Mass acceleration or deceleration causes collisions with nearby particles, which collide with farther away masses, and so on, and the disturbance {wave, physics} continues outward at speed that depends on medium particle-connection strength.
mechanical waves
Water-table waves illustrate transverse mechanical waves. Long springs, such as slinkys, illustrate longitudinal mechanical waves. Tuning forks, guitar strings, bongs, and glasses with water at different levels illustrate mechanical longitudinal sound waves. Mechanical waves are in media, which determine wave velocity by electric forces between molecules.
longitudinal wave
Disturbances, such as collisions, can be along line between two masses. Imparting force requires acceleration. Molecules move toward nearby masses, hit them, and bounce backward. Hit molecules accelerate, move toward next masses, hit them, and bounce backward, and so on. Bounce-backs return masses to where they were before, and only heat remains, so no net mass moves. Only disturbance and energy move outward. Wave velocity depends on material elasticity.
transverse wave
Disturbances, such as plucking strings, can be perpendicular to line between two masses. Molecules accelerate transverse to line between two masses. Nearby molecules feel transverse pull, because molecules attract. Attractions eventually stop transverse motion and reverse it. Cycle repeats until only heat remains. No net mass moves along, or transverse to, line between masses. Only disturbance and energy move down line, in both directions. Wave velocity depends on material elasticity.
movement
Waves have to travel, because they must pass from mass to mass. Waves involve acceleration and decelerations.
properties
Mechanical waves displace mass from equilibrium position. Waves have maximum displacement amplitude before they return to equilibrium point. Wave trains have frequency of disturbances passing space point per second. Wave trains have period between disturbances. Waves have wavelength between first and second equilibrium points and have wavelength inverse or wave number. Waves have phase angle of displacement to amplitude. Waves have speed of disturbance travel.
electromagnetic waves
Charge acceleration or deceleration causes force-field change {half-wave, charge acceleration}, which travels outward at light speed. Charge-acceleration moments make photons, because photons have spin. After first acceleration or deceleration, reverse deceleration or acceleration can add half-wave disturbance in opposite direction, to make one complete wave. Repeated acceleration and deceleration can make wave train. Electromagnetic waves do not have position displacement, only field displacement.
Electromagnetic induction requires changing electric and magnetic fields. Electromagnetic-induction rate determines light speed and depends on electric-force strength. Changing electric and magnetic fields move induction point away from accelerating charge. Therefore, light cannot be at rest. Behind moving point, fields cancel. Photons are only at one point, so light has no motion relative to other reference points, and in vacuum, light has same speed for stationary and moving observers.
Electromagnetic induction does not need or have medium. Because light does not move in medium, light speed is not relative to medium. Light speed is absolute maximum speed.
Photons have no mass, so light has no inertia and moves as fast as anything can move. Light speed is maximum physical speed.
Light electric and magnetic fields from several sources add, because electromagnetic inductions add. In media, atoms and molecules absorb and emit light, and this slows light speed but does not change frequency or intensity.
Trigonometric functions {wave equation}| can describe waves. y = A * sin(2 * pi * f * t), where y is displacement, A is amplitude, f is frequency, and t is time. y = A * sin(2 * pi * x / l), where y is displacement, A is amplitude, x is position, and l is wavelength.
position and time
Wave equations are differential equations and include length and time. (D^2)H(x,t) / Dt^2 = (v^2) * (D^2)H(x,t) / Dx^2, where (D^2) indicates second partial derivative, H is function of displacement and time, v is wave velocity, x is position, and t is time. Solutions are waves. In springs, velocity depends on mass and material elasticity {spring constant, oscillation}. For strings, velocity depends on density, tension, and material. For solids, velocity depends on density and material elasticity {Young's modulus, oscillation}. For liquids, velocity depends on density and material elasticity {bulk modulus}. For gases, velocity depends on density, pressure, and molecule type: monatomic, diatomic, triatomic, and so on. For light, velocity depends on material magnetic permeability and electric permittivity.
Devices can reproduce input frequency with constant amplitude and/or phase (no distortion). Devices can reproduce input frequency with varying frequency, amplitude, and/or phase {distortion}. Devices can vary output with input frequency {linear distortion} or with voltage {nonlinear distortion} below or above linear-response range.
compression
Large voltages can have less relative gain than small voltages {compression, audio}. Compression creates lower harmonics.
clipping
Voltage can have limits {clipping}. Clipping creates higher harmonics.
overdriven harmonics
Non-linearly amplifying a tone and its fifth (ratio 3/2) can generate sum and difference frequencies of harmonic tones: higher and lower octaves, fifths, and fourths {overdriven harmonics}.
Sound changes frequency with source or observer movement {Doppler effect}|.
stationary case
When stationary sources emit sounds or light waves with one wavelength and frequency, stationary observers hear one pitch or see one color. See Figure 1. Only wave moves, at constant velocity, because medium does not change.
Source x emits maximum positive amplitude, a line in the diagram, once each cycle. In the diagram, wave travels left two spaces for each cycle line. From one cycle line to the next, observer encounters one peak. There is no Doppler effect.
moving-toward case
When sound-wave or light-wave source moves toward stationary observer, or observer moves toward stationary wave source, observer hears pitch increase or sees shift toward blue color. This is Doppler effect. When frequency increases, wavelength decreases, because only sound medium or electromagnetic-induction speed determines constant wave velocity. See Figure 2.
In the diagram, observer travels right one space for each line, at half wave speed. Observer movement brings it closer to next wave peak. From one line to the next, observer encounters one and one-half wave peaks. Frequency has increased.
See Figure 3. In the diagram, source travels left one space for each line, at half wave speed. Source movement brings it closer to previous wave peak. From one line to the next, observer encounters two wave peaks. Frequency has increased.
moving-away case
When sound-wave or light-wave source moves away from stationary observer, or observer moves away from stationary wave source, observer hears pitch decrease or sees shift toward red color. When frequency decreases, wavelength increases, because wave speed is constant. See Figure 4.
In the diagram, observer travels left one space for each line, at half wave speed. Observer movement brings it farther from next wave peak. From one line to the next, observer encounters one-half wave peaks. Frequency has decreased.
See Figure 5. In the diagram, source travels right one space for each line, at half wave speed. Source movement brings it farther from previous wave peak. From one line to the next, observer encounters two-thirds wave peaks. Frequency has decreased.
examples
As sound-emitting vehicles move closer, sound has higher pitch. As they move away, sound has lower pitch.
As light-emitting stars and galaxies move away from Earth as universe expands, Doppler effect makes emitted light have decreased frequencies, so light becomes redder {red-shift}.
Vibration can be along motion direction {longitudinal wave}|. Sound waves are longitudinal waves.
