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Diffraction

Diffraction

Diffraction is the bending and spreading of waves when they meet an obstruction. It can occur with any type of wave, including sound waves, water waves, and electromagnetic waves such as light and radio waves. Diffraction also occurs when any group of waves of a finite size is propagating; for example, a narrow beam of light waves from a laser must, because of diffraction of the beam, eventually diverge into a wider beam at a sufficient distance from the laser. As a simple example of diffraction, if you speak into one end of a cardboard tube, the sound waves emerging from the other end spread out in all directions, rather than propagating in a straight line like a stream of water from a garden hose.

Introduction

Diffraction is one particular type of wave interference, caused by the partial obstruction or lateral restriction of a wave. Not all interference is diffraction; for example, sound waves emitted by two stereo speakers will interfere with each other if they are of the same frequency and have a definite phase relationship, but this is not diffraction. Diffraction will not occur if the wave is not coherent, and diffraction effects become weaker (and ultimately undetectable) as the size of obstruction is made larger and larger compared to the wavelength. In well-defined cases, a diffraction pattern may be observed. Diffraction is not the same as refraction, although both are phenomena in which a wave does not propagate in a single direction. Refraction is not an interference phenomenon, and, e.g., can occur without coherence. It is the diffraction of "particles," such as electrons, which stood as one of the powerful arguments in favor of quantum mechanics. It is possible to observe diffraction of particles such as neutrons or electrons and hence we are able to infer the existence of wave-particle duality. Indeed, this diffraction is a useful tool; the wavelengths of these particle-waves are small enough that they are used as probes of the atomic structure of crystals. See electron diffraction and neutron diffraction.

image:doubleslitdiffraction.png
Double-slit diffraction

image:Laserdiffraction.jpg
Double-slit diffraction
(red laser light)

image:Diffraction2vs5.jpg
2-slit and 5-slit diffraction

The most conceptually simple example of diffraction is double-slit diffraction in which both slits have relatively narrow widths compared to the wavelength of the wave. Suppose, for the sake of visualization, that these are water waves. After passing through the slits, two overlapping patterns of semicircular ripples are formed, as shown in the first figure. Where a crest overlaps with a crest, a double-height crest will be formed; this is constructive interference. Constructive interference also occurs where a trough overlaps another trough. However, when a trough and a crest overlap, they cancel out; the interference is destructive. The second figure shows the result of this process with light waves of a single wavelength originating from a laser. The constructive-interference locations are called maxima, because they have maximum brightness. The destructive-interference locations are the minima. Historically, the first proof that light was a wave phenomenon came from the double-slit experiment of Thomas Young.

General facts about diffraction

Several qualitative observations can be made:
- When the dimensions of the diffracting object are reduced, the angular spacing of the diffraction pattern is increased in inverse proportion. (More precisely, this is true of the sines of the angles.)
- The diffraction angles are invariant under scaling; that is, they depend only on the ratio of the wavelength to a dimension, a, of the diffracting object.
- When the diffracting object is repeated, the effect is to narrow each maximum, concentrating its energy within a narrower range of angles. The third figure, for example, shows a comparison of a double-slit pattern with a pattern formed by five slits, both sets of slits having the same spacing, a, between the center of one slit and the next.

Mathematical description

It is mathematically easier to consider the case of far-field or Fraunhofer diffraction, where the diffracting obstruction is many wavelengths distant from the point at which the wave is measured. The more general case is known as near-field or Fresnel diffraction, and involves more complex mathematics. As the observation distance is increased the results predicted by the Fresnel theory converge towards those predicted by the simpler Fraunhofer theory. This article considers far-field diffraction, which is commonly observed in nature. Quantitatively, the angular positions of the minima in multiple-slit diffraction are given by the equation :

\sin \theta = \frac m,

where m is an integer that labels the order of each minimum. The central maximum is two orders wide, however, so m = 0, θ = 0 is the absolute maximum of the distribution and intensity functions. This is a form of Bragg's law (see below).

image:diffraction1.png
Graph and image

Quantitative analysis of single-slit diffraction

As an example, we will now derive an exact equation for the intensity of the diffraction pattern as a function of angle in the case of single-slit diffraction. We will start with a mathematical representation of Huygens' principle. Consider a monochromatic complex plane wave

\Psi^\prime

of wavelength λ incident on a slit of width a. Let the slit lie in the x′-y′ plane, with its center at the origin. Then we shall assume that diffraction generates a complex wave ψ, traveling radially in the r direction away from the slit, and this is given by: :

\Psi = \int_ \frac \Psi^\prime e^\,dslit

let (x′,y′,0) be a point inside the slit over which we are integrating; and let (x,0,z) be the location at which we are computing the intensity of the diffraction pattern. The slit extends from

x^\prime=-a/2

+a/2\,

, and from

y'=-\infty

\infty

. The distance r from the slot is: :

r = \sqrt

r = z \left(1 + \frac\right)^\frac

We assume Fraunhofer diffraction, so that

z >> \big|\left(x - x^\prime\right)\big|

. In other words, the distance to the target is much larger than the diffraction width on the target. By the binomial expansion rule, ignoring terms quadratic and higher, we can estimate our quantity on the right to be: :

r \approx z \left( 1 + \frac \frac \right)

r \approx z + \frac

We see that our 1/r in front of the equation is non-oscillatory, i.e. its contribution to the magnitude of the intensity is small compared to our exponential factors. Therefore, we will lose little accuracy by approximating it as z. To make things cleaner, we will use a placeholder 'C' to denote constants in our equation. It is important to keep in mind that C can contain imaginary numbers, thus our wave function will be complex, however at the end, we will bracket our ψ, which will eliminate any imaginary components. Now, in Fraunhoffer diffraction,

kx^/z

is small, so

e^\frac \approx 1

. The same approximation holds for

e^\frac

. Thus, taking

C = \Psi^\prime \sqrt

, we have: Now we note that

\sin x = \frac

and

\sin \theta = \frac

\Psi = C \frac

Now, substituting in

\frac = k

, the intensity I of the diffracted waves at an angle θ is given by: where the sinc function is given by sinc(x) = sin(x)/x.

