock, where the amount of water that empties from a container represents the amount of time that has passed. Galileo just deduced that light travels at least ten times faster than sound.In 1675, the Danish astronomer Ole Roemer noticed, while observing Jupiter's moons that the times of the eclipses of the moons of Jupiter seemed to depend on the relative positions of Jupiter and Earth. If Earth was close to Jupiter, the orbits of her moons appeared to speed up. If Earth was far from Jupiter, they seemed to slow down. Reasoning that the moons orbital velocities should not be affected by their separation, he deduced that

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the apparent change must be due to the extra time for light to travel when Earth was more distant from Jupiter. Using the commonly accepted value for the diameter of the Earth's orbit, he came to the conclusion that light must have traveled at 200,000 Km/s.

In 1728, James Bradley an English physicist, estimated the speed of light in vacuum to be around 301,000 km/s. He used stellar aberration to calculate the speed of light. Stellar aberration causes the apparent position of stars to change due to the motion of Earth around the sun. Stellar aberration is approximately the ratio of the speed that the earth orbits the sun to the speed of light. He knew the speed of Earth around the sun and he could also measure this stellar aberration angle. These two facts enabled him to calculate the speed of light in vacuum.In 1849, A French physist, Fizeau, shone a light between the teeth of a rapidly rotating toothed wheel. A mirror more than 5 miles away reflected the beam back through the same gap between the teeth of the wheel. There were over a hundred teeth in the wheel. The wheel rotated at hundreds of times a second;

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therefore a fraction of as second was easy to measure. By varying the speed of the wheel, it was possible to determine at what speed the wheel was spinning too fast for the light to pass through the gap between the teeth, to the remote mirror, and then back through the same gap.  He knew how far the light traveled and the time it took. By dividing that distance by the time, he got the speed of light. Fizeau measured the speed of light to be 313,300 Km/s.

In 1926, Another French physicist, Leon Foucault, used a similar method to Fizeau. He shone a light to a rotating mirror, then it bounced back to a remote fixed mirror and then back to the first rotating mirror. But because the first mirror was rotating, the light from the rotating mirror finally bounced back at an angle slightly different from the angle it

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initially hit the mirror with.  By measuring this angle, it was possible to measure the speed of the light.

Foucault continually increased the accuracy of this method over 50 years. His final measurement in 1926 determined that light traveled at 299,796 Km/s.Visible light has some definite properties which are:

1) Reflection2) Refraction3) Diffraction4) Interference5) Dispersion

ReflectionLight is known to behave in a very predictable manner. If a ray of light could be observed approaching and reflecting off of a flat mirror, then the behavior of the light as it reflects would follow a predictable known as the law of reflection. This diagram illustrates the law of reflection.

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In the diagram, the ray of light approaching the mirror is known as the incident ray (labeled I in the diagram). The ray of light which leaves the mirror is known as the reflected ray (labeled R in the diagram). At the point of incidence where the ray strikes the mirror, a line can be drawn perpendicular to the surface of the mirror. This line is known as a normal line (labeled N in the diagram). The normal line divides the angle between the incident ray and the reflected ray into two equal angles. The angle between the incident ray and the normal is known as the angle of incidence. The angle between the reflected ray and the normal is known as the angle of reflection. (These two angles are labeled with the Greek letter "theta" accompanied by a subscript; read as "theta-I" for angle of incidence and "theta-r" for angle of reflection.) The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.It is common to observe this law at work in a Physics lab. To view an image of a pencil in a mirror, you must sight along a line at the image location. As you sight at the image, light travels

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to your eye along the path shown in the diagram below. The diagram shows that the light reflects off the mirror in such a manner that the angle of incidence is equal to the angle of reflection.

It just so happens that the light which travels along the line of sight to our eye follows the law of reflection. If we were to sight along a line at a different location than the image location, it would be impossible for a ray of light to come from the object, reflect off the mirror according to the law of reflection, and subsequently travel to our eye. Only when we sight at the image, does light from the object reflect off the mirror in accordance with the law of reflection and travel to our eye. This truth is depicted in the diagram below.

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For example, in Diagram A above, the eye is sighting along a line at a position above the actual image location. For light from the object to reflect off the mirror and travel to the eye, the light would have to reflect in such a way that the angle of incidence is less than the angle of reflection. In Diagram B above, the eye is sighting along a line at a position below the actual image location. In this case, for light from the object to reflect off the mirror and travel to the eye, the light would have to reflect in such a way that the angle of incidence is more than the angle of reflection. Neither of these cases would follow the law of reflection. In fact, in each case, the image is not seen when sighting along the indicated line of sight. It is because of the law of reflection that an eye must sight at the image location in order to see the image of an object in a mirror.