Mechanical-wave vibrations can be across motion direction {transverse wave}|. Guitar or violin strings vibrate transversely. Molecular interactions are at right angles to direction that wave travels, which is down string and back. Longer strings make lower frequency. Tighter strings make higher frequency. Larger diameter strings decrease frequency. Electromagnetic waves have oscillating transverse electric and magnetic fields.
Acceleration amount determines maximum displacement {amplitude, wave}. Mass displacement has distance oscillation. Zero-rest-mass displacement, as in electromagnetic waves, has field oscillation.
Sound and light have energy flow per second per area {intensity, wave}|, which is power per area.
Wavelength has an inverse {wave number}|.
Light rays travel in straight lines {straight-line motion}, because they follow least-action path.
At space points, wave trains can add {superposition, wave}|. Waves add without affecting each other. Waves are independent. Filtering other waves is subtracting and can leave one wave.
Wavelets add by superposition to make a wavefront {Huygen's principle} {Huygen principle}. See Figure 1.
When two different-frequency waves start from same source, waves superpose {heterodyning}| to make net wave with frequency {beat frequency} equal to difference between the original frequencies. Two frequencies can mix to make lower difference frequency. For example, if frequency-2 wave superposes with frequency-3 wave, frequency-1 wave results.
Light can have different wave-front shapes, such as plane, helix, or double helix {orbital angular momentum, light}. Diffraction gratings with fork or helical lens change plane-polarized light. After such transformation, light in phase makes circles with dark centers {cancellation by superposition}.
Spectrum low frequency can double in frequency {self-referencing}, to interfere with spectrum higher frequencies.
When light waves hit surfaces, surface points re-radiate light {wavelet}|.
If plate has one vertical slit {slit experiment, wave}, light diffracts around edge and makes horizontal diffraction pattern. The most-intense light goes straight through. Lesser light amounts are farther from center. If plate has two vertical slits {double-slit experiment} {Young's experiment} {Young experiment}, light diffracts through both slits and makes horizontal interference pattern, because the diffraction patterns add.
Double-slit experiments can have ring pattern with no interference or striped pattern with interference. Detectors that detect only half the particles cause half-striped and half-ring pattern.
Light can bounce off surfaces {reflection, light}|, as surface molecules absorb and re-emit light. Reflections are like elastic collisions. Plane mirrors and wave tanks show reflections.
wavefront
Wavefronts are moving space disturbances. Behind wavefronts, all wavelets cancel each other, because wavelets have random phases. Beyond wavefronts, nothing has reached yet. Wavefronts are moving edges. Wavefront oscillation and movement carry energy. At surfaces, wavefronts re-radiate.
angles
Reflection angle equals incidence angle. Because light travels straight, light has no sideways motion components, and light plane stays the same. Angles are the same, because light effects are symmetric.
images
Images from flat mirrors appear to be behind mirror and so are virtual images. Images appear at same distance from mirror as distance that objects are from mirror. Images have same size and orientation as objects. Reflections from flat surfaces only reverse right and left.
surfaces
Dielectrics can be mirrors.
polarization
At incidence angle 45 degrees, if reflection from plane mirror has 90-degree angle between reflected and refracted beams, light polarizes.
In reflection, incident light hits surface at angle {angle of incidence}| {incidence angle} to perpendicular.
In reflection, reflected light leaves surface at angle {reflection angle} {angle of reflection}| to perpendicular, as superposed wavelets add to make wavefront. Reflection angle equals incidence angle and is in same plane.
Curved mirrors {curved mirror} focus incoming parallel light rays onto point {focus, mirror}.
types
Curved mirrors {spherical mirror} can have constant radius. Spherical mirrors {convex mirror} can curve out. Curvature radius is positive if curve is convex. For convex mirrors, image is always virtual and erect. For convex mirrors, if object is inside focal point, image is bigger. For convex mirrors, if object is outside focal point, image is smaller.
Spherical mirrors {concave mirror} can curve in. Curvature radius is negative if curve is concave. For concave mirrors, if object is outside focal point, image is real and inverted. For concave mirrors, if object is inside focal point, image is virtual, erect, and bigger.
Curved mirrors {parabolic mirror} can have changing radius.
magnification
Ratio of image size I to object size O equals ratio of distance q of image from mirror to distance p of object from mirror: I/O = q/p.
focal length
Focal length F is spherical-mirror curvature radius R divided by two: F = R/2.
Image distance I and object distance O relate to focal point distance F {lens equation, mirror}: 1/F = 1/I + 1/O.
Find object image using incoming straight lines from object and outgoing straight lines to image {method of rays} {rays method}, which reflect from spherical mirror points.
Light can go from one medium into another medium {refraction}|.
reflection
Some light enters second medium, and some light reflects from surface. For greater refraction-index difference, reflection is greater, because electric fields interact more.
refraction
As wavefront hits surface between media, surface re-radiates light waves, and wavelets add, to make new wavefront in second material.
planar
Incident light and refracted light have same plane, because light travels straight and so has no transverse motion component.
speed
If second medium has different refractive index, incident light and refracted light have different speeds.
frequency
Light frequency stays the same in both materials, because electromagnetic induction does not use medium.
wavelength
Because velocity changes and frequency stays constant, wavelength changes, and incident light and refracted light have different angles to perpendicular. If second medium has higher refractive index, light bends toward perpendicular, because wavelength becomes shorter. If second medium has lower refractive index, light bends away from perpendicular, because wavelength becomes longer.
examples
Glass with different refractive indices appears warped. Refraction from air to water causes coins in fish tanks to appear in different positions than they actually are. Prisms, water glasses, and camera lenses use refraction.
Vacuums have no matter or electric or magnetic fields. Media have subatomic-particle electric and magnetic fields {refractive index}| {index of refraction}, which attract and repel light-wave electric and magnetic fields, decreasing light speed. Refractive index depends on electrical permittivity and magnetic permeability. Vacuum has refractive index 1. Glasses have refractive index near 1.5. Dense polar salts have refractive index 2.5. Teflon is transparent to microwaves but has high refractive index. Plasmas and metals have negative permittivity. No natural substances have negative permeability.
speed
In materials, velocity v equals light speed in vacuum c divided by refractive index n: v = c/n.
In crystals {anisotropic crystal}, refractive index can vary with light-propagation direction {birefringence}|. In birefringence, incident light divides into two light rays that polarize in planes at right angles. Isotropic crystals, glasses, liquids, and gases have the same physical properties in all directions. Most crystals are isotropic.
Different-frequency light does not focus at same point, because refractive index differs for different frequencies {chromatic aberration}|.
Higher frequencies refract more than lower frequencies {dispersion, refraction}. Higher frequencies travel slower than lower frequencies, because dielectric-dipole capacitance is higher, photon energy is higher, and electric forces are higher. Because wavelength is lower, percentage change is higher. Dispersion causes prism rainbows.