Quantitative analysis of n-slit diffraction

Let us again start with the mathematical representation of Huygens' principle. :

\Psi = \int_ \frac \Psi^\prime e^\,dslit

Consider n slits in the prime plane of the equal size (a,

\infty

, 0) and spacing d spread along the x′ axis. As above, the distance r from the slit 1 is: :

r = z \left(1 + \frac\right)^\frac

To generalize this to n slits, we make the observation that while z and y remain constant, x′ shifts by :

x_^ = x_0^\prime - j d

Thus :

r_j = z \left(1 + \frac\right)^\frac

and the sum of all n contributions to the wave function is: :

\Psi = \sum_^ C \int_^ e^\frac e^\frac \,dx^\prime

Again noting that

\frac

is small, so

e^\frac \approx 1

, we have: Now, we can use the following identity

\sum_^ e^ = \frac.

Substituting into our equation, we find: We now make our k substitution as before and represent all non-oscillating constants by the

I_0

variable as in the 1-slit diffraction and bracket the result. Remember that :

\langle e^ \Big| e^\rangle\ = e^0 = 1

This allows us to discard the tailing exponent and we have our answer: :

I\left(\theta\right)\,

=I_0 \left[ \operatorname \left( \frac \sin \theta \right) \right]^2

\left[\frac\right]^2

Other cases

Bragg diffraction

Diffraction from multiple slits, as described above, is similar to what occurs when waves are scattered from a periodic structure, such as atoms in a crystal or rulings on a diffraction grating. Each scattering center (e.g., each atom) acts as a point source of spherical wavefronts; these wavefronts undergo constructive interference to form a number of diffracted beams. The direction of these beams is described by Bragg's law: :

m \lambda = 2 d \sin \theta,\,

where λ is the wavelength, d is the distance between scattering centers, θ is the angle of diffraction and m is an integer known as the order of the diffracted beam. Bragg diffraction is used in X-ray crystallography to deduce the structure of a crystal from the angles at which X-rays are diffracted from it. Since the diffraction angle θ is dependent on the wavelength λ, diffaction gratings impart angular dispersion on a beam of light. The most common demonstration of Bragg diffraction is the spectrum of colors seen reflected from a compact disc: the closely-spaced tracks on the surface of the disc form a diffraction grating, and the individual wavelengths of white light are diffracted at different angles from it, in accordance with Bragg's law.

Diffraction limit of telescopes

compact disc of the binary star zeta Boötis.]] For diffraction through a circular aperture, there is a series of concentric rings surrounding a central Airy disc. The mathematical result is similar to a radially symmetric version of the equation given above in the case of single-slit diffraction. A wave does not have to pass through an aperture to diffract; for example, a beam of light of a finite size also undergoes diffraction and spreads in diameter. This effect limits the minimum size d of spot of light formed at the focus of a lens, known as the diffraction limit: :

d = 2.44 \lambda \frac,\,

where λ is the wavelength of the light, f is the focal length of the lens, and a is the diameter of the beam of light, or (if the beam is filling the lens) the diameter of the lens. (See Rayleigh criterion). By use of Huygens' principle, it is possible to compute the diffraction pattern of a wave from any arbitrarily shaped aperture. If the pattern is observed at a sufficient distance from the aperture, it will appear as the two-dimensional Fourier transform of the function representing the aperture.

External links

- [http://www.falstad.com/wave2d/ 2-D wave java applet] displays diffraction patterns of various slit configurations.
- [http://www.falstad.com/diffraction/ Diffraction java applet] displays diffraction patterns of various 2-D apertures.
- [http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm Diffraction Limited Photography] understanding how airy disks, lens aperture and pixel size limit the absolute resolution of any camera. Category:Optics Category:Wave mechanics ja:回折

