Thursday, January 19, 2012

Light


Light

Light, form of energy visible to the human eye that is radiated by moving charged particles. Light from the Sun provides the energy needed for plant growth. Plants convert the energy in sunlight into storable chemical form through a process called photosynthesis. Petroleum, coal, and natural gas are the remains of plants that lived millions of years ago, and the energy these fuels release when they burn is the chemical energy converted from sunlight. When animals digest the plants and animals they eat, they also release energy stored by photosynthesis.
Scientists have learned through experimentation that light behaves like a particle at times and like a wave at other times. The particle-like features are called photons. Photons are different from particles of matter in that they have no mass and always move at the constant speed of about 300,000 km/sec (186,000 mi/sec) when they are in a vacuum. When light diffracts, or bends slightly as it passes around a corner, it shows wavelike behavior. The waves associated with light are called electromagnetic waves because they consist of changing electric and magnetic fields.
II
THE NATURE OF LIGHT
To understand the nature of light and how it is normally created, it is necessary to study matter at its atomic level. Atoms are the building blocks of matter, and the motion of one of their constituents, the electron, leads to the emission of light in most sources.
A
Light Emission
Light Absorption and Emission
When a photon, or packet of light energy, is absorbed by an atom, the atom gains the energy of the photon, and one of the atom’s electrons may jump to a higher energy level. The atom is then said to be excited. When an electron of an excited atom falls to a lower energy level, the atom may emit the electron’s excess energy in the form of a photon. The energy levels, or orbitals, of the atoms shown here have been greatly simplified to illustrate these absorption and emission processes. For a more accurate depiction of electron orbitals, see the Atom article.

Light can be emitted, or radiated, by electrons circling the nucleus of their atom. Electrons can circle atoms only in certain patterns called orbitals, and electrons have a specific amount of energy in each orbital. The amount of energy needed for each orbital is called an energy level of the atom. Electrons that circle close to the nucleus have less energy than electrons in orbitals farther from the nucleus. If the electron is in the lowest energy level, then no radiation occurs despite the motion of the electron. If an electron in a lower energy level gains some energy, it must jump to a higher level, and the atom is said to be excited. The motion of the excited electron causes it to lose energy, and it falls back to a lower level. The energy the electron releases is equal to the difference between the higher and lower energy levels. The electron may emit this quantum of energy in the form of a photon.
Each atom has a unique set of energy levels, and the energies of the corresponding photons it can emit make up what is called the atom’s spectrum. This spectrum is like a fingerprint by which the atom can be identified. The process of identifying a substance from its spectrum is called spectroscopy. The laws that describe the orbitals and energy levels of atoms are the laws of quantum theory. They were invented in the 1920s specifically to account for the radiation of light and the sizes of atoms.
B
Electromagnetic Waves
Electromagnetic Waves

The waves that accompany light are made up of oscillating, or vibrating, electric and magnetic fields, which are force fields that surround charged particles and influence other charged particles in their vicinity. These electric and magnetic fields change strength and direction at right angles, or perpendicularly, to each other in a plane (vertically and horizontally for instance). The electromagnetic wave formed by these fields travels in a direction perpendicular to the field’s strength (coming out of the plane). The relationship between the fields and the wave formed can be understood by imagining a wave in a taut rope. Grasping the rope and moving it up and down simulates the action of a moving charge upon the electric field. It creates a wave that travels along the rope in a direction that is perpendicular to the initial up and down movement.
Because electromagnetic waves are transverse—that is, the vibration that creates them is perpendicular to the direction in which they travel, they are similar to waves on a rope or waves traveling on the surface of water. Unlike these waves, however, which require a rope or water, light does not need a medium, or substance, through which to travel. Light from the Sun and distant stars reaches Earth by traveling through the vacuum of space.
The waves associated with natural sources of light are irregular, like the water waves in a busy harbor. Scientists think of such waves as being made up of many smooth waves, where the motion is regular and the wave stretches out indefinitely with regularly spaced peaks and valleys. Such regular waves are called monochromatic because they correspond to a single color of light.