Incidence angle I and reflection angle R relate by media refractive indexes n {Snell's law} {Snell law}: nI * sin(I) = nR * sin(R).
If incidence angle is more than angle {critical angle}|, all light reflects, in total reflection, because reflection angle is 90 degrees or more. Critical angle depends on media refractive indexes.
If incidence angle is more than critical angle, all light reflects {total reflection}|, because refraction angle is 90 degrees or more.
Materials {opaque material}| that have free electrons absorb all light.
Materials {translucent material}| that have weakly bound electrons absorb some light and transmit some light, making blurry images.
Materials {transparent material}| that have tightly bound electrons have no absorption and transmit light with clear images.
Transparent curved surfaces {lens, physics}| can refract parallel light rays to point.
convex
For convex lenses, if object is inside focal point, image is virtual, erect, and smaller. For convex lenses, if object is outside focal point, image is real and inverted.
concave
For concave lenses, image is virtual and erect. For concave lenses, if object is inside focal point, image is bigger. For concave lenses, if object is outside focal point, image is smaller.
focus
Focal length F depends on lens refractive index n and radii R of sides: 1/F = (n - 1) * ((1 / Ri) - (1 / Ro)).
curvature radius
Curvature radius is positive if curve is convex. Curvature radius is negative if curve is concave.
size
Ratio of image size I to object size O equals ratio of distance q of image from lens to distance p of object from lens. I/O = q/p.
wavelets
Lenses perform spatial Fourier transforms.
Mirror or lens angular size {aperture}| is angle at focal point between two radii from ends of a spherical-mirror or spherical-lens diameter.
Spherical mirrors or lenses with large aperture deviate from parabolic reflection {spherical aberration}| at edges. Edges do not refract to focal point.
Units {diopter} can measure how much lenses converge or diverge light {dioptric power}. Zero diopters converges light from object at one meter to focus at one meter. Three diopters converges light from object at one meter to focus at one-third meter. Minus three diopters diverges light from object at one meter to focus at three meters.
Parallel light rays from one lens side go through lens to a point {focus, lens} {focal point}| on other lens side.
Images {real image} {image, object}| can form from actual light rays. Images {virtual image} can appear to be in locations where light rays cannot go. Images {erect image} can have same orientation as objects. Images {inverted image} can have opposite orientation as objects. Images can magnify or reduce objects.
Image distance I and object distance O relate to focal point distance F {lens equation, lens}: 1/F = 1/I + 1/O.
Lens surface can curve in {concave lens}.
Lens surface can curve out {convex lens}.
Lens combinations {achromatic lens} can eliminate chromatic aberration.
Lenses {aplanatic lens} can correct spherical aberration.
Microscopes {microscope}| have large lens that collects light to focal point, and second small, high-curvature lens that focuses small but near image. Microscopes {phase contrast microscope} can look for different light phases.
Two waves {standing wave} can travel in opposite directions from point and then reflect back from end barriers, so they reinforce each other {resonance, wave}| when they meet again, because they are in phase.
node
Resonating waves are stationary. In stationary waves, some points {node, wave} always have zero displacement.
wavelength
Fundamental standing-wave wavelength is two times distance between endpoints. Closed tubes have resonant wavelength one-quarter tube length. Open tubes have resonant wavelength one-half tube length. String resonant frequency is lower if string length is longer.
Systems can have standing waves {fundamental wave}| with lowest frequency.
Waves {harmonic wave, physics}| {overtone} can have frequencies that are fundamental-frequency multiples.
Waves can have frequency fundamental frequency times two {octave, wave}|, three {twelfth}, four {fifteenth}, five {seventeenth}, six {nineteenth}, and so on. Higher frequencies must have more energy to have significant amplitude.
Solitary, non-linear, stationary or moving waves {soliton}| can maintain size and shape. As wave components travel, solitons reinforce components by superposition. High-frequency components increase at same rate as they spread out, because they have different speeds. Solitons can be in plasma, crystal-lattice, elementary-particle, ocean, molecular-biology, and semiconductor boundary layers.
vacuum
Vacuum with periodic vacuum states can make soliton-antisoliton pairs.
quanta
Perhaps, massive elementary particles of 1000 GeV, or magnetic monopoles, are solitons. Solitons can allow bosons to make fermions and allow fermions to split.
One-dimensional soliton-antisoliton pairs can be in two or three dimensions and require vector fields {Sine-Gordon theory}.
Light appears to bend {diffraction}| around corners and edges. If light rays meet corners, corner re-radiates light in all directions, so some light goes to region behind edge. Wavelets add to form wavefront there. At most wavefront points, wavelets cancel each other, so light intensity is zero. At some wavefront points, sum is positive, and light appears behind edge at regular intervals. Shadows have diffraction patterns at edges.
sound
Diffraction is how people can hear sound around corners.
size
If obstacle or edge is smaller than wavelength, wave goes farther around obstacle or edge. If obstacle or edge is larger than wavelength, diffraction has smaller angle.
frequency
Higher-frequency light and sound have smaller diffraction, because wavelengths are smaller. Lower-frequency light and sound bend more.
Materials {diffraction grating}| can have regular repeating opening or ruling patterns, so surfaces are like many edges. Diffraction gratings can be for parallel rays {Fraunhofer grating} or spherical rays {Fresnel grating}. The many edges cause strong diffraction pattern, because more wavelets add together to make higher amplitude. If openings are small or rulings have close spacing, diffraction is more, because smaller edge can re-radiate more behind edge.
Transparent plates {phase plate} with varying thickness can delay light slightly, to change phase. Phase plates are diffraction gratings. If only parallel light rays reach phase plate, diffraction is regular. Phase differences cause intensity differences at various points, by interference effects.
Shadows {shadow}| have umbra and penumbra.
Shadows have a lighter part {penumbra}|, where diffracted light enters.
Shadows have a dark part {umbra}|, where no diffracted light enters.
If light wavelength is less than object diameter, light bounces off object {scattering, light}|. If light wavelength is more than object diameter, light goes around object.
example
Sky is blue, because blue light has small enough wavelength to scatter from air molecules, but other colors have longer wavelengths. Air molecules are large enough to block blue and some green light from Sun, but longer wavelengths go around air molecules. Scattered blue light goes all over sky to make it blue instead of clear. Sun is red at horizon, because light goes through more atmosphere to eye, and air scatters blue, green, and yellow light.
X-rays can have elastic scattering {Compton scattering} from stationary electrons in light elements. Scattered-radiation frequency decreases with increasing angle, so high frequencies are at narrow angles.
Two vibrators at similar frequency soon have same frequency and phase {entrainment}| {mode-locking}.
Two oscillators with similar frequencies soon have same frequency {virtual governor} {mutual entrainment}.