Wave

:This article is about waves in the most general scientific sense; a separate article focuses on ocean waves. For other meanings see wave (disambiguation). Soundwave redirects here. for the Transformers character, see Soundwave (Transformers) A wave is a disturbance that propagates in a periodically repeating fashion, often transferring energy. A mechanical wave exists in a medium (which on deformation is capable of producing elastic restoring forces) through which they travel and can transfer energy from one place to another without any of the particles of the medium being displaced permanently; there is no associated mass transport. Instead, any particular point oscillates around a fixed position. However, electromagnetic radiation, and probably gravitational radiation are not mechanical waves, and can travel through a vacuum, without a medium. Waves are characterised by crests (highs) and troughs (lows), either perpendicular (in the case of transverse waves) or parallel (in the case of longitudinal waves) to wave motion.
The medium which carries a wave
A medium that can carry a wave is classified by one or more of the following properties:
- A linear medium if the amplitudes of different waves at any particular point in the medium can be added.
- A bounded medium if it is finite in extent, otherwise unbounded.
- A uniform medium if its physical properties are unchanged at different locations in space.
- An isotropic medium if its physical properties are the same in different directions.
Examples of waves
troughs
- Ocean surface waves, which are perturbations that propagate through water (see also surfing and tsunami).
- Visible light, radio waves, x-rays, gamma rays, infrared rays, and ultraviolet rays make up electromagnetic radiation. In this case propagation is possible without a medium, through vacuum. These electromagnetic waves travel at about 300,000 km/s.
- Sound - a mechanical wave that propagates through air, liquid or solids, and is of a frequency detected by the auditory system. Similar are seismic waves in earthquakes, of which there are the S, P and L kinds.
- Gravitational waves, which are fluctuations in the gravitational field predicted by General relativity. These waves are nonlinear.
Characteristic properties
All waves have common behaviour under a number of standard situations. All waves can experience the following:
- Reflection – the change of direction of waves, due to hitting a reflective surface.
- Refraction – the change of direction of a wave due to them entering a new medium.
- Diffraction – the spreading out of waves, for example when they travel through a small slit.
- Interference – the superposition of two waves that come into contact with each other.
- Dispersion – the splitting up of waves by frequency.
- Rectilinear propagation – the movement of waves in straight lines.
Transverse and longitudinal waves
Rectilinear propagation Transverse waves are those with vibrations perpendicular to the direction of the propagation of the wave; examples include waves on a string and electromagnetic waves. Longitudinal waves are those with vibrations parallel to the direction of the propagation of the wave; examples include most sound waves. Ripples on the surface of a pond are actually a combination of transverse and longitudinal waves; therefore, the points on the surface follow elliptical paths.
Polarization
Transverse waves can be polarized. Unpolarised waves can oscillate in any direction in the plane perpendicular to the direction of travel, while polarized waves oscillate in only one direction perpendicular to the line of travel.
Physical description of a wave
Image:wave.png Waves can be described using a number of standard variables including: frequency, wavelength, amplitude and period. The amplitude of a wave is the measure of the magnitude of the maximum disturbance in the medium during one wave cycle, and is measured in units depending on the type of wave. For examples, waves on a string have an amplitude expressed as a distance (meters), sound waves as pressure (pascals) and electromagnetic waves as the amplitude of the electric field (volts/meter). The amplitude may be constant (in which case the wave is a c.w. or continuous wave) or may vary with time and/or position. The form of the variation of amplitude is called the envelope of the wave. The period (T) is the time for one complete cycle for an oscillation of a wave. The frequency (F) is how many periods per unit time (for example one second) and is measured in hertz. These are related by: : $f=\frac$ When waves are expressed mathematically, the angular frequency (ω, radians/second) is often used; it is related to the frequency f by: : $f=\frac$ .
Travelling waves
Waves that remain in one place are called standing waves - e.g. vibrations on a violin string. Waves that are moving are called travelling waves, and have a disturbance that varies both with time t and distance z. This can be expressed mathematically as: : $y=A(z,t) \cos (\omega t - kz + \phi),\,f$ where A(z, t) is the amplitude envelope of the wave, k is the wave number and φ is the phase. The velocity v of this wave is given by: : $v=\frac= \lambda f,$ where λ is the wavelength of the wave.
Propagation through strings
The speed of a wave travelling along a string (v) is directly proportional to the square root of the tension (T) over the linear density (ρ): : $v=\sqrt.$ This equation can be found using dimensional analysis
The wave equation
The wave equation is a differential equation which describes a harmonic wave passing through a medium, discussed above. The equation has different forms depending on how the wave is transmitted, and on what medium. Not all waves are sinusoidal. One example of a non-sinusoidal wave is a pulse that travels down a rope resting on the ground, extending in direction x, travelling at velocity c. The height of the pulse above the ground is φ. The distance the pulse travels between some time t and time 0 is ct. In one dimension the wave equation has the form : $\frac\frac=\frac. \$ A general solution, given by d'Alembert is : $\phi(x,t)=F(x-ct)+G(x+ct). \$ considered to be the shapes of two pulses travelling down the rope, F in the +x direction, and G in the -x direction. If we substitute for x above, instead directions x, y, z, we then can describe a wave propagating in three dimensions. A non-linear wave-equation can cause mass transport. The Schrödinger equation describes the wave-like behaviour of particles in quantum mechanics. Solutions of this equation are wave functions which can be used to describe the probability density of a particle. Quantum mechanics also describes particle properties that other waves, such as light and sound, have on the atomic scale and below.
External links

- [http://www.lightandmatter.com/area1book3.html Vibrations and Waves] - an online textbook
- [http://kestrel.nmt.edu/~raymond/classes/ph13xbook/node1.html A Radically Modern Approach to Introductory Physics] - an online physics textbook that starts with waves rather than mechanics
See also

- List of wave topics
- Capillary waves
- Doppler effect
- Group velocity
- Phase velocity
- Ripple tank
- Standing wave
- Audience wave
- Ocean surface wave
- Waving Category:Partial differential equations ko:파동 ms:Gelombang ja:波動 simple:Wave

Water

:This article focuses on water as it is experienced in everyday life. See water (molecule) for information on the chemical and physical properties of pure water (H₂O, hydrogen oxide). Water (from the Old English word wæter; c.f German "Wasser", from PIE
- wod-or, "water") is a tasteless, odorless, and nearly colorless (it has a slight hint of blue) substance in its pure form that is essential to all known forms of life and is known also as the most universal solvent. Water is an abundant substance on Earth. It exists in many places and forms. It appears mostly in the oceans and polar ice caps, but also as clouds, rain water, rivers, freshwater aquifers, and sea ice. On the planet, water is continuously moving through the cycle involving evaporation, precipitation, and runoff to the sea. Water fit for human consumption is called potable water. This natural resource is becoming more scarce in certain places as human population in those places increases, and its availability is a major social and economic concern.