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Wavelength, Frequency, and Amplitude
The wavelength of a monochromatic wave is the distance between two consecutive wave peaks. Wavelengths of visible light can be measured in meters or in nanometers (nm), which are one-billionth of a meter (or about 0.4 ten-millionths of an inch). Frequency corresponds to the number of wavelengths that pass by a certain point in space in a given amount of time. This value is usually measured in cycles per second, or hertz (Hz). All electromagnetic waves travel at the same speed, so in one second, more short waves will pass by a point in space than will long waves. This means that shorter waves have a higher frequency than longer waves. The relationship between wavelength, speed, and frequency is expressed by the equation: wave speed equals wavelength times frequency, or
c = lf
Where c is the speed of a light wave in m/sec (3x108 m/sec in a vacuum), l is the wavelength in meters, and f is the wave’s frequency in Hz.
The amplitude of an electromagnetic wave is the height of the wave, measured from a point midway between a peak and a trough to the peak of the wave. This height corresponds to the maximum strength of the electric and magnetic fields and to the number of photons in the light.
B2
Electromagnetic Spectrum
Electromagnetic Spectrum
The electromagnetic spectrum includes radio waves, microwaves, infrared light, visible light, ultraviolet light, x rays, and gamma rays. Visible light, which makes up only a tiny fraction of the electromagnetic spectrum, is the only electromagnetic radiation that humans can perceive with their eyes.

The electromagnetic spectrum refers to the entire range of frequencies or wavelengths of electromagnetic waves (see Electromagnetic Radiation). Light traditionally refers to the range of frequencies that can be seen by humans. The frequencies of these waves are very high, about one-half to three-quarters of a million billion (5 x 1014 to 7.5 x 1014) Hz. Their wavelengths range from 400 to 700 nm. X rays have wavelengths ranging from several thousandths of a nanometer to several nanometers, and radio waves have wavelengths ranging from several meters to several thousand meters.
Waves with frequencies a little lower than the range of human vision (and with wavelengths correspondingly longer) are called infrared. Waves with frequencies a little higher and wavelengths shorter than human eyes can see are called ultraviolet. About half the energy of sunlight at Earth’s surface is visible electromagnetic waves, about 3 percent is ultraviolet, and the rest is infrared.
Each different frequency or wavelength of visible light causes our eye to see a slightly different color. The longest wavelength we can see is deep red at about 700 nm. The shortest wavelength humans can detect is deep blue or violet at about 400 nm. Most light sources do not radiate monochromatic light. What we call white light, such as light from the Sun, is a mixture of all the colors in the visible spectrum, with some represented more strongly than others. Human eyes respond best to green light at 550 nm, which is also approximately the brightest color in sunlight at Earth’s surface.
B3
Polarization
Polarized Light
Polarized light consists of individual photons whose electric field vectors are all aligned in the same direction. Ordinary light is unpolarized because the photons are emitted in a random manner, while laser light is polarized because the photons are emitted coherently. When light passes through a polarizing filter, the electric field interacts more strongly with molecules having certain orientations. This causes the incident beam to separate into two beams, whose electric vectors are perpendicular to each other. A horizontal filter, such as the one shown, absorbs photons whose electric vectors are vertical. The remaining photons are absorbed by a second filter turned 90° to the first. At other angles the intensity of transmitted light is proportional to the square of the cosine of the angle between the two filters. In the language of quantum mechanics, polarization is called state selection. Because photons have only two states, light passing through the filter separates into only two beams.

Polarization refers to the direction of the electric field in an electromagnetic wave. A wave whose electric field is oscillating in the vertical direction is said to be polarized in the vertical direction. The photons of such a wave would interact with matter differently than the photons of a wave polarized in the horizontal direction. The electric field in light waves from the Sun vibrates in all directions, so direct sunlight is called unpolarized. Sunlight reflected from a surface is partially polarized parallel to the surface. Polaroid sunglasses block light that is horizontally polarized and therefore reduce glare from sunlight reflecting off horizontal surfaces.
C
Photons
Photons may be described as packets of light energy, and scientists use this concept to refer to the particle-like aspect of light. Photons are unlike conventional particles, such as specks of dust or marbles, however, in that they are not limited to a specific volume in space or time. Photons are always associated with an electromagnetic wave of a definite frequency. In 1900 the German physicist Max Planck discovered that light energy is carried by photons. He found that the energy of a photon is equal to the frequency of its electromagnetic wave multiplied by a constant called h, or Planck's constant. This constant is very small because one photon carries little energy. Using the watt-second, or joule, as the unit of energy, Planck’s constant is 6.626 x 10-34 (a decimal point followed by 33 zeros and then the number 6626) joule-seconds in exponential notation. The energy consumed by a one-watt light bulb in one second, for example, is equivalent to two and a half million trillion photons of green light. Sunlight warms one square meter at the top of Earth’s atmosphere at noon at the equator with the equivalent of about 14 100-watt light bulbs. Light waves from the Sun, therefore, produce a very large number of photons.