Molecular-vibration waves {sound, physics} can move through materials.
process
Molecules from outside material can collide with material, causing material molecules to move. Molecular movement causes collision with adjacent molecules. First molecules bounce backward, and second molecules move, causing collision with adjacent molecules, and so on. Collisions send longitudinal wave down motion line.
Sound compresses {compression, sound} material in front of it, leaving slight vacuum {rarefaction} behind compression. Compression pushes next material bit forward. Original bit bounces back to original position, so material does not move. Compression wave travels through material. Only wave and energy move.
speed
Medium determines sound-wave speed. Sound-wave speed increases with stronger interactions between molecules. Wave frequency and amplitude do not affect speed.
amplitude
Sound has kinetic energy {loudness, sound}. Kinetic-energy increase increases sound-wave amplitude, by moving molecules farther. Frequency, wavelength, and speed do not affect wave amplitude.
pitch
Sound has number {frequency, sound} of vibrations per second. People can hear sounds of 20 to 20,000 Hz.
Sound has frequencies at two, three, four, and so on, times fundamental frequency {harmonics, physics}. Higher harmonics have lower amplitude.
Outside-material vibration frequency determines sound-wave frequency. Materials can have resonance frequencies.
Sound waves travel in a medium, and the medium can be moving, making net sound-wave velocity faster or slower {Mach effect}.
Vibration quanta {phonon}| are sound-wave packets. Crystal phonon vibrations cause temperature gradient sideways to phonon direction, analogous to Hall effect for electromagnetism.
Surfaces can have acoustic waves {Rayleigh wave}. Earthquakes and radio waves can put Rayleigh waves in Earth or ionosphere. Ultrasonic surface acoustic waves can store, recognize, filter, and channel electronic signals in semiconductors, at 10^9 Hz.
Moving objects make sound {sonic boom} as they push air aside {shock wave}|. If object speed becomes the same as sound speed, waves of pushed-aside air travel as fast as sound. Waves are in phase and grow to make large wave. If plane travels faster than sound speed, sound is behind pushed-aside air, waves do not build up, and no shock wave builds.
Objects can go through air faster than air sound speed. Sound from object contact with air cannot travel away faster than sound waves build up. Wave constructive interference creates shock wave, which carries extra energy away when object breaks sound barrier, causing sonic boom. After passing sound speed, acoustic waves at sound speed are slower than object speed, with no more constructive interference.
Speech sounds {speech sound} have frequency range from 250 Hz to 2000 Hz and loudness range from 63 to 95 decibels.
Sounds {ultrasonic sound}| can have frequency greater than 20,000 Hz. Ultrasonic sound can visualize body insides and clean dishware.
Rooms {whispering gallery} can have focal points, where sound focuses {echo}|. Canyons and buildings can echo sound. Echoes work best with low amplitude and high frequency.
High-frequency sound can locate objects by echo pattern {echolocation}| {sonar, location}.
Electric charges have virtual photons streaming outward as straight lines in all directions, making electric field. Electric fields begin at electron edge, which emits virtual photons. Electric-field lines indicate electric-force direction. Each line is one photon stream, so electric-field lines are not about electric-force strength or electric-field strength. Electric-field-line area density, photons per area, is electric-field strength. Because area varies directly with squared dimension, electric force decreases as distance squared: 1/r^2. Electric field has virtual kinetic energy, which can transfer to other charges at field positions to become potential energy.
moving charges
Maximum charge velocity is typically one-tenth light speed. For constant-velocity charge, electric field moves at same speed and direction as charge. Virtual photons stream outward as straight lines in all directions.
Constant-velocity fields have no transverse or longitudinal field changes, and so no waves.
moving charges: magnetic force
According to special relativity, constant-velocity charge causes observer transverse to charge-motion-direction to see length contraction and so increased charge-motion-direction charge density. Length contraction makes flattened-spheroid charge shape, with short axis in motion direction and long axes in transverse-direction plane. Because total charge is same for moving and stationary charge, total field strength stays the same. Relativistically increased charge density along vertical direction causes increased electric force along horizontal direction. Therefore, relativistic length contraction makes electric field appear to observer stronger horizontally. According to special relativity, observer in front or back of constant-velocity charge does not see length contraction, only that charge approaching or receding. Total electric field strength is same as for stationary electron, because total charge is same. Because total charge is same as before, charge density must be less as observed from vertical direction, so electric field appears to observer weaker vertically. Vertical electric field is foreshortened in motion direction, because electron catches up to virtual photons. Vertical electric field is lengthened opposite to motion direction, because electron moves away from virtual photons.
Electric force due to relativistic length contraction and charge-density change, and not due to total charge, is magnetic force. (Stationary charges have no relativistic motion and so no relativistic electric force.) Adjacent magnetic force is a torus around moving charge. Just as electric forces act only on electric forces, magnetic forces act only on magnetic forces, because magnetic is perpendicular to electric and so does not affect electric.
Electric force has electric field. Electric force and electric field have same direction and relative strength. Because magnetic force is relativistic electric force, magnetic force has magnetic field. Magnetic force and magnetic field have same relative strength but perpendicular direction, because force is due to transverse relativistic length contraction and so is perpendicular to motion and field. Therefore, magnetic forces have magnetic fields perpendicular to electric force/magnetic force and perpendicular to charge-motion orientation. Moving-charge magnetic field is a torus adjacent to and around charge, transverse to motion direction. See Figure 1.
For positive charge moving in right-hand thumb direction, magnetic field is in curling index-finger direction, in a circle around moving proton, and magnetic force is outward from palm (right-hand rule). For proton moving vertically downward, magnetic field is in on left and out on right. Electron has negative charge, so magnetic field is out on left and in on right.
Magnetic field has virtual photons and so has virtual kinetic energy, which can transfer to other charges at field positions to become potential energy. Stationary charge has no magnetic field, because it has no relativistic length contraction.
accelerating charge
Charge acceleration pushes electric-field line transversely and stretches it sideways, causing tension and restoring force. Charge acceleration causes transverse electric field, while keeping radial field. Because virtual photons continually leave charge, transverse component moves outward along field line, so spatial transverse waves travel outward. See Figure 2.
Charge acceleration pushes magnetic-field line transversely and stretches it sideways, causing tension and restoring force. Charge acceleration causes magnetic field in charge-motion direction, transverse to magnetic field.
When stationary charge accelerates to constant velocity, electric-field lines curve toward motion direction, because charge and adjacent photon have higher velocity. When constant-velocity charge decelerates to zero velocity, electric-field lines curve away from motion direction, because charge and adjacent photon have lower velocity.
See Figure 3. Force causing electron deceleration also puts transverse upward pushing force on field lines and distorts electric-field lines. As electron slows down, electric-field-lines beginning at electron edge slow down, so horizontal electric-field lines begin to have transverse component upward.