Molecular properties

Forms of water

potable water] Water takes many different shapes on earth: water vapor and clouds in the sky, waves and icebergs in the sea, glaciers in the mountain, aquifers in the ground, to name but a few. Through evaporation, precipitation, and runoff, water is continuously flowing from one form to another, in what is called the water cycle. Because of the importance of precipitation to agriculture, and to mankind in general, different names are given to its various forms: while rain is common in most countries, other phenomena are quite surprising when seen for the first time. Hail, snow, fog or dew are examples. When appropriately lit, water drops in the air can refract sunlight to produce rainbows. Similarly, water runoffs have played major roles in human history as rivers and irrigation brought the water needed for agriculture. Rivers and seas offered opportunity for travel and commerce. Through erosion, runoffs played a major part in shaping the environment providing river valleys and deltas which provide rich soil and level ground for the establishment of population centers. Water also infiltrates the ground and goes into aquifers. This groundwater later flows back to the surface in springs, or more spectacularly in hot springs and geysers. Groundwater is also extracted artificially in wells. Because water can contain many different substances, it can taste or smell very differently. In fact, humans and other animals have developed their senses to be able to evaluate the drinkability of water: animals generally dislike the taste of salty sea water and the putrid swamps and favor the purer water of a mountain spring or aquifer.

Water in biology

From a biological standpoint, water has many distinct properties that are critical for the proliferation of life that set it apart from other substances. Water carries out this role by allowing organic compounds to react in ways that ultimately allows replication. It is a good solvent and has a high surface tension, and thus allows organic compounds and living things to be transported in it. Fresh water has its greatest density at 4°C, then becoming less dense as it freezes or heats up from this point. As a stable, polar molecule prevalent in the atmosphere, it plays an important atmospheric role as an absorber of infrared radiation, crucial in the atmospheric greenhouse effect without of which, the average surface temperature would be −18° Celsius. Water also has an unusually high specific heat, which plays many roles in regulating global and regional climate, such as the Gulf Stream climate, allowing life to survive. Water is a very good solvent, chemically not unlike ammonia, and dissolves many types of substances, such as various salts and sugar, and facilitates their chemical interaction, which aids complex metabolisms. Some substances, however, do not mix well with water, including oils and other hydrophobic substances. Cell membranes, composed of lipids and proteins, take advantage of this property to carefully control interactions between their contents and external chemicals. This is facilitated somewhat by the surface tension of water. Water drops are stable due to the high surface tension of water caused by the strong intermolecular forces called cohesive forces. This can be seen when small quantities of water are put onto a nonsoluble surface such as polythene: the water stays together as drops. On extremely clean glass the water may form a thin film because the molecular forces between glass and water molecules (adhesive forces) are stronger than the cohesive forces. This property plays a key role in plant transpiration. A simple but environmentally important and unique property of water is that its common solid form, ice, floats on the liquid. This solid phase is less dense than liquid water, due to the geometry of the strong hydrogen bonds which are formed only at lower temperatures. For almost all other substances and for all other 11 uncommon phases of water ice except ice-XI, the solid form is more dense than the liquid form. Fresh water is most dense at 4°C, and will sink by convection as it cools to that temperature, and if it becomes colder it will rise instead. This reversal will cause deep water to remain warmer than shallower freezing water, so that ice in a body of water will form first at the surface and progress downward, while the majority of the water underneath will hold a constant 4°C. This effectively insulates a lake floor from the cold. While this behavior may seem obvious, even intuitive, it should be noted that almost all other chemicals are denser as solids than they are as liquids, and freeze from the bottom up. Life on earth has evolved with and adapted itself to the important features of water. The existence of abundant liquid, vapor and solid forms of water on Earth has been an important factor in the abundant colonization of Earth's various environments by life-forms adapted to those varying and often extreme conditions. Civilizations have historically flourished around rivers and major waterways; Mesopotamia, the so-called cradle of civilization, is situated between two major rivers. Large metropolises like London, Paris, New York, and Tokyo owe their success in part to their easy accessibility via water and the resultant expansion of trade. Islands with safe water ports, like Singapore and Hong Kong, have flourished for precisely this reason. In places such as North Africa and the Middle East, where water is scarcer, access to clean drinking water was and is a major factor in human development.

Astronomical position of Earth and impact on its water

Mesopotamia The coexistence of the solid, liquid, and gaseous phases of water on Earth is vital to the origin, evolution, and continued existence of life on Earth. However, if the Earth's location in the solar system were even marginally closer or further from the Sun (ie, a million miles or so), the conditions which allow the three forms to be present simultaneously would be far less likely to exist. Earth's mass allows gravity to hold an atmosphere. Water vapor and carbon dioxide in the atmosphere provides a greenhouse effect which helps maintain a relatively steady surface temperature. If Earth were less massive, a thinner atmosphere would cause temperature extremes preventing the accumulation of water except in polar ice caps (as on Mars). According to the solar nebula model of the solar system's formation, Earth's mass may be largely due to its distance from the Sun. The distance between Earth and the Sun and the combination of solar radiation received and the greenhouse effect of the atmosphere ensures that its surface is neither too cold nor too hot for liquid water. If Earth were more distant, most water would be frozen. If Earth were nearer to the Sun, its higher surface temperature would limit the formation of ice caps, or cause water to exist only as vapor. In the former case, the low albedo of oceans would cause Earth to absorb more solar energy. In the second case, a runaway greenhouse effect and inhospitable conditions similar to Venus would result. It has been proposed that life itself may maintain the conditions that have allowed its continued existence. The surface temperature of Earth has been relatively constant through geologic time despite varying solar flux, indicating that a dynamic process governs Earth's temperature via a combination of greenhouse gases and surface or atmospheric albedo. This proposal is known as the Gaia hypothesis.