D
Sources of Light
Sources of light differ in how they provide energy to the charged particles, such as electrons, whose motion creates the light. If the energy comes from heat, then the source is called incandescent. If the energy comes from another source, such as chemical or electric energy, the source is called luminescent (see Luminescence).
D1
Incandescence
In an incandescent light source, hot atoms collide with one another. These collisions transfer energy to some electrons, boosting them into higher energy levels. As the electrons release this energy, they emit photons. Some collisions are weak and some are strong, so the electrons are excited to different energy levels and photons of different energies are emitted. Candle light is incandescent and results from the excited atoms of soot in the hot flame. Light from an incandescent light bulb comes from excited atoms in a thin wire called a filament that is heated by passing an electric current through it.
The Sun is an incandescent light source, and its heat comes from nuclear reactions deep below its surface. As the nuclei of atoms interact and combine in a process called nuclear fusion, they release huge amounts of energy. This energy passes from atom to atom until it reaches the surface of the Sun, where the temperature is about 6000°C (11,000°F). Different stars emit incandescent light of different frequencies—and therefore color—depending on their mass and their age.
All thermal, or heat, sources have a broad spectrum, which means they emit photons with a wide range of energies. The color of incandescent sources is related to their temperature, with hotter sources having more blue in their spectra, or ranges of photon energies, and cooler sources more red. About 75 percent of the radiation from an incandescent light bulb is infrared. Scientists learn about the properties of real incandescent light sources by comparing them to a theoretical incandescent light source called a black body. A black body is an ideal incandescent light source, with an emission spectrum that does not depend on what material the light comes from, but only its temperature.
D2
Luminescence
A luminescent light source absorbs energy in some form other than heat, and is therefore usually cooler than an incandescent source. The color of a luminescent source is not related to its temperature. A fluorescent light is a type of luminescent source that makes use of chemical compounds called phosphors. Fluorescent light tubes are filled with mercury vapor and coated on the inside with phosphors. As electricity passes through the tube, it excites the mercury atoms and makes them emit blue, green, violet, and ultraviolet light. The electrons in phosphor atoms absorb the ultraviolet radiation, then release some energy to heat before emitting visible light with a lower frequency.
Phosphor compounds are also used to convert electron energy to light in a television picture tube. Beams of electrons in the tube collide with phosphor atoms in small dots on the screen, exciting the phosphor electrons to higher energy levels. As the electrons drop back to their original energy level, they emit some heat and visible light. The light from all the phosphor dots combines to form the picture.
In certain phosphor compounds, atoms remain excited for a long time before radiating light. A light source is called phosphorescent if the delay between energy absorption and emission is longer than one second. Phosphorescent materials can glow in the dark for several minutes after they have been exposed to strong light.
The aurora borealis and aurora australis (northern and southern lights) in the night sky in high latitudes are luminescent sources. Electrons in the solar wind that sweeps out from the Sun become deflected in Earth’s magnetic field and dip into the upper atmosphere near the north and south magnetic poles. The electrons then collide with atmospheric molecules, exciting the molecules’ electrons and making them emit light in the sky.
Chemiluminescence occurs when a chemical reaction produces molecules with electrons in excited energy levels that can then radiate light. The color of the light depends on the chemical reaction. When chemiluminescence occurs in plants or animals it is called bioluminescence. Many creatures, from bacteria to fish, make light this way by manufacturing substances called luciferase and luciferin. Luciferase helps luciferin combine with oxygen, and the resulting reaction creates excited molecules that emit light. Fireflies use flashes of light to attract mates, and some fish use bioluminescence to attract prey, or confuse predators.
D3
Synchrotron Radiation
Not all light comes from atoms. In a synchrotron light source, electrons are accelerated by microwaves and kept in a circular orbit by large magnets. The whole machine, called a synchrotron, resembles a large artificial atom. The circulating electrons can be made to radiate very monochromatic light at a wide range of frequencies.
D4
Lasers
Laser

A laser is a special kind of light source that produces very regular waves that permit the light to be very tightly focused. Laser is actually an acronym for Light Amplification by Stimulated Emission of Radiation. Each radiating charge in a nonlaser light source produces a light wave that may be a little different from the waves produced by the other charges. Laser sources have atoms whose electrons radiate all in step, or synchronously. As a result, the electrons produce light that is polarized, monochromatic, and coherent, which means that its waves remain in step, with their peaks and troughs coinciding, over long distances.