See Figure 3. As electron slows down, electric-field upward transverse component increases over time. Changing electric-field flux (changing electric force) through an area causes relativistic length contraction transverse to area (in same plane) and magnetic-force change in toward or out from area (in same plane), and so causes induced magnetic field around area. Magnetic force has gradient in or out and so makes induced-magnetic-field gradient around. Faster change makes larger gradient.
Electric and magnetic fields interact, so they push/pull adjacent electric and magnetic fields. Interaction is strong and happens at light speed, so adjacency effect travels at light speed. Interaction is constant, so light speed is constant. All interactions are elastic, with no losses to heat or other energy, so induction has same effect later as at beginning.
Transverse effect travels inward and outward at light speed. Outward effect sees only undisturbed field line and so is the only effect and carries energy outward. Inward effect sees restoring force from stretched field line and so forces cancel and line returns to equilibrium, with no energy carried.
Electric-field increase (or decrease) causes magnetic-field increase (or decrease) that opposes electric-field increase (or decrease), by energy conservation.
See Figure 3. Induced magnetic field increases over time. Changing magnetic-field flux (perpendicularly changing magnetic force) through an area causes relativistic length contraction transverse to area (in same plane) and electric-force change around area (in same plane), and so causes induced electric field around area. Electric force has gradient in or out and so makes induced-electric-field gradient in or out. Faster change makes larger gradient.
Magnetic-field increase (or decrease) causes electric-field increase (or decrease) that opposes magnetic-field increase (or decrease), by energy conservation.
Changing electric field and magnetic field are in phase, because they both increase together and both gradients are in same direction.
Gradient and wave leading edge travels outward at constant light speed.
See Figure 3. Horizontal electric-field lines continue moving at constant velocity, because lines have same momentum, inertia, and kinetic energy as before.
See Figure 4. As electron slows down more, electric-field-line points at electron edge slow down more, so horizontal electric-field lines have greater transverse component. Electric-field upward transverse component increases more over time and so makes bigger induced-magnetic-field gradient. Induced magnetic field increases more over time and so makes bigger induced-electric-field gradient. Transverse fields have potential energy, so horizontal electric-field lines at transverse fields have less kinetic energy. Horizontal electric-field lines continue moving at constant velocity, because lines have same momentum, inertia, and kinetic energy as before.
See Figure 5. Metal plate stops electron within one electron width, so distance and time are small, and deceleration is high. Electron is at zero velocity, so current is zero. Electron has no kinetic energy and momentum. Original electric field is symmetric. Original electric field has same potential energy. Original magnetic field is zero. Original magnetic field has no potential energy.
See Figure 5. As electron stops, electric-field-line ends stop, so horizontal electric-field lines have maximum transverse component. As electron stops, electric-field upward transverse component has increased to maximum over time and so makes induced-magnetic-field gradient. Induced magnetic field has increased to maximum over time and so makes induced-electric-field gradient. Induced electric field is maximum.
See Figure 5. Horizontal electric-field lines continue moving at constant velocity, because lines have momentum, inertia, and kinetic energy.
See Figure 6. Deceleration has stopped, so electron and adjacent fields stop feeling upward force. Transverse electric-field stays constant at zero, and so makes no magnetic-field gradient and no magnetic field. Magnetic-field line feels no force, so transverse magnetic field stays constant at zero, and so makes no electric-field gradient and no electric field. Electron and adjacent electric-field line have no velocity, momentum, or kinetic energy. Gradient and wave leading edge travels outward at constant light speed. Adjacent virtual photon leaves electron and travels horizontally at light speed. Transverse electric-field-line component stretches farther downward. Transverse electric-field-line component moves outward at light speed. All interactions are elastic, with no losses to heat or other energy, so gradient has same effect later as at beginning. Original virtual photons of horizontal electric-field lines continue moving at constant velocity, because lines have momentum, inertia, and kinetic energy.
phase
When stationary charge accelerates to constant velocity, electric-field and magnetic-field transverse component increase in same direction and at same time (in phase). When constant-velocity charge decelerates to zero velocity, electric-field and magnetic-field transverse component decrease in same direction and at same time (in phase).
induction
Electric-field change over time (flux) through an area makes magnetic field around area, because of relativistic length contraction. Electric current makes magnetic-field torus around current. See Figure 1.
Magnetic-field change over time (flux) through an area makes electric field around area, because of relativistic length contraction. Magnetic-field flux change through torus cross-section makes electric field around torus cross-section. Current goes through torus hole, around, and back again to complete the circuit (displacement current). See Figure 1.
Stationary electric field has constant force, and so uses no energy to make magnetic field. Moving electric field changes over time and makes constant magnetic-field gradient, because electric-field-movement kinetic energy increases magnetic-field potential-energy over space. Accelerating electric field makes increasing magnetic-field gradient, because electric-field force increases magnetic-field acceleration over space. Accelerating magnetic or electric fields over space have force that causes increasing electric or magnetic fields over time. Fields over space have potential energy, and fields over time have kinetic energy, so energy alternates between kinetic and potential, making waves.
Constant stationary magnetic field has no affect, because it has no force, so magnetic-field energy remains potential energy. Moving magnetic field changes over time and makes constant electric-field gradient, because magnetic-field-movement kinetic energy increases electric-field potential-energy over space. Accelerating magnetic field makes increasing electric-field gradient, because magnetic-field force increases electric-field acceleration over space.
induction: energy conservation
Increasing (or decreasing) magnetic field increases (or decreases) electric field, which makes magnetic field that opposes original magnetic field, by energy conservation. Decreasing (or increasing) electric field decreases (or increases) magnetic field, which makes electric field that opposes original electric field, by energy conservation.
For downward current, acceleration increases magnetic field, and that makes upward electric field, which decreases magnetic field. For downward current, deceleration decreases magnetic field, and that makes downward electric field, which increases magnetic field.
Charge deceleration is against restoring force and builds potential energy. When deceleration stops, restoring force pulls back toward equilibrium, but potential energy transfers to kinetic energy and carries past equilibrium until restoring force pulls back to equilibrium.
Energy goes into adjacent electric-field transverse movement, as interchange between electric and magnetic fields makes wave travel outward. Therefore, energy dies down at past points.
Magnetic-field and electric-field changes have same displacement amount, but electric field has approximately one hundred times more energy. Most light-wave energy is in electric field, not magnetic field, because magnetism is relativistic effect.
To make electric field, virtual photons stream outward at light speed from electron in all directions. Electric-field lines are virtual photon streams. At electron constant velocity, photons also have same velocity as electron, so electric-field lines are straight.
The figure shows virtual photons streaming outward horizontally from electron transverse to electron motion direction. Electron and electric-field lines move downward at same velocity.
Because electric-field and magnetic field interact along line, line has tension, just as a taut string has tension, so line has restoring force if accelerated sideways, just like a taut string has restoring force. All interactions are elastic, with no heat losses, so forces and energies are the same all along electric-field lines from beginning to infinity.