Human uses of water

Gaia hypothesis All known forms of life depend on water. Water is a vital part of many metabolic processes within the body. Significant quantities of water are used during the digestion of food. (Note however that some bacteria and plant seeds can enter a cryptobiotic state for an indefinite period when dehydrated, and come back to life when returned to a wet environment) About 72% of the fat free mass of the human body is made of water. To function properly the body requires between one and seven litres of water per day to avoid dehydration, the precise amount depending on the level of activity, temperature, humidity, and other factors. It is not clear how much water intake is needed by healthy people. However, for those who do not have kidney problems, it is rather difficult to drink too much water, but (especially in warm humid weather and while exercising) dangerous to drink too little. People do often drink far more water than necessary while exercising, however, putting them at risk of water intoxication, which is frequently fatal. The "fact" that a person should consume eight glasses of water per day cannot be traced back to a scientific source. However, leading dieticians and nutritionists will tell you that this is the RDI (Recommended Daily Intake) of water. [http://ajpregu.physiology.org/cgi/content/full/283/5/R993]. The latest dietary reference intake report by the National Research Council recommended 2.7 liters of water total (including food sources) for women and 3.7 liters for men[http://www.iom.edu/report.asp?id=18495]. Water is lost from the body in urine and feces, through sweating, and by exhalation of water vapor in the breath. Humans require water that does not contain too much salt or other impurities. Common impurities include chemicals and/or harmful bacteria, such as crypto sporidium. Some solutes are acceptable and even desirable for perceived taste enhancement and to provide needed electrolytes.

Water as a precious resource

:See water resources for information about fresh water supplies. fresh water Because of the growth of world population and other factors, the availability of drinking water per capita is shrinking. The issue of water shortage can be solved through more production, better distribution and less waste of it. For this reason, water is a strategic resource for many countries. Many battles and wars, such as the Six-Day War in the Middle East, have been fought to gain access to it. Experts predict more trouble ahead because of the world's growing population, increasing contamination through pollution, and global warming. UNESCO's World Water Development Report (WWDR, 2003) from its World Water Assessment Program indicates that, in the next 20 years, the quantity of water available to everyone is predicted to decrease by 30%. 40% of the world's inhabitants currently have insufficient fresh water for minimal hygiene. More than 2.2 million people died in 2000 from diseases related to the consumption of contaminated water or drought. In 2004, the UK charity WaterAid reported that a child dies every 15 seconds due to easily preventable water-related diseases. Some have predicted that clean water will become the "next oil", making Canada, with this resource in abundance, possibly the richest country in the world.

Regulating water distribution

Drinking water is often collected at springs or extracted from artificial borings in the ground, or wells. Building more wells in adequate places is thus a possible way to produce more water assuming the aquifers can supply an adequate flow. Other water sources are the rainwater and river or lake water. This surface water, however, must be purified for human consumption. This may involve removal of undissolved substances, dissolved substances and harmful microbes. Popular methods are filtering with sand which only removes undissolved material while chlorination and boiling kill harmful microbes. Distillation does all three functions. More advanced techniques exist, such as reverse osmosis. Desalination of abundant ocean or seawater is a more expensive solution used in coastal arid climates. The distribution of drinking water is done through municipal water systems or as bottled water. Governments in many countries have programs to distribute water to the needy at no charge. Others argue that the market mechanism and free enterprise are best to manage this rare resource, and to finance the boring of wells or the construction of dams and reservoirs. Reducing waste, that is using drinking water only for human consumption, is another option. In some cities, such as Hong Kong, sea water is extensively used for flushing toilets citywide in order to conserve fresh water resources. Polluting water may be the biggest single misuse of water; to the extent that a pollutant limits other uses of the water, it becomes a waste of the resource, regardless of benefits to the pollutor. Pharmaceuticals consumed by humans often end up in the waterways and can have detrimental effects on aquatic life if they bioaccumulate and if they are not biodegradable.

The impact of water on human culture

Water is considered a purifier in most religions, including Christianity, Islam, Judaism, and Shinto. For instance, baptism in Christian churches is done with water. In addition, a ritual bath in pure water is performed for the dead in many religions including Judaism and Islam. In Islam, the daily Salah can only be done after ablution (Wodoo), that is, washing parts of the body in clean water. In Shinto, water is used in almost all rituals to cleanse a person or an area. Water is often believed to have spiritual powers. In Celtic mythology, Sulis is the local goddess of thermal springs; in Hinduism, the Ganga is also personified as a goddess. Alternatively, gods can be patrons of particular springs, river or lakes: for example in Greek and Roman mythology, Peneus was a river god, one of the three thousand Oceanids. The Greek philosopher Empedocles held that water is one of the four classical elements along with fire, earth and air, and was regarded as the ylem, or basic stuff of the universe. Water was considered cold and moist. In the theory of the four bodily humours, water was associated with phlegm. Water was also one of the Five Elements in traditional Chinese philosophy, along with earth, fire, wood, and metal. A common misconception about water is that it is a powerful conductor of electricity. Any electrical properties observable in water are due to the ions of mineral salts and carbon dioxide dissolved in it. Water does self-ionize (two water molecules become one hydroxide anion and one hydronium cation), but only at a very slight, almost immeasurable level. Pure water can also be electrolized into oxygen and hydrogen gases but without any dissolved ions, this is a very slow process and thus very little current is conducted. Many bottled water companies exploit another common misconception, advertising both purity and taste, even though pure water is tasteless.