This coherence is made possible by the phenomenon of stimulated emission. If an atom is immersed in a light wave with a frequency, polarization, and direction the same as light that the atom could emit, then the radiation already present stimulates the atom to emit more of the same, rather than emit a slightly different wave. So the existing light is amplified by the addition of one more photon from the atom. A luminescent light source can provide the initial amplification, and mirrors are used to continue the amplification.
Lasers have many applications in medicine, scientific research, military technology, and communications. They provide a very focused, powerful, and controllable energy source that can be used to perform delicate tasks. Laser light can be used to drill holes in diamonds and to make microelectronic components. The precision of lasers helps doctors perform surgery without damaging the surrounding tissue. Lasers are useful for space communications because laser light can carry a great deal of information and travel long distances without losing signal strength.
E
Detection of Light
For each way of producing light there is a corresponding way of detecting it. Just as heat produces incandescent light, for example, light produces measurable heat when it is absorbed by a material.
E1
Photoelectric Effect
The photoelectric effect is a process in which an atom absorbs a photon that has so much energy that the photon sets one of the atom’s electrons free to move outside the atom. Part of the photon’s energy goes toward releasing the electron from the atom. This energy is called the activation energy of the electron. The rest of the photon’s energy is transferred to the released electron in the form of motion, or kinetic energy. Since the photon energy is proportional to frequency, the released electron, or photoelectron, moves faster when it has absorbed high-frequency light.
Metals with low activation energies are used to make photodetectors and photoelectric cells whose electrical properties change in the presence of light. Solar cells use the photoelectric effect to convert sunlight into electricity. Solar cells are used in place of electric batteries in remote applications like space satellites or roadside emergency telephones (see Solar Energy). Hand-held calculators and watches often use solar cells so that battery replacement is unnecessary.
E2
Photochemical Detection
The change induced in photographic film exposed to light is an example of photochemical detection of photons. Light induces a chemical change in photosensitive chemicals on film. The film is then processed to convert the chemical change into a permanent image and to remove the photosensitive chemicals from the film so it will not continue to change when it is viewed in full light.
Human vision works on a similar principle. Light of different frequencies causes different chemical changes in the eye. The chemical action generates nerve impulses that our brains interpret as color, shape, and location of objects.
III
BEHAVIOR OF LIGHT
Interference of Light in Bubbles
The different colors that appear to streak the surface of soap bubbles correspond to different wavelengths of visible light interfering with each other at that point on the bubble’s surface.

Light behavior can be divided into two categories: how light interacts with matter and how light travels, or propagates through space or through transparent materials. The propagation of light has much in common with the propagation of other kinds of waves, including sound waves and water waves.
A
Interaction with Material
Separation of White Light into Colored Light
Light from many sources, such as the Sun, appears white. When white light passes through a prism, however, it separates into a spectrum of different colors. The prism separates the light by refracting, or bending, light of different colors at different angles. Red light bends the least and violet light bends the most.

When light strikes a material, it interacts with the atoms in the material, and the corresponding effects depend on the frequency of the light and the atomic structure of the material. In transparent materials, the electrons in the material oscillate, or vibrate, while the light is present. This oscillation momentarily takes energy away from the light and then puts it back again. The result is to slow down the light wave without leaving energy behind. Denser materials generally slow the light more than less dense materials, but the effect also depends on the frequency or wavelength of the light. Under certain laboratory conditions, scientists can slow light down. In 2001 scientists brought a beam of light to a halt by temporarily trapping it within an extremely cold cloud of sodium atoms.
Materials that are not completely transparent either absorb light or reflect it. In absorbing materials, such as dark colored cloth, the energy of the oscillating electrons does not go back to the light. The energy instead goes toward increasing the motion of the atoms, which causes the material to heat up. The atoms in reflective materials, such as metals, re-radiate light that cancels out the original wave. Only the light re-radiated back out of the material is observed. All materials exhibit some degree of absorption, refraction, and reflection of light. The study of the behavior of light in materials and how to use this behavior to control light is called optics.
A1
Refraction
Refraction of Light
Refraction is the bending of a light ray as it passes from one substance to another. The light ray bends at an angle that depends on the difference between the speed of light in one substance and the next. Sunlight reflecting off a fish in water, for instance, changes to a higher speed and bends when it enters air. The light appears to originate from a place in the water above the fish’s actual position.