Deceleration can knock field lines through space. Stronger deceleration makes farther and stronger fields.
gradient
Field induction around area circumference makes space gradients as tangents to circumferences. When electric-field flux change through area makes magnetic field around area, magnetic field has gradient around area. When magnetic-field flux change through area makes electric field around area, electric field has gradient around area.
speed
Because electric force is strong, electric and magnetic fields interact at light speed. Because magnetic field and electric field couple {electromagnetic wave induction}|, transverse field-line component moves outward along electric-field line at light speed. Electromagnetic interaction strength is constant, so light speed is constant.
wave
Waves are local effects that travel. Traveling field changes are independent of original charges.
For downward current, deceleration decreases magnetic field, and that makes downward electric field, which increases magnetic field. Electric and magnetic fields are in phase. Electric-field-line disturbance moves away from charge at light speed in a straight line. Transverse component makes traveling wave half {half-wave, wave}. All disturbances to electric-field lines travel outward at light speed. Previous points have no more disturbances, so only one half-wave exists at any time. No disturbances are left behind, because all energy has traveled away. Disturbance reaches farther positions in sequence out to infinity. See Figure 1 through Figure 7. Wave exists only at induction point and can only go straight-ahead. Wave has no physical effect except at moving single point.
elastic
Electric and magnetic interactions are elastic, with no losses to heat or other energies. Therefore, disturbances travel without losing energy. Inductions continue to infinity.
strength with distance
Inductions and other electric-field-line disturbances are transverse to electric-field lines. Because electric field oscillates in a plane, not area, intensity decreases directly with distance, not with distance squared. Transverse effects happen in one dimension, so wave strength decreases directly with distance: 1/r. At later times, transverse field component stretches more over space.
electric-field-line tension and restoring force
Guitar-string molecules attract each other by electric forces. Taut guitar strings have tension from these restraining forces. Pulling string sideways puts potential energy into the string, by stretching string electric forces, like springs. After releasing string, electric forces, like springs, pull string back by restoring force. Potential energy transfers to kinetic energy. Molecule kinetic energy carries molecules past equilibrium point, so they pull on string molecules in other direction.
Adjacent to pull and release point, molecule electric forces pull-and-restore adjacent string molecules, so transverse waves travel along string. Wave speed depends on molecule electric-force strength. Wave takes energy with it, so no energy is left at original disturbance point, and it no longer oscillates. Molecule electric forces bring displacement back to equilibrium at zero.
Electric-field lines are like strings. Like guitar strings, electric-field lines have tension, because electric fields couple to adjacent magnetic fields, and magnetic fields couple to adjacent electric fields. Electric-field and magnetic-field inductions cause adjacent electric-field line points to attract, like molecule electric forces. Pushing electric-field line sideways adds potential energy. Electric-field and magnetic-field inductions make restoring force that transfers potential to kinetic energy.
Electric-field-line-point transverse disturbance displaces adjacent points, which displace their adjacent points, so disturbance travels outward along electric-field line. Electromagnetic interactions are at light speed, so wave has light speed. Wave takes energy with it, so no energy is left at original disturbance point, and it no longer oscillates. After disturbance, electric-field and magnetic-field mutual-induction restoring force brings displacement back to equilibrium at zero.
metal plate
Plate-molecule electric force decelerates electron and so decelerates electric-field line and magnetic-field line at electron edge, transverse to motion direction.
electric and magnetic forces
When electric-field-line disturbance reaches test charges far away from original charge, test charges move along charge-motion direction, because transverse electric field is voltage and electromotive force. Electric-field change and magnetic-field change reach test charge at same time. Magnetic-force effect is one-hundredth electric force. For far-away test charges, radial electric force is smaller than disturbance force, because radial force decreases with distance squared but transverse force decreases with distance. Original-charge velocity and acceleration have only negligible effect on far test charges, because waves move at light speed but charges move much slower.
Test charges along accelerating-charge direction have no transverse effects, because push or pull is in same direction as accelerated charge.
not stationary
Stationary oscillating electromagnetic fields cannot exist, because electromagnetic induction requires field movement. Standing waves result from traveling-wave superposition.
medium
Light needs no medium, because electric/magnetic fields are their own medium.
situations: antenna
Alternating current accelerates many charges back and forth along one orientation (antenna), making transverse electric-field waves that expand in planes that go through acceleration direction. Electric-field lines transverse to oscillation direction have maximum transverse component. Electric-field line along oscillation direction has no transverse components. Electric-field lines between transverse and oscillation direction have decreasing transverse component.
Electric-field change causes magnetic-field change one quarter cycle later, by relativistic length contraction, and magnetic-field change causes electric-field change one quarter cycle later, by relativistic length contraction, so phases lag each other by 90 degrees. If magnetic-field gradient first increases to north, then electric-field gradient increases to east, then magnetic-field gradient increases to south, then electric-field gradient increases to west, and then magnetic-field gradient increases to north, and so on, because each drives the other along by transverse electric force. Inductions are at right angles, rotating around direction of motion by 90 degrees. 90-degree rotations result in linearly polarized waves.
Source charge accelerations affect electric and magnetic fields at same time, so changing electric field makes magnetic field and changing magnetic field makes electric field simultaneously, so electric field and magnetic field are always in phase.
As electric field increases, magnetic field increases, because magnetic fields are relativistic effects of electric fields. As electric field decreases, magnetic field decreases. When electric field maximizes, becomes zero, or maximizes in opposite direction, magnetic field maximizes, becomes zero, or maximizes in opposite direction. Magnetic-field and electric-field changes increase and decrease in synchrony (phase), because both fields couple. Transverse magnetic-field and electric-field accelerations are equal, in phase, and perpendicular.
When electric field and magnetic field are zero, and potential energy is zero, electric-field change and magnetic-field change maximize in space and time. When electric field and magnetic field maximize, and potential energy maximizes, electric-field change and magnetic-field change are zero in space and time. When electric-field change is zero and electric field maximizes, voltage maximizes and current is zero. When electric-field change maximizes and electric field is zero, voltage is zero and current is zero. When magnetic-field change is zero and magnetic field maximizes, voltage is zero and current maximizes. When magnetic-field change maximizes and magnetic field is zero, voltage maximizes and current is zero.
Fields elastically exchange potential and kinetic energy and make harmonic oscillations. Photons continue at same frequency.
Starting from stationary charge, voltage accelerates charge and adds kinetic energy. Increasing magnetic field increases electric field until increasing electric field has slowed increasing magnetic field and both are maximum, with potential energy maximum. The slower changing electric field decreases magnetic field, which decreases electric field, so both fall in phase, as potential energy becomes kinetic energy. As kinetic energy becomes potential energy in the opposite direction, and then potential energy becomes kinetic energy, the half-cycle repeats in the opposite direction, to complete one cycle. Oscillating current repeats the cycle, and the cycles move outward at light speed. Oscillating current induces electromagnetic waves of same frequency.