External links

- [http://www.lsbu.ac.uk/water/phase.html Phase diagrams of water]
- [http://www.publicforuminstitute.org/issues/oceans/index.htm Oceans and Water Issues Page]
- [http://www.greenfacts.org/water-disinfectants/index.htm Scientific Facts on Water disinfectants] A faithful summary by GreenFacts of a leading scientific consensus report on Drinking Water Disinfectants published by the International Programme on Chemical Safety of the WHO.
- [http://www.hkc22.com/residentialwater.html Residential water problems and markets] Study paper from Helmut Kaiser Consultancy
- [http://www.hkc22.com/watermarketsworldwide.html Water markets worldwide] Study paper from Helmut Kaiser Consultancy
- [http://www.worldwaterforum.org/ World Water Forum]
- [http://www.unesco.org/water/wwap/ World Water Assessment Program]
- [http://unesdoc.unesco.org/images/0012/001295/129556e.pdf United Nations' World Water Development Report]
- [http://www.gemswater.org/ United Nations GEMS/Water Programme]
- [http://www.lsbu.ac.uk/water/ Water Structure and Behaviour]
- [http://www.wateraid.org/ WaterAid]
- [http://www.sahra.arizona.edu/newswatch/ SAHRA—Global Water Newswatch]
- [http://www.siwi.org/ Stockholm International Water Institute] (SIWI)
- [http://www.c-win.org/ California Water Impact Network (C-WIN)]
- [http://news.bbc.co.uk/2/hi/science/nature/3752590.stm BBC: The water debate]
- [http://www.geocities.com/tapvsbottled/ Tap Water Vs Bottled Water] - Interesting site providing facts about tap and bottled water.
- [http://www.emagazine.com/september-october_2003/0903feat1.html E the Environmental Magazine piece on bottled water] (Oct 2003).
- [http://www.iapws.org/ International Association for the Properties of Water and Steam]
- [http://ga.water.usgs.gov/edu/watercycle.html US Geological Survey: Comprehensive discussion of the water cycle, in many languages]
- [http://www.dartmouth.edu/~etrnsfer/water.htm Why is water blue?]
- [http://www.water.org.uk/home/resources-and-links/water-for-health/ask-about/adults Water requirements in adults]
- [http://www.hkc22.com/environmentaltechnology.html/ Climate change raises markets for environmental technology, drinking water and clean energies]

References

- OA Jones, JN Lester and N Voulvoulis, Pharmaceuticals: a threat to drinking water? TRENDS in Biotechnology 23(4): 163, 2005
- Category:Beverages Category:Hydrology Category:Materials Category:Natural resources Category:Nutrition zh-min-nan:Chúi als:Wasser ko:물 ja:水 ms:Air simple:Water th:น้ำ

Light

Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of any wavelength. The three basic dimensions of light (i.e., all electromagnetic radiation) are:
- Intensity (or brilliance or amplitude), which is related to the human perception of brightness of the light,
- Frequency (or wavelength), perceived by humans as the color of the light, and
- Polarization (or angle of vibration), which is not perceptible by humans under ordinary circumstances. Due to wave-particle duality, light simultaneously exhibits properties of both waves and particles. The precise nature of light is one of the key questions of modern physics.

Visible electromagnetic radiation

Visible light is the portion of the electromagnetic spectrum between the frequencies of 380 THz (3.8×10¹⁴ hertz) and 750 THz (7.5×10¹⁴ hertz). The speed (

c

), frequency (

f

\nu

), and wavelength (

\lambda

) of a wave obey the relation: :

c = f~\lambda \,\!

Because the speed of light in a vacuum is fixed, visible light can also be characterised by its wavelength of between 400 nanometres (abbreviated 'nm') and 800 nm (in a vacuum). Light entering the eye is absorbed by light-sensitive pigments within the rod cells and cone cells in the retina, triggering a cascade of events that creates electrical nerve impulses that travel through the optic nerve to the brain, producing vision.

Speed of light

Although some people speak of the "velocity of light", the word velocity should be reserved for vector quantities, that is, those with both magnitude and direction. The speed of light is a scalar quantity, having only magnitude and no direction, and therefore speed is the correct term. The speed of light has been measured many times, by many physicists. The best early measurement is Ole Rømer's (a Danish physicist), in 1676. By observing the motions of Jupiter and one of its moons, Io, with a telescope, and noting discrepancies in the apparent period of Io's orbit, Rømer calculated a speed of 227,000 kilometres per second (approximately 141,050 miles per second). The first successful measurement of the speed of light using an earthbound apparatus was carried out by Hippolyte Fizeau in 1849. Fizeau directed a beam of light at a mirror several thousand metres away, and placed a rotating cog wheel in the path of the beam from the source to the mirror and back again. At a certain rate of rotation, the beam could pass through one gap in the wheel on the way out and the next gap on the way back. Knowing the distance to the mirror, the number of teeth on the wheel, and the rate of rotation, Fizeau measured the speed of light as 313,000 kilometres per second. Léon Foucault used rotating mirrors to obtain a value of 298,000 km/s (about 185,000 miles/s) in 1862. Albert A. Michelson conducted experiments on the speed of light from 1877 until his death in 1931. He refined Foucault's results in 1926 using improved rotating mirrors to measure the time it took light to make a round trip from Mt. Wilson to Mt. San Antonio in California. The precise measurements yielded a speed of 186,285 mile/s (299,796 km/s [1,079,265,600 km/h]). In daily use, the figures are rounded off to 300,000 km/s and 186,000 miles/s.

Refraction

All light propagates at a finite speed. Even moving observers always measure the same value of c, the speed of light in vacuum, as c = 299,792,458 metres per second (186,282.397 miles per second). When light passes through a transparent substance, such as air, water or glass, its speed is reduced, and it undergoes refraction. The reduction of the speed of light in a denser material can be indicated by the refractive index, n, which is defined as: :

n = \frac \;\!

Thus, n=1 in a vacuum and n>1 in matter. When a beam of light enters a medium from vacuum or another medium, it keeps the same frequency and changes its wavelength. If the incident beam is not orthogonal to the edge between the media, the direction of the beam will change. Refraction of light by lenses is used to focus light in magnifying glasses, spectacles and contact lenses, microscopes and refracting telescopes.

Optics

The study of light and the interaction of light and matter is termed optics. The observation and study of optical phenomena such as rainbows offers many clues as to the nature of light as well as much enjoyment.