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RefractionRefraction is the bending of a wave when it enters a medium where its speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell's Law.

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As the speed of light is reduced in the slower medium, the wavelength is shortened proportionately. The frequency is unchanged; it is a characteristic of the source of the light and unaffected by medium changes.The index of refraction is defined as the speed of light in vacuum divided by the speed of light in the medium.

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The indices of refraction of some common substances are given below with a more complete description of the indices for optical glasses . The values given are approximate and do not account for the small variation of index with light wavelength which is called dispersion.

Snell's Law relates the indices of refraction n of the two media to the directions of propagation in terms of the angles to the normal. Snell's law can be derived from Fermat's Principle or from the Fresnel Equations.

If the incident medium has the larger index of refraction, then the angle with the normal is increased by refraction. The larger index medium is commonly called the "internal" medium, since air with n=1 is usually the surrounding or "external" medium. We can

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calculate the condition for total internal reflection by setting the refracted angle = 90° and calculating the incident angle. Since we can't refract the light by more than 90°, all of it will reflect for angles of incidence greater than the angle which gives refraction at 90°.

DiffractionThe effects of diffraction can be readily seen in everyday life. The most colorful examples of

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diffraction are those involving light; for example, the closely spaced tracks on a CD or DVD act as a diffraction grating to form the familiar rainbow pattern we see when looking at a disk. This principle can be extended to engineer a grating with a structure such that it will produce any diffraction pattern desired; the hologram on a credit card is an example. Diffraction in the atmosphere by small particles can cause a bright ring to be visible around a bright light source like the sun or the moon. A shadow of a solid object, using light from a compact source, shows small fringes near its edges. The speckle pattern which is observed when laser light falls on an optically rough service is also a diffraction phenomenon. All these effects are a consequence of the fact that light is a wave.Diffraction can occur with any kind of wave. Ocean waves diffract around jetties and other obstacles. Sound waves can diffract around objects, this is the reason we can still hear someone calling us even if we are hiding behind a tree. Diffraction can also be a concern in some technical applications; it sets a fundamental limit to the resolution of a camera, telescope, or microscope.The effects of diffraction of light were first carefully observed and characterized by

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Francesco Maria Grimaldi, who also coined the term diffraction, from the Latin diffringere, 'to break into pieces', referring to light breaking up into different directions. The results of Grimaldi's observations were published posthumously in 1665. Isaac Newton studied these effects and attributed them to inflexion of light rays. James Gregory (1638–1675) observed the diffraction patterns caused by a bird feather, which was effectively the first diffraction grating. In 1803 Thomas Young did his famous experiment observing interference from two closely spaced slits. Explaining his results by interference of the waves emanating from the two different slits, he deduced that light must propagate as waves. Augustin-Jean Fresnel did more definitive studies and calculations of diffraction, published in 1815 and 1818, and thereby gave great support to the wave theory of light that had been advanced by Christiaan Huygens and reinvigorated by Young, against Newton's particle theory.

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Thomas young sketch that was presented to the royal society in 1803.

Diffraction arises because of the way in which waves propagate; this is described by the Huygens–Fresnel principle. The propagation of a wave can be visualized by considering every point on a wavefront as a point source for a secondary radial wave. The subsequent propagation and addition of all these radial waves form the new wavefront. When waves are added together, their sum is determined by the relative phases as well as the amplitudes of the individual waves, an effect which is often known as wave interference. The summed amplitude of the waves can have any value between zero and the sum of the individual amplitudes. Hence, diffraction patterns usually have a series of maxima and minima.To determine the form of a diffraction pattern, we must determine the phase and amplitude of each of the Huygens wavelets at each point in space and then find the sum of these waves. There are various analytical models which can be used to do this including the Fraunhoffer diffraction equation for the far field and the Fresnel Diffraction equation for the near-field. Most configurations cannot be solved

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analytically; solutions can be found using various numerical analytical methods including Finite element and boundary element methods.