Light waves have electric-field and magnetic-field linear polarizations, at right angles. Electric field oscillates in plane that goes through charge-motion direction. Magnetic field oscillates in plane perpendicular to charge-motion direction.
Leading edge of wave rises transversely at angle determined by frequency, which depends on deceleration amount. Higher frequencies have steeper angles. Higher frequencies have greater curvatures at maximum displacement, because higher frequency means turnaround is faster.
situations: dipoles
For dipoles, charge acceleration increases as charge separation increases.
situations: atoms
Atom and molecule electrons can accelerate or decelerate and so change orbits, absorbing or making radiation. Molecule dipoles can rotate, vibrate, or translate, and so accelerate electrons, absorbing or making radiation.
situations: devices
Free charges in electric and magnetic fields accelerate free charges, as in vacuum tubes. When moving electrons hit metal plates, they decelerate and can make x-rays.
Electric-charge accelerations start electromagnetic waves {wave initiation} {initiation, wave}, because force makes radial electric field have transverse component adjacent to charge. Transverse component travels outward along electric-field line {wave propagation} {propagation, wave}, because electric-field (and magnetic-field) changes interact at light speed, because electromagnetic force is strong. Waves travel away from charges, because all energy travels outward, so no energy is left behind, and only wave leading edge (wave front) exists at any time. Wave has kinetic energy directly proportional to force that caused charge acceleration.
charge: stationary
Stationary charge makes constant electric field and no magnetic field. See Figure 1.
charge: moving
Charge moving at constant speed makes moving electric field and constant magnetic field. See Figure 2. Magnetic field is perpendicular to electric field, because magnetic field comes from relativistic length contraction that causes increased charge density along charge-motion direction, which observers see from side.
charge: acceleration
Accelerating charge increases current, because charge speed increases. Increasing current makes increasing magnetic field. Accelerating charge makes faster moving electric field. See Figure 3. (Decelerating charge decreases current, decreases magnetic field, and makes slower moving electric field.)
initiation
As charge accelerates, electric and magnetic fields accelerate, and magnetic field increases. See Figure 4.
propagation
Electric-field (and magnetic-field) change cause magnetic-field (and electric-field) gradient, by Maxwell's laws, so electric and magnetic fields interact. Interaction is at light speed. See Figure 5.
When induced electric field and magnetic field reach far-away test charge, electric-field vertical component accelerates test charge. See Figure 6.
When induced electric field and magnetic field pass far-away test charge, test charge continues at constant velocity. See Figure 7.
propagation: direction
Electromagnetic-induction is only at wave front, because all energy is there. Behind wave front, electric and magnetic fields return to zero, as fields, coming from many points with all phases, cancel. Waves propagate outward from accelerated charge, because electromagnetic-induction electric and magnetic fields behind have all phases and cancel.
propagation: no medium
Electromagnetic waves can propagate through empty space, because electric and magnetic fields are their own medium.
propagation: induction rate and wave speed
Electric-force strength determines electromagnetic-induction rate, which is light speed. Material electric charges, relativistic apparent electric charges, other electric fields, and other magnetic fields exert force on electromagnetic waves, and so reduce electromagnetic-wave speed.
Unaccelerated Charge Makes No Electromagnetic Wave
Unaccelerated moving charge makes moving constant electric field and constant concentric magnetic field. See Figure 4. No acceleration makes no force, so fields stay constant. Only radial force affects test charge, so it has no transverse motion.
Charge Acceleration Makes Traveling Electric Field
See Figure 5. Collision, gravity, or electric force can accelerate charge. Acceleration makes force, so fields change. Acceleration is transverse to radial electric-field line, so test charge has transverse motion. See Figure 6.
pure electric waves
There are no pure electric non-magnetic waves, because waves require electric-field changes, which always make transverse relativistic electric fields, which are magnetic fields. There are no pure magnetic non-electric waves, because waves require magnetic-field changes, which always make transverse relativistic electric fields.
Waves {light}| {electromagnetic wave} can begin by charge accelerations or electronic transitions and propagate by electromagnetic induction. Charge-acceleration or electronic-transition energy change determines electromagnetic-wave frequency.
Accelerating charge makes a photon field, which differs near source {near field} and far from source {far field}. Far field is what lenses, mirrors, and instruments see. Point charges or nearby detectors can examine near field.
Equations {Maxwell's equations} {Maxwell equations} can find all electric and magnetic properties. For stationary and moving charges, electric-field and magnetic-field relations are Gauss's law, Gauss's law for magnets, Faraday's law, and Ampere's law.
stationary
Partial derivative of electric field with distance equals negative of partial derivative of magnetic field with time. Partial second derivative of electric field with distance equals electric permittivity times magnetic permeability times partial second derivative of electric field with time.
tensors
Maxwell's equations are equivalent to two equations. For magnetostatics and magnetodynamics equations, exterior derivative of electromagnetic-field tensor F equals zero: dF = 0. Electromagnetic-field tensor is a linear operator on velocity vector. Electromagnetic-field tensor has covariant components. This tensor is equivalent to delta function. For electrostatics and electrodynamics equations, exterior derivative of electromagnetic-field-tensor dual F* equals four times pi times four-current dual J*: dF* = 4 * pi * J*. This tensor is equivalent to delta scalar product.
current
The four-current has one component for charge density and three components for current densities in three spatial directions.
duals
Rank-x antisymmetric tensors relate to rank 4 - x antisymmetric tensors {dual, tensor}. Dual of dual gives original tensor, if rank is greater than two.
invariant
Electromagnetism invariant is current squared minus light speed times charge density squared, which equals negative of momentum times light speed squared.
retarded and advanced
Electromagnetic-field changes follow charge accelerations {retarded solution}. However, field changes can happen before charge accelerations {advanced solution}, because equations are symmetric. Other solutions can be linear retarded-solution and advanced-solution combinations.