Color and wavelengths

The different wavelengths are detected by the human eye and then interpreted by the brain as colors, ranging from red at the longest wavelengths of about 700 nm. (lowest frequencies) to violet at the shortest wavelengths of about 400 nm. (highest frequencies). The intervening frequencies are seen as orange, yellow, green, cyan, blue, and, conventionally, indigo.
indigo
The wavelengths of the electromagnetic spectrum immediately outside the range that the human eye is able to perceive are called ultraviolet (UV) at the short wavelength (high frequency) end and infrared (IR) at the long wavelength (low frequency) end. Some animals, such as bees, can see UV radiation while others, such as pit viper snakes, can see infrared light. UV radiation is not normally directly perceived by humans except in a very delayed fashion, as overexposure of the skin to UV light can cause sunburn, or skin cancer, and underexposure can cause vitamin D deficiency. However, because UV is a higher frequency radiation than visible light, it very easily can cause materials to fluoresce visible light. Cameras that can detect IR and convert it to light are called, depending on their application, night-vision cameras or infrared cameras. These are different from image intensifier cameras, which only amplify available visible light. When intense radiation (of any frequency) is absorbed in the skin, it causes heating which can be felt. Since hot objects are strong sources of infrared radiation, IR radiation is commonly associated with this sensation. Any intense radiation that can be absorbed in the skin will have the same effect, however.

Measurement of light

The following quantities and units are used to measure the quantity or "brightness" of light. Light can also be characterised by:
- amplitude,
- color, wavelength, or frequency, and
- polarization (or angle of vibration).

Light sources

polarization There are many sources of light. The most common light sources are thermal: a body at a given temperature emits a characteristic spectrum of black body radiation. Examples include sunlight (the radiation emitted by the chromosphere of the Sun at around 6,000 K peaks in the visible region of the electromagnetic spectrum), incandescent light bulbs (which emit only around 10% of their energy as visible light and the remainder as infrared), and glowing solid particles in flames. The peak of the blackbody spectrum is in the infrared for relatively cool objects like human beings. As the temperature increases, the peak shifts to shorter wavelengths, producing first a red glow, then a white one, and finally a blue color as the peak moves out of the visible part of the spectrum and into the ultraviolet. These colors can be seen when metal is heated to "red hot" or "white hot". The blue color is most commonly seen in a gas flame or a welder's torch. Atoms emit and absorb light at characteristic energies. This produces "emission lines" in the spectrum of each atom. Emission can be spontaneous, as in light-emitting diodes, gas discharge lamps (such as neon lamps and neon signs, mercury-vapor lamps, etc.), and flames (light from the hot gas itself—so, for example, sodium in a gas flame emits characteristic yellow light). Emission can also be be stimulated, as in a laser or a microwave maser. Acceleration of a free charged particle, such as an electron, can produce visible radiation: cyclotron radiation, synchrotron radiation, and bremsstrahlung radiation are all examples of this. Particles moving through a medium faster than the speed of light in that medium can produce visible Cherenkov radiation. Certain chemicals produce visible radiation by chemoluminescence. In living things, this process is called bioluminescence. For example, fireflies produce light by this means, and boats moving through water can disturb plankton which produce a glowing wake. Certain substances produce light when they are illuminated by more energetic radiation, a process known as fluorescence. This is used in fluorescent lights. Some substances emit light slowly after excitation by more energetic radiation. This is known as phosphorescence. Phosphorescent materials can also be excited by bombarding them with subatomic particles. Cathodoluminescence is one example of this. This mechanism is used in cathode ray tube televisions. Certain other mechanisms can produce light:
- scintillation
- scintillator
- electroluminescence
- sonoluminescence
- triboluminescence
- radioactive decay
- particle-antiparticle annihilation

Theories about light

Early Greek ideas

In 55 BC Lucretius, continuing the ideas of earlier atomists, wrote that light and heat from the Sun were composed of minute particles. Ptolemy also wrote about the refraction of light.

10th century optical theory

The scientist Abu Ali al-Hasan ibn al-Haytham (965-c.1040), also known as Alhazen, developed a broad theory that explained vision, using geometry and anatomy, which stated that each point on an illuminated area or object radiates light rays in every direction, but that only one ray from each point, which strikes the eye perpendicularly, can be seen. The other rays strike at different angles and are not seen. He used the example of the pinhole camera, which produces an inverted image, to support his argument. Alhazen held light rays to be streams of minute particles that travelled at a finite speed. He improved Ptolemy's theory of the refraction of light. Alhazen's work did not become known in Europe until the late 16th century.

The 'plenum'

René Descartes (1596-1650) held that light was a disturbance of the plenum, the continuous substance of which the universe was composed. In 1637 he published a theory of the refraction of light which wrongly assumed that light travelled faster in a denser medium, by analogy with the behaviour of sound waves. Descartes' theory is often regarded as the forerunner of the wave theory of light.

Particle theory

Pierre Gassendi (1592-1655), an atomist, proposed a particle theory of light which was published posthumously in the 1660s. Isaac Newton studied Gassendi's work at an early age, and preferred his view to Descartes' theory of the plenum. He stated in his Hypothesis of Light of 1675 that light was composed of corpuscles (particles of matter) which were emitted in all directions from a source. One of Newton's arguments against the wave nature of light was that waves were known to bend around obstacles, while light travelled only in straight lines. He did, however, explain the phenomenon of the diffraction of light (which had been observed by Francesco Grimaldi) by allowing that a light particle could create a localised wave in the aether. Newton's theory could be used to predict the reflection of light, but could only explain refraction by incorrectly assuming that light accelerated upon entering a denser medium because the gravitational pull was greater. Newton published the final version of his theory in his Opticks of 1704. His reputation helped the particle theory of light to dominate physics during the 18th century.