Refraction is the bending of light when it passes from one kind of material into another. Because light travels at a different speed in different materials, it must change speeds at the boundary between two materials. If a beam of light hits this boundary at an angle, then light on the side of the beam that hits first will be forced to slow down or speed up before light on the other side hits the new material. This makes the beam bend, or refract, at the boundary. Light bouncing off an object underwater, for instance, travels first through the water and then through the air to reach an observer’s eye. From certain angles an object that is partially submerged appears bent where it enters the water because light from the part underwater is being refracted.
The refractive index of a material is the ratio of the speed of light in a vacuum to the speed of light inside the material. Because light of different frequencies travels at different speeds in a material, the refractive index is different for different frequencies. This means that light of different colors is bent by different angles as it passes from one material into another. This effect produces the familiar colorful spectrum seen when sunlight passes through a glass prism. The angle of bending at a boundary between two transparent materials is related to the refractive indexes of the materials through Snell’s Law, a mathematical formula that is used to design lenses and other optical devices to control light.
A2
Reflection
Reflection also occurs when light hits the boundary between two materials. Some of the light hitting the boundary will be reflected into the first material. If light strikes the boundary at an angle, the light is reflected at the same angle, similar to the way balls bounce when they hit the floor. Light that is reflected from a flat boundary, such as the boundary between air and a smooth lake, will form a mirror image. Light reflected from a curved surface may be focused into a point, a line, or onto an area, depending on the curvature of the surface.
A3
Scattering
Scattering occurs when the atoms of a transparent material are not smoothly distributed over distances greater than the length of a light wave, but are bunched up into lumps of molecules or particles. The sky is bright because molecules and particles in the air scatter sunlight. Light with higher frequencies and shorter wavelengths is scattered more than light with lower frequencies and longer wavelengths. The atmosphere scatters violet light the most, but human eyes do not see this color, or frequency, well. The eye responds well to blue, though, which is the next most scattered color. Sunsets look red because when the Sun is at the horizon, sunlight has to travel through a longer distance of atmosphere to reach the eye. The thick layer of air, dust and haze scatters away much of the blue. The spectrum of light scattered from small impurities within materials carries important information about the impurities. Scientists measure light scattered by the atmospheres of other planets in the solar system to learn about the chemical composition of the atmospheres.
B
How Light Travels

Diffraction and Interference of Light
When light passes through a slit with a size that is close to the light’s wavelength, the light will diffract, or spread out in waves. When light passes through two slits, the waves from one slit will interefere with the waves from the other. Constructive interference occurs when a wavefront, or crest, from one wave coincides with a wavefront from another, forming a wave with a larger crest. Destructive interference occurs when a wavefront of one wave coincides with a trough of another, cancelling each other to produce a smaller wave or no wave at all.

The first successful theory of light wave motion in three dimensions was proposed by Dutch scientist Christiaan Huygens in 1678. Huygens suggested that light wave peaks form surfaces like the layers of an onion. In a vacuum, or a uniform material, the surfaces are spherical. These wave surfaces advance, or spread out, through space at the speed of light. Huygens also suggested that each point on a wave surface can act like a new source of smaller spherical waves, which may be called wavelets, that are in step with the wave at that point. The envelope of all the wavelets is a wave surface. An envelope is a curve or surface that touches a whole family of other curves or surfaces like the wavelets. This construction explains how light seems to spread away from a pinhole rather than going in one straight line through the hole. The same effect blurs the edges of shadows. Huygens’s principle, with minor modifications, accurately describes all forms of wave motion.
B1
Interference
Interference in waves occurs when two waves overlap. If a peak of one wave is aligned with the peak of the second wave, then the two waves will produce a larger wave with a peak that is the sum of the two overlapping peaks. This is called constructive interference. If a peak of one wave is aligned with a trough of the other, then the waves will tend to cancel each other out and they will produce a smaller wave or no wave at all. This is called destructive interference.
In 1803 English scientist Thomas Young studied interference of light waves by letting light pass through a screen with two slits. In this configuration, the light from each slit spreads out according to Huygens’s principle and eventually overlaps with light from the other slit. If a screen is set up in the region where the two waves overlap, a point on the screen will be light or dark depending on whether the two waves interfere constructively or destructively. If the difference between the distance from one slit to a point on the screen and the other slit to the same point on the screen is an exact number of wavelengths, then light waves arriving at that point will be in step and constructively interfere, making the point bright. If the difference is an exact odd number of half wavelengths, then light waves will arrive out of step, with one wave’s trough arriving at the same time as another wave’s peak. The waves will destructively interfere, making the point dark. The resulting pattern is a series of parallel bright and dark lines on the screen.