Light speed {speed of light} {light speed}| is the same relative to any observer, moving or not. Light speed is invariant and absolute, in space with no electric fields.
speed
Light speed depends on electric-force strength, which determines electromagnetic-induction strength. In vacuum, light speed is 3.02 x 10^8 m/s (Hippolyte Fizeau and Bernard Foucault) [1849]. Light speed is fast, because electric forces are strong. All zero-rest-mass particles travel at light speed, because added energy does not affect them. Gravity does not affect zero-rest-mass particles.
space
Light does not travel through time, because it has no medium and so no reference frame or space-time. Light only travels through space, not time. Light has zero time.
cause
Observers see invariant speed, because light never has time component and so cannot go slower. Light cannot go faster, because it uses all of space already. When observers see light, light length appears to be zero and time appears to be at maximum dilation. Observer motion does not affect light speed observed, because light has no medium. Observer motion contracts length and dilates time, but light already has maximum length and shortest time. If observer moves at higher velocity, both time dilation and space contraction happen, so light speed stays the same.
space-time velocity
All objects travel through space-time at light speed. Light travels only in space. Stationary objects travel only in time. Moving masses travel in space and time.
terminal velocity
Light speed is like terminal velocity through space-time. Electromagnetic induction pushes wave, and forces in universe retard wave. Resistance to light motion can come from effects of all universe masses and charges.
mass
No object with mass can go faster than light. For mass at light speed, stationary observers see infinite mass, zero length, and zero time. To make infinite mass requires infinite energy. Infinite mass exerts infinite gravitational force. Infinite mass attracts and red-shifts light, dimming universe. Infinite mass, moving at light speed, appears to have infinite frequency and zero wavelength.
phase velocity
Light pulses contain wave sets. Light-pulse envelope carries energy. Envelope speed {group velocity} must be light speed or less. However, individual waves can have speed higher or lower than light speed {phase velocity}. Negative refraction cannot exist.
Perhaps, light travels in a stationary medium {luminiferous ether} {the ether} {æther}, not vacuum. As such, because light has constant velocity in any reference frame, ether is an absolute reference frame. It is fluid but does not disperse, has no viscosity, and has high tension and is rigid. It has zero rest mass and is transparent, continuous, and incompressible. Perhaps, it appears rigid to high-velocity objects or high-frequency waves but fluid to low velocity objects or low-frequency waves. Michelson and Morley [1887] measured interference of light traveling in Earth-motion direction and in opposite direction {Michelson-Morley experiment} and found no interference and no Doppler effect, leaving no physical properties to ether and so indicating that there was no ether.
Light can carry enough electric energy to knock electrons out of atoms {photoelectric effect}|. If light frequency is below threshold for material, atoms emit no electrons, because photoelectric effect requires minimum energy. Light with higher frequency than threshold imparts more speed to liberated electrons but does not emit more electrons. Higher-intensity light, which has more photons with enough energy, makes more electrons leave.
Radiation has entropy {entropy, radiation} {radiation entropy}. If space is isotropic and unpolarized, entropy S equals four times energy U divided by three times temperature T: (4*U) / (3*T). If system has more wavelengths or more directions, radiation entropy increases. Universe can absorb radiation and everything else without limit, so entropy continually rises.
Light has subatomic particles {photon, light}|. Photon is like wave packet. Continuous light {light ray} {ray, light} is many wave packets.
straight
Light rays and photons travel in straight lines.
energy
Photon energy E is frequency v times Planck constant h: E = h*v.
observers
What do people see as photon goes past? In empty space, people see particle contracted to zero length, with no mass but with frequency and wavelength. People see time standing still on photon.
What does photon see? In empty space, photon travels at light speed. Other objects pass by at light speed, with infinite mass and zero wavelength. Photon sees time as standing still on other things. Photon sees only point straight-ahead, and sees nothingness on sides, so photon sees along one-dimensional line.
Light can travel in two dimensions {plasmon}| and so travel in plane. Photons that hit interface between conductor and insulator induce surface electrons to vibrate at same or similar frequency and cause traveling wave. Wave reflections make resonances. Plasmons {plasmonics} can have same or shorter wavelength as impinging light.
Light intensity {illuminance}| is light flux (in lumens) per area. Light intensity depends on amplitude squared, photon number, and frequency squared.
Light intensity {Poynting vector} has maximum of half times light speed times permittivity e times electric field E squared: 0.5 * c * e * E^2. Poynting vector equals half times electric field E times magnetic field H: 0.5 * E * H.
At high intensity, wave electric field can affect molecule electric fields {Kerr effect} {optical Kerr effect}.
Radiation has pressure {radiation pressure} {pressure, radiation} from photon flow. Pressure P equals energy U divided by three times volume V: P = U / (3*V).
Light meters {photometer}| can measure light intensity.
Radiation has frequency {radiation frequency}.
Deceleration as electrons hit metal makes radiation {Bremsstrahlung radiation}| with wavelength 10^-12 meters.
Beta-particle electrons, with velocity higher than light speed in water, emit blue light {Cerenkov radiation}| {blue glow} as shock waves when they enter water. Water surrounding nuclear-reactor cores, which emit high-velocity electrons, has blue glow.
process
Electrons traveling in water use some energy to polarize water molecules along travel direction. After electrons pass, polarized water molecules emit light. If electrons travel slower than light speed in water, emitted radiation appears low, because electromagnetic waves emitted by molecules along path are random and destructively interfere. If electrons travel faster than light speed in water, emitted radiation appears high because electromagnetic waves emitted by molecules along path are shock waves that constructively interfere.
Infrared-light rotational and vibrational energies cause differences in visible light reflected from molecules {Raman scattering}|.
In atmosphere, secondary cosmic rays {spallation}| arise if cosmic ray hits atomic nucleus.
Charged particles accelerated by spiraling in magnetic field can emit microwaves {synchrotron radiation}|. Synchrotron radiation happens when electric field is parallel to electron-orbit plane.
Electromagnetic radiation has frequency range and wavelength range {spectrum, light}|.
low frequency
electric wave. radio wave. short wave. very-high-frequency TV wave. ultra-high-frequency TV wave. microwave radiation. infrared ray.
visible
Visible light is 4 x 10^14 Hz with wavelength 6.8 x 10^-7 meters for red light, orange, yellow, wavelength 5.5 x 10^-7 meters for yellow-green, green, wavelength 4.4 x 10^-7 meters for blue light, indigo or ultramarine, and 7.5 x 10^14 Hz with wavelength 4.1 x 10^-7 meters for violet light.
Violet is 380 to 435 nanometer, with middle at 408 nanometer. Blue is 435 to 500 nanometer, with middle at 463 nanometer. Cyan is 500 to -520 nanometer, with middle at 510 nanometer. Green is 520 to 565 nanometer, with middle at 543 nanometer. Yellow is 565 to 590 nanometer, with middle at 583 nanometer. Orange is 590 to 625 nanometer, with middle at 608 nanometer. Red is 625 to 740 nanometer, with middle at 683 nanometer.
high frequency
near ultraviolet. ultraviolet. far ultraviolet. X ray. gamma ray. secondary cosmic ray. cosmic ray. primary cosmic ray.
Smallest frequencies and longest wavelengths {electric wave}| are 3 to 60 Hz and 10^8 to 5 x 10^6 meters.
Next smallest frequency and wavelength {radio wave}| are 10^3 Hz and 3 x 10^5 meters.
High-frequency radio waves {short wave}| are for global communication.
Typical TV frequencies and wavelengths {very high frequency TV wave}| (VHF) are 10^8 Hz and 3 meters.
higher TV frequencies and wavelengths {