Wave theory

In the 1660s, Robert Hooke published a wave theory of light. Christian Huygens worked out his own wave theory of light in 1678, and published it in his Treatise on light in 1690. He proposed that light was emitted in all directions as a series of waves in a medium called the aether. As waves are not affected by gravity, it was assumed that they slowed down upon entering a denser medium. The wave theory predicted that light waves could interfere with each other like sound waves (as noted in the 18th century by Thomas Young), and that light could be polarized. Young showed by means of a diffraction experiment that light behaved as waves. He also proposed that different colors were caused by different wavelengths of light, and explained color vision in terms of three-colored receptors in the eye. Another supporter of the wave theory was Euler. He argued in Nova theoria lucis et colorum (1746) that diffraction could more easily be explained by a wave theory. Later, Fresnel independently worked out his own wave theory of light, and presented it to the Académie des Sciences in 1817. Simeon Denis Poisson added to Fresnel's mathematical work to produce a convincing argument in favour of the wave theory, helping to overturn Newton's corpuscular theory. The weakness of the wave theory was that light waves, like sound waves, would need a medium for transmission. A hypothetical substance called the luminiferous aether was proposed, but its existence was cast into strong doubt by the Michelson-Morley experiment. Newton's corpuscular theory implied that light would travel faster in a denser medium, while the wave theory of Huygens and others implied the opposite. At that time, the speed of light could not be measured accurately enough to decide which theory was correct. The first to make a sufficiently accurate measurement was Léon Foucault, in 1850. His result supported the wave theory, and the classical particle theory was finally abandoned.

Electromagnetic theory

In 1845, Faraday discovered that the angle of polarisation of a beam of light as it passed through a polarising material could be altered by a magnetic field, an effect now known as Faraday rotation. This was the first evidence that light was related to electromagnetism. Faraday proposed in 1847 that light was a high-frequency electromagnetic vibration, which could propagate even in the absence of a medium such as the aether. Faraday's work inspired James Clerk Maxwell to study electromagnetic radiation and light. Maxwell discovered that self-propagating electromagnetic waves would travel through space at a constant speed, which happened to be equal to the previously measured speed of light. From this, Maxwell concluded that light was a form of electromagnetic radiation: he first stated this result in 1862 in On Physical Lines of Force. In 1873, he published A Treatise on Electricity and Magnetism, which contained a full mathematical description of the behaviour of electric and magnetic fields, still known as Maxwell's equations. The technology of radio transmission was, and still is, based on this theory. The constant speed of light predicted by Maxwell's equations contradicted the mechanical laws of motion that had been unchallenged since the time of Galileo, which stated that all speeds were relative to the speed of the observer. A solution to this contradiction would later be found by Albert Einstein.

Particle theory revisited

The wave theory was accepted until the late 19th century, when Einstein described the photoelectric effect, by which light striking a surface caused electrons to change their momentum, which indicated a particle-like nature of light. This clearly contradicted the wave theory, and for years physicists tried in vain to resolve this contradiction.

Quantum theory

In 1900, Max Planck described quantum theory, in which light is considered to be as a particle that could exist in discrete amounts of energy only. These packets were called quanta, and the particle of light was given the name photon, to correspond with other particles being described around this time, such as the electron and proton. A photon has an energy, E, proportional to its frequency, f, by :

E_f = hf = \frac \,\!

where h is Planck's constant,

\lambda

is the wavelength and c is the speed of light. As it originally stood, this theory did not explain the simultaneous wave-like nature of light, though Planck would later work on theories that did. The Nobel Committee awarded Planck the Physics Prize in 1918 for his part in the founding of quantum theory.

Wave-particle duality

The modern theory that explains the nature of light is wave-particle duality, described by Albert Einstein in the early 1900s, based on his work on the photoelectric effect and Planck's results. Einstein determined that the energy of a photon is proportional to its frequency. More generally, the theory states that everything has both a particle nature and a wave nature, and various experiments can be done to bring out one or the other. The particle nature is more easily discerned if an object has a large mass, so it took until an experiment by Louis de Broglie in 1924 to realise that electrons also exhibited wave-particle duality. Einstein received the Nobel Prize in 1921 for his work with the wave-particle duality on photons, and de Broglie followed in 1929 for his extension to other particles.

A light wave

1929 that oscillate perpendicular to each other and to the direction of motion (a transverse wave).]] The electric and magnetic fields are perpendicular to the direction of travel and to each other. This picture depicts a very special case, linearly polarized light. See Polarization for a description of the general case and an explanation of linear polarization. While these relations of the electric and magnetic fields are always true, the subtle difference in the general case is that the direction and amplitude of the magnetic (or electric) field can vary, in one place, with time, or, in one instant, can vary along the direction of propagation.

Radio waves

:For other uses, see Radio wave (disambiguation) Radio wave (disambiguation) Radio frequency, or RF, refers to that portion of the electromagnetic spectrum in which electromagnetic waves can be generated by alternating current fed to an antenna. Such frequencies account for the following parts of the spectrum shown in the table below.
Radio frequency spectrum

Notes:
Above 300 GHz, the absorption of electromagnetic radiation by Earth's atmosphere is so great that the atmosphere is effectively opaque to higher frequencies of electromagnetic radiation, until the atmosphere becomes transparent again in the so-called infrared and optical window frequency ranges. The ELF, SLF, ULF, and VLF bands overlap the AF (audio frequency) spectrum, which is approximately 20–20,000 Hz. However, sounds are transmitted by atmospheric compression and expansion, and not by electromagnetic energy. The SHF and EHF bands are often considered to be not part of the radio spectrum and form their own microwave spectrum.
Named frequency bands

General

- Band III - 174–245 MHz
- ISM band ... specific frequencies vary...
Amateur radio frequencies
The range of allowed frequencies vary between countries. These are just some of the more common bands. In the article about amateur radio is another list.
IEEE US

EU, NATO

See also

- Radio propagation
- Frequency allocation
External links

- [http://www.sengpielaudio.com/calculator-wavelength.htm Radio and light waves conversion: frequency to wavelength and vice versa]
References
Category:Radio spectrum Category:Wireless communications ja:電波の周波数による分類