Instruments called interferometers use various arrangements of reflectors to produce two beams of light, which are allowed to interfere. These instruments can be used to measure tiny differences in distance or in the speed of light in one of the beams by observing the interference pattern produced by the two beams.
Holography is another application of interference. A hologram is made by splitting a light wave in two with a partially reflecting mirror. One part of the light wave travels through the mirror and is sent directly to a photographic plate. The other part of the wave is reflected first toward a subject, a face for example, and then toward the plate. The resulting photograph is a hologram. Instead of being an image of the face, it is an image of the interference pattern between the two beams. A normal photograph records only the light and dark features of the face and ignores the positions of peaks and troughs of the light wave that form the interference pattern. Since the full light wave is restored when a hologram is illuminated, the viewer can see whatever the original wave contained, including the three-dimensional quality of the original face.
B2
Diffraction
Diffraction is the spreading of light waves as they pass through a small opening or around a boundary. Young’s principle of interference can be applied to Huygens’s explanation of diffraction to explain fringe patterns in diffracted light. As a beam of light emerges from a slit in an illuminated screen, the light some distance away from the screen will consist of overlapping wavelets from different points of the light wave in the opening of the slit. When the light strikes a spot on a display screen across from the slit, these points are at different distances from the spot, so their wavelets can interfere and lead to a pattern of light and dark regions. The pattern produced by light from a single slit will not be as pronounced as a pattern from two slits. This is because there are an infinite number of interfering waves, one from each point emerging from the slit, and their interference patterns overlap one another.
IV
MEASURING LIGHT
Monochromatic light, or light of one color, has several characteristics that can be measured. As discussed in the section on electromagnetic waves, the length of light waves is measured in meters, and the frequency of light waves is measured in hertz. The wavelength can be measured with interferometers, and the frequency determined from the wavelength and a measurement of the velocity of light in meters per second. Monochromatic light also has a well-defined polarization that can be measured using devices called polarimeters. Sometimes the direction of scattered light is also an important quantity to measure.
When light is considered as a source of illumination for human eyes, its intensity, or brightness, is measured in units that are based on a modernized version of the perceived brightness of a candle. These units include the rate of energy flow in light, which, for monochromatic light traveling in a single direction, is determined by the rate of flow of photons. The rate of energy flow in this case can be stated in watts, or Joules per second. Usually light contains many colors and radiates in many directions away from a source such as a lamp.
A
Brightness
Scientists use the units candela and lumen to measure the brightness of light as perceived by humans. These units account for the different response of the eye to light of different colors. The lumen measures the total amount of energy in the light radiated in all directions, and the candela measures the amount radiated in a particular direction. The candela was originally called the candle, and it was defined in terms of the light produced by a standard candle. It is now defined as the energy flow in a given direction of a yellow-green light with a frequency of 540 x 1012 Hz and a radiant intensity, or energy output, of 1/683 watt into the opening of a cone of one steradian. The steradian is a measure of angle in three dimensions.
The lumen can be defined in terms of a source that radiates one candela uniformly in all directions. If a sphere with a radius of one foot were centered on the light source, then one square foot of the inside surface of the sphere would be illuminated with a flux of one lumen. Flux means the rate at which light energy is falling on the surface. The illumination, or luminance, of that one square foot is defined to be one foot-candle.
The illumination at a different distance from a source can be calculated from the inverse square law: One lumen of flux spreads out over an area that increases as the square of the distance from the center of the source. This means that the light per square foot decreases as the inverse square of the distance from the source. For instance, if 1 square foot of a surface that is 1 foot away from a source has an illumination of 1 foot-candle, then 1 square foot of a surface that is 4 feet away will have an illumination of 1/16 foot-candle. This is because 4 feet away from the source, the 1 lumen of flux landing on 1 square foot has had to spread out over 16 square feet. In the metric system, the unit of luminous flux is also called the lumen, and the unit of illumination is defined in meters and is called the lux.