(Single slit Diffraction)

InterferenceWhat happens when two waves meet while they travel through the same medium? What affect

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will the meeting of the waves have upon the appearance of the medium? Will the two waves bounce off each other upon meeting (much like two billiard balls would) or will the two waves pass through each other? These questions involving the meeting of two or more waves along the same medium pertain to the topic of wave interference.Wave interference is the phenomenon which occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape which results from the net effect of the two individual waves upon the particles of the medium. To begin our exploration of wave interference, consider two pulses of the same amplitude traveling in different directions along the same medium. Let's suppose that each displaced upward 1 unit at its crest and has the shape of a sine wave. As the sine pulses move towards each other, there will eventually be a moment in time when they are completely overlapped. At that moment, the resulting shape of the medium would be an upward displaced sine pulse with an amplitude of 2 units. The diagrams below depict the before and during interference snapshots of the medium for two such pulses. The individual sine pulses are

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drawn in red and blue and the resulting displacement of the medium is drawn in green.

This type of interference is sometimes called constructive interference. Constructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the same direction. In this case, both waves have an upward displacement; consequently, the medium has an upward displacement which is greater than the displacement of the two interfering pulses. Constructive interference is observed at any location where the two interfering waves are displaced upward. But it is also observed when both interfering waves are displaced downward. This is shown in the diagram below for two downward displaced pulses.

In this case, a sine pulse with a maximum displacement of -1 unit (negative means a downward displacement) interferes with a sine pulse with a maximum displacement of -1 unit.

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These two pulses are drawn in red and blue. The resulting shape of the medium is a sine pulse with a maximum displacement of -2 units.Destructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. For instance, when a sine pulse with a maximum displacement of +1 unit meets a sine pulse with a maximum displacement of -1 unit, destructive interference occurs. This is depicted in the diagram below.

In the diagram above, the interfering pulses have the same maximum displacement but in opposite directions. The result is that the two pulses completely destroy each other when they are completely overlapped. At the instant of complete overlap, there is no resulting displacement of the particles of the medium. This "destruction" is not a permanent condition. In fact, to say that the two waves destroy each other can be partially misleading. When it is said that the two pulses destroy each other, what is meant is that when overlapped, the affect of one of the pulses on the displacement

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of a given particle of the medium is destroyed or canceled by the affect of the other pulse. Recall from Lesson 1 that waves transport energy through a medium by means of each individual particle pulling upon its nearest neighbor. When two pulses with opposite displacements (i.e., one pulse displaced up and the other down) meet at a given location, the upward pull of one pulse is balanced (canceled or destroyed) by the downward pull of the other pulse. Once the two pulses pass through each other, there is still an upward displaced pulse and a downward displaced pulse heading in the same direction which they were heading before the interference. Destructive interference leads to only a momentary condition in which the medium's displacement is less than the displacement of the largest-amplitude wave.The two interfering waves do not need to have equal amplitudes in opposite directions for destructive interference to occur. For example, a pulse with a maximum displacement of +1 unit could meet a pulse with a maximum displacement of -2 units. The resulting displacement of the medium during complete overlap is -1 unit.

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This is still destructive interference since the two interfering pulses have opposite displacements. In this case, the destructive nature of the interference does not lead to complete cancellation.Interestingly, the meeting of two waves along a medium does not alter the individual waves or even deviate them from their path. This only becomes an astounding behavior when it is compared to what happens when two billiard balls meet or two football players meet. Billiard balls might crash and bounce off each other and football players might crash and come to a stop. Yet two waves will meet, produce a net resulting shape of the medium, and then continue on doing what they were doing before the interference.

 The task of determining the shape of the resultant demands that the principle of

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superposition is applied. The principle of superposition is sometimes stated as follows:

When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.

DispersionIn optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Media having such a property are termed dispersive media.The most familiar example of dispersion is probably a rainbow, in which dispersion causes the spatial separation of a white light into components of different wavelengths (different colors). However, dispersion also has an effect in many other circumstances: for example, it causes pulses to spread in optical fibers, degrading signals over long distances; also, a cancellation between dispersion and nonlinear effects leads to soliton waves. Dispersion is most often described for light waves, but it may

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occur for any kind of wave that interacts with a medium or passes through an inhomogeneous geometry (e.g. a waveguide), such as sound waves. Dispersion is sometimes called chromatic dispersion to emphasize its wavelength-dependent nature.

There are generally two sources of dispersion: material dispersion and waveguide dispersion. Material dispersion comes from a frequency-dependent response of a material to waves. For example, material dispersion leads to undesired chromatic aberration in a lens or the separation of colors in a prism. Waveguide dispersion occurs when the speed of a wave in a waveguide (such as an optical fiber) depends on

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its frequency for geometric reasons, independent of any frequency dependence of the materials from which it is constructed. More generally, "waveguide" dispersion can occur for waves propagating through any inhomogeneous structure (e.g. a photonic crystal), whether or not the waves are confined to some region. In general, both types of dispersion may be present, although they are not strictly additive. Their combination leads to signal degradation in optical fibers for telecommunications, because the varying delay in arrival time between different components of a signal "smears out" the signal in time.

Optical FibersAn optical fiber (or fibre) is a glass or plastic fiber that carries light along its length. Fiber

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optics is the overlap of applied science and engineering concerned with the design and application of optical fibers. Optical fibers are widely used in fiber-optic communications, which permits transmission over longer distances and at higher data rates (a.k.a "bandwidth"), than other forms of communications. Fibers are used instead of metal wires because signals travel along them with less loss, and they are immune to electromagnetic interference. Fibers are also used for illumination, and in bundles can be used to carry images, allowing viewing in tight spaces. Specially designed fibers are used for a variety of other applications, including as sensors and fiber lasers.

Light is kept in the "core" of the optical fiber by total internal reflection. This causes the fiber to act as a waveguide. Fibers which support many propagation paths or transverse modes are called multimode fibers (MMF). Fibers which support only a single mode are called singlemode fibers (SMF). Multimode fibers

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generally have a large-diameter core, and are used for short-distance communication links or for applications where high power must be transmitted. Singlemode fibers are used for most communication links longer than 200 meters.Joining lengths of optical fiber is more complex than joining electrical wire or cable. The ends of the fibers must be carefully cleaved, and then spliced together either mechanically or by fusing them together with an electric arc. Special connectors are used to make removable connections.Guiding of light by refraction, the principle that makes fiber optics possible, was first demonstrated by Daniel Colladon and Jacques Babinet in Paris in the 1840s, with Irish inventor John Tyndall offering public displays using water-fountains ten years later. Practical applications, such as close internal illumination during dentistry, appeared early in the twentieth century. Image transmission through tubes was demonstrated independently by the radio experimenter Clarence Hansell and the television pioneer John Logie Baird in the 1920s.

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The principle was first used for internal medical examinations by Heinrich Lamm in the following decade. In 1952, physicist Narinder Singh Kapany conducted experiments that led to the invention of optical fiber, based on Tyndall's earlier studies; modern optical fibers, where the glass fiber is coated with a transparent cladding to offer a more suitable refractive index, appeared later in the decade. Development then focused on fiber bundles for image transmission. The first fiber optic semi-flexible gastroscope was patented by Basil Hirschowitz, C. Wilbur Peters, and Lawrence E. Curtiss, researchers at the University of Michigan, in 1956. In the process of developing the gastroscope, Curtiss produced the first glass-clad fibers; previous optical fibers had relied on air or impractical oils and waxes as the low-index cladding material. A variety of other image transmission applications soon followed.In 1965, Charles K. Kao and George A. Hockham of the British company Standard Telephones and Cables (STC) were the first to promote the idea that the attenuation in optical fibers could be reduced below 20 dB per kilometer, allowing fibers to be a practical medium for communication. They proposed that the attenuation in fibers available at the time was caused by impurities, which could be removed,

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rather than fundamental physical effects such as scattering. The crucial attenuation level of 20 dB was first achieved in 1970, by researchers Robert D. Maurer, Donald Keck, Peter C. Schultz, and Frank Zimar working for American glass maker Corning Glass Works, now Corning Incorporated They demonstrated a fiber with 17 dB optic attenuation per kilometer by doping silica glass with titanium. A few years later they produced a fiber with only 4 dB/km using germanium dioxide as the core dopant. Such low attenuations ushered in optical fiber telecommunications and enabled the Internet. In 1981, General Electric produced fused quartz ingots that could be drawn into fiber optic strands 25 miles long. Attenuations in modern optical cables are far less than those in electrical copper cables, leading to long-haul fiber connections with repeater distances of 50–80 km. The erbium-doped fiber amplifier, which reduced the cost of long-distance fiber systems by reducing or even in many cases eliminating the need for optical-electrical-optical repeaters, was co-developed by teams led by David N. Payne of the University of Southampton, and Emmanuel Desurvire at Bell Laboratories in 1986. The more robust optical fiber commonly used today utilizes glass for both core and sheath and is

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therefore less prone to aging processes. It was invented by Gerhard Bernsee in 1973 of Schott Glass in Germany. In 1991, the emerging field of photonic crystals led to the development of photonic crystal fiber which guides light by means of diffraction from a periodic structure, rather than total internal reflection. The first photonic crystal fibers became commercially available in 2000. Photonic crystal fibers can be designed to carry higher power than conventional fiber, and their wavelength dependent properties can be manipulated to improve their performance in certain applications.Glass optical fibers are almost always made from silica, but some other materials, such as fluorozirconate, fluoroaluminate, and chalcogenide glasses, are used for longer-wavelength infrared applications. Like other glasses, these glasses have a refractive index of about 1.5. Typically the difference between core and cladding is less than one percent.Plastic optical fibers (POF) are commonly step-index multimode fibers with a core diameter of 0.5 mm or larger. POF typically have higher attenuation co-efficients than glass fibers, 1 dB/m or higher, and this high attenuation limits the range of POF-based systems.

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Optical fiber can be used as a medium for telecommunication and networking because it is flexible and can be bundled as cables. It is especially advantageous for long-distance communications, because light propagates through the fiber with little attenuation compared to electrical cables. This allows long distances to be spanned with few repeaters. Additionally, the per channel light signals propagating in the fiber can be modulated at rates as high as 111 Gb/s [7]. (In 2001 the limit was at 40 Gb/s [8]. In today's DWDM systems the net data rate (data rate without overhead bytes) per fiber is the per channel data rate reduced by the FEC overhead multiplied by the number of channels (usually up to 80 channels in commercially available systems as of 2008). (Some communication companies are revealing that net data rates as fast as 1Tb/s are currently being developed.), and each fiber can carry many independent channels, each by a different wavelength of light (wavelength-division multiplexing). Over short distances, such as networking within a building, fiber saves space in cable ducts because a single fiber can carry much more data than a single electrical cable. Fiber is also immune to electrical interference, which prevents cross-talk between signals in different cables and pickup of environmental noise. Also, wiretapping is more difficult

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compared to electrical connections, and there are concentric dual core fibers that are said to be tap-proof. Because they are non-electrical, fiber cables can bridge very high electrical potential differences and can be used in environments where explosive fumes are present, without danger of ignition.Although fibers can be made out of transparent plastic, glass, or a combination of the two, the fibers used in long-distance telecommunications applications are always glass, because of the lower optical attenuation. Both multi-mode and single-mode fibers are used in communications, with multi-mode fiber used mostly for short distances (up to 500 m), and single-mode fiber used for longer distance links. Because of the tighter tolerances required to couple light into and between single-mode fibers (core diameter about 10 micrometers), single-mode transmitters, receivers, amplifiers and other components are generally more expensive than multi-mode components.

Application examples: TOSLINK.(optic fiber connector)

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Fibers are widely used in illumination applications. They are used as light guides in medical and other applications where bright light needs to be shone on a target without a clear line-of-sight path. In some buildings, optical fibers are used to route sunlight from the roof to other parts of the building (see non-imaging optics). Optical fiber illumination is also used for decorative applications, including signs, art, and artificial Christmas trees. Swarovski boutiques use optical fibers to illuminate their crystal showcases from many different angles while only employing one light source. Optical fiber is an intrinsic part of the light-transmitting concrete building product, LiTraCon.( is a translucent concrete building material. Made of fine concrete embedded with 5% by weight of optical glass fibers, it was developed in 2001 by Hungarian architect Áron Losonczi working with scientists at the Technical University of Budapest.)

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Fiber with large (greater than 10 μm) core diameter may be analyzed by geometric optics. Such fiber is called multimode fiber, from the electromagnetic analysis (see below). In a step-index multimode fiber, rays of light are guided along the fiber core by total internal reflection. Rays that meet the core-cladding boundary at a high angle (measured relative to a line normal to the boundary), greater than the critical angle for this boundary, are completely reflected. The critical angle (minimum angle for total internal reflection) is determined by the difference in index of refraction between the core and cladding materials. Rays that meet the boundary at a low angle are refracted from the core into the cladding, and do not convey light and hence information along the fiber. The critical angle determines the acceptance angle of the fiber, often reported as a numerical aperture. A high numerical aperture allows light to propagate down the fiber in rays both close to the axis and at various angles, allowing efficient coupling of light into the fiber. However, this high numerical aperture increases the amount of dispersion as rays at different angles have different path lengths and therefore take different times to traverse the fiber. A low numerical aperture may therefore be desirable.

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Fiber with a core diameter less than about ten times the wavelength of the propagating light cannot be modeled using geometric optics. Instead, it must be analyzed as an electromagnetic structure, by solution of Maxwell's equations as reduced to the electromagnetic wave equation. The electromagnetic analysis may also be required to understand behaviors such as speckle that occur when coherent light propagates in multi-mode fiber. As an optical waveguide, the fiber supports one or more confined transverse modes by which light can propagate along the fiber. Fiber supporting only one mode is called single-mode or mono-mode fiber. The behavior of larger-core multimode fiber can also be modeled using the

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wave equation, which shows that such fiber supports more than one mode of propagation (hence the name). The results of such modeling of multi-mode fiber approximately agree with the predictions of geometric optics, if the fiber core is large enough to support more than a few modes.

Lenses

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A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens is a lens consisting of a single optical element. A compound lens is an array of simple lenses (elements) with a common axis; the use of multiple elements allows more optical aberrations to be corrected than is possible with a single element. Manufactured lenses are typically made of glass or transparent plastic. Elements which refract electromagnetic radiation outside the visual spectrum are also called lenses: for instance, a microwave lens can be made from paraffin wax.The oldest lens artefact is the Nimrud lens, which is over three

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thousand years old, dating back to ancient Assyria. David Brewster proposed that it may have been used as a magnifying glass, or as a burning-glass to start fires by concentrating sunlight. Assyrian craftsmen made intricate engravings, and could have used such a lens in their work. Another early reference to magnification dates back to ancient Egyptian hieroglyphs in the 8th century BC, which depict "simple glass meniscal lenses".The earliest written records of lenses date to Ancient Greece, with Aristophanes' play The Clouds (424 BC) mentioning a burning-glass (a biconvex lens used to focus the sun's rays to produce fire). The writings of Pliny the Elder (23–79) also show that burning-glasses were known to the Roman Empire, and mentions what is arguably the earliest use of a corrective lens: Nero was said to watch the gladiatorial games using an emerald(presumably concave to correct for myopia, though the reference is vague). Both Pliny and Seneca the Younger (3 BC–65) described the magnifying effect of a glass globe filled with water.The word lens comes from the Latin name of the lentil, because a double-convex lens is lentil-shaped. The genus of the lentil plant is Lens,

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and the most commonly eaten species is Lens culinaris. The lentil plant also gives its name to a geometric figure.The Arabian physicist and mathematician, Ibn Sahl (c.940–c.1000), used what is now known as Snell's law to calculate the shape of lenses. Ibn al-Haytham (965–1038), known in the West as Alhazen, wrote the first major optical treatise, the Book of Optics, which described how the lens in the human eye formed an image on the retina. The earliest "historical proof of a magnifying device, a convex lens forming a magnified image," also dates back to the Book of Optics. Its translation into Latin in the 12th century was instrumental to the invention of eyeglasses in 13th century Italy.Excavations at the Viking harbour town of Fröjel, Gotland, Sweden discovered in 1999 the rock crystal Visby lenses, produced by turning on pole-lathes at Fröjel in the 11th to 12th century, with an imaging quality comparable to that of 1950s aspheric lenses. The Viking lenses concentrate sunlight enough to ignite fires.Widespread use of lenses did not occur until the use of reading stones in the 11th century and the invention of spectacles, probably in Italy in the 1280s. Nicholas of Cusa is believed to have been the first to discover the benefits of

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concave lenses for the treatment of myopia in 1451.The Abbe sine condition, due to Ernst Abbe (1860s), is a condition that must be fulfilled by a lens or other optical system in order for it to produce sharp images of off-axis as well as on-axis objects. It revolutionized the design of optical instruments such as microscopes, and helped to establish the Carl Zeiss company as a leading supplier of optical instruments.

Positive lens(Real image formation):If a luminous object is placed at a distance greater than the focal length away from a convex lens, then it will form an inverted real image on the opposite side of the lens.

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If the distances from the object to the lens and from the lens to the image are S1 and S2 respectively, for a lens of negligible thickness, in air, the distances are related by the thin lens formula:

Negative lens(Virtual image formation):

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Diverging lenses form reduced, erect, virtual images.

The formulas above may also be used for negative (diverging) lens by using a negative focal length (f), but for these lenses only virtual images can be formed.For the case of lenses that are not thin, or for more complicated multi-lens optical systems, the same formulas can be used, but S1 and S2 are interpreted differently