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Light &
Optics
E
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.
So 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.
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).
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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 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.
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Reasoning that the moons orbital velocities should not be affected by their separation,
he deduced that 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; 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
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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 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) Reflection
2) Refraction
3) Diffraction
4) Interference
5) Dispersion
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Reflection
Light 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.
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 to your eye along the path shown in the diagram below. The diagram
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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.
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
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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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Refraction
Refraction 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.
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.
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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 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°.
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Diffraction
The effects of diffraction can be readily seen in everyday life. The most colorful
examples of 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
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
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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. AugustinJean 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.
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.
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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
analytically; solutions can be found using various numerical analytical methods
including Finite element and boundary element methods.
(Single slit Diffraction)
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Interference
What happens when two waves meet while they travel through the same medium?
What affect 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 drawn in red and blue and the resulting
displacement of the medium is drawn in green.
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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. 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.
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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 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
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.
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Dispersion
In 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 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.
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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 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.
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Optical Fibers
An optical fiber (or fibre) is a glass or plastic fiber that carries light along its length.
Fiber 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 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
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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. 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.
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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, 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-electricaloptical 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
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
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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 longerwavelength 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.
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 longdistance 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
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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
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 lighttransmitting 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.)
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
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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.
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
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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 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.
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Lenses
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
thousand years old, dating back to ancient Assyria.
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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, 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.
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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 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.
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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.
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:
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Negative lens(Virtual image formation):
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
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