B
The Speed of Light
Scientists have defined the speed of light in a vacuum to be exactly 299,792,458 meters per second (about 186,000 miles per second). This definition is possible because since 1983, scientists have known the distance light travels in one second more accurately than the definition of the standard meter. Therefore, in 1983, scientists defined the meter as 1/299,792,458, the distance light travels through a vacuum in one second. This precise measurement is the latest step in a long history of measurement, beginning in the early 1600s with an unsuccessful attempt by Italian scientist Galileo to measure the speed of lantern light from one hilltop to another.
The first successful measurements of the speed of light were astronomical. In 1676 Danish astronomer Olaus Roemer noticed a delay in the eclipse of a moon of Jupiter when it was viewed from the far side as compared with the near side of Earth’s orbit. Assuming the delay was the travel time of light across Earth’s orbit, and knowing roughly the orbital size from other observations, he divided distance by time to estimate the speed.
English physicist James Bradley obtained a better measurement in 1729. Bradley found it necessary to keep changing the tilt of his telescope to catch the light from stars as Earth went around the Sun. He concluded that Earth’s motion was sweeping the telescope sideways relative to the light that was coming down the telescope. The angle of tilt, called the stellar aberration, is approximately the ratio of the orbital speed of Earth to the speed of light. (This is one of the ways scientists determined that Earth moves around the Sun and not vice versa.)
In the mid-19th century, French physicist Armand Fizeau directly measured the speed of light by sending a narrow beam of light between gear teeth in the edge of a rotating wheel. The beam then traveled a long distance to a mirror and came back to the wheel where, if the spin were fast enough, a tooth would block the light. Knowing the distance to the mirror and the speed of the wheel, Fizeau could calculate the speed of light. During the same period, the French physicist Jean Foucault made other, more accurate experiments of this sort with spinning mirrors.
Scientists needed accurate measurements of the speed of light because they were looking for the medium that light traveled in. They called the medium ether, which they believed waved to produce the light. If ether existed, then the speed of light should appear larger or smaller depending on whether the person measuring it was moving toward or away from the ether waves. However, all measurements of the speed of light in different moving reference frames gave the same value.
In 1887 American physicists Albert A. Michelson and Edward Morley performed a very sensitive experiment designed to detect the effects of ether. They constructed an interferometer with two light beams—one that pointed along the direction of Earth’s motion, and one that pointed in a direction perpendicular to Earth’s motion. The beams were reflected by mirrors at the ends of their paths and returned to a common point where they could interfere. Along the first beam, the scientists expected Earth’s motion to increase or decrease the beam’s velocity so that the number of wave cycles throughout the path would be changed slightly relative to the second beam, resulting in a characteristic interference pattern. Knowing the velocity of Earth, it was possible to predict the change in the number of cycles and the resulting interference pattern that would be observed. The Michelson-Morley apparatus was fully capable of measuring it, but the scientists did not find the expected results.
The paradox of the constancy of the speed of light created a major problem for physical theory that German-born American physicist Albert Einstein finally resolved in 1905. Einstein suggested that physical theories should not depend on the state of motion of the observer. Instead, Einstein said the speed of light had to remain constant, and all the rest of physics had to be changed to be consistent with this fact. This special theory of relativity predicted many unexpected physical consequences, all of which have since been observed in nature.
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HISTORY OF LIGHT THEORIES
The earliest speculations about light were hindered by the lack of knowledge about how the eye works. The Greek philosophers from as early as Pythagoras, who lived during the 5th century bc, believed light issued forth from visible things, but most also thought vision, as distinct from light, proceeded outward from the eye. Plato gave a version of this theory in his dialogue Timaeus, written in the 3rd century bc, which greatly influenced later thought.
Some early ideas of the Greeks, however, were correct. The philosopher and statesman Empedocles believed that light travels with finite speed, and the philosopher and scientist Aristotle accurately explained the rainbow as a kind of reflection from raindrops. The Greek mathematician Euclid understood the law of reflection and the properties of mirrors. Early thinkers also observed and recorded the phenomenon of refraction, but they did not know its mathematical law. The mathematician and astronomer Ptolemy was the first person on record to collect experimental data on optics, but he too believed vision issued from the eye. His work was further developed by Egyptian scientist Ibn al Haythen, who worked in Iraq and Egypt and was known to Europeans as Alhazen. Through logic and experimentation, Alhazen finally discounted Plato’s theory that vision issued forth from the eye. In Europe, Alhazen was the most well known among a group of Islamic scholars who preserved and built upon the classical Greek tradition. His work influenced all later investigations on light.
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Early Scientific Theories
The early modern scientists Galileo, Johannes Kepler of Germany, and René Descartes of France all made contributions to the understanding of light. Descartes discussed optics and reported the law of refraction in his famous Discours de la méthode (Discourse on Method), published in 1637. The Dutch astronomer and mathematician Willebrord Snell independently discovered the law of refraction in 1620, and the law is now named after him.
During the late 1600s, an important question emerged: Is light a swarm of particles or is it a wave in some pervasive medium through which ordinary matter freely moves? English physicist Sir Isaac Newton was a proponent of the particle theory, and Huygens developed the wave theory at about the same time. At the time it seemed that wave theories could not explain optical polarization because waves that scientists were familiar with moved parallel, not perpendicular, to the direction of wave travel. On the other hand, Newton had difficulty explaining the phenomenon of interference of light. His explanation forced a wavelike property on a particle description. Newton’s great prestige coupled with the difficulty of explaining polarization caused the scientific community to favor the particle theory, even after English physicist Thomas Young analyzed a new class of interference phenomena using the wave theory in 1803.
The wave theory was finally accepted after French physicist Augustin Fresnel supported Young’s ideas with mathematical calculations in 1815 and predicted surprising new effects. Irish mathematician Sir William Hamilton clarified the relationship between wave and particle viewpoints by developing a theory that unified optics and mechanics. Hamilton’s theory was important in the later development of quantum mechanics.
Between the time of Newton and Fresnel, scientists developed mathematical techniques to describe wave phenomena in fluids and solids. Fresnel and his successors were able to use these advances to create a theory of transverse waves that would account for the phenomenon of optical polarization. As a result, an entire wave theory of light existed in mathematical form before British physicist James Clerk Maxwell began his work on electromagnetism. In his theory of electromagnetism, Maxwell showed that electric and magnetic fields affect each other in such a way as to permit waves to travel through space. The equations he derived to describe these electromagnetic waves matched the equations scientists already knew to describe light. Maxwell’s equations, however, were more general in that they described electromagnetic phenomena other than light and they predicted waves throughout the electromagnetic spectrum. In addition, his theory gave the correct speed of light in terms of the properties of electricity and magnetism. When German physicist Gustav Hertz later detected electromagnetic waves at lower frequencies, which the theory predicted, the basic correctness of Maxwell’s theory was confirmed.
Maxwell’s work left unsolved a problem common to all wave theories of light. A wave is a continuous phenomenon, which means that when it travels, its electromagnetic field must move at each of the infinite number of points in every small part of space. When we add heat to any system to raise its temperature, the energy is shared equally among all the parts of the system that can move. When this idea is applied to light, with an infinite number of moving parts, it appears to require an infinite amount of heat to give all the parts equal energy. But thermal radiation, the process in which heated objects emit electromagnetic waves, occurs in nature with a finite amount of heat. Something that could account for this process was missing from Maxwell’s theory. In 1900 Max Planck provided the missing concept. He proposed the existence of a light quantum, a finite packet of energy that became known as the photon.
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Modern Theory
Planck’s theory remained mystifying until Einstein showed how it could be used to explain the photoelectric effect, in which the speed of ejected electrons was related not to the intensity of light but to its frequency. This relationship was consistent with Planck’s theory, which suggested that a photon’s energy was related to its frequency. During the next two decades scientists recast all of physics to be consistent with Planck’s theory. The result was a picture of the physical world that was different from anything ever before imagined. Its essential feature is that all matter appears in physical measurements to be made of quantum bits, which are something like particles. Unlike the particles of Newtonian physics, however, a quantum particle cannot be viewed as having a definite path of movement that can be predicted through laws of motion. Quantum physics only permits the prediction of the probability of where particles may be found. The probability is the squared amplitude of a wave field, sometimes called the wave function associated with the particle. For photons the underlying probability field is what we know as the electromagnetic field. The current world view that scientists use, called the Standard Model, divides particles into two categories: fermions (building blocks of atoms, such as electrons, protons, and neutrons), which cannot exist in the same place at the same time, and bosons, such as photons, which can (see Elementary Particles). Bosons are the quantum particles associated with the force fields that act on the fermions. Just as the electromagnetic field is a combination of electric and magnetic force fields, there is an even more general field called the electroweak field. This field combines electromagnetic forces and the weak nuclear force. The photon is one of four bosons associated with this field. The other three bosons have large masses and decay, or break apart, quickly to lighter components outside the nucleus of the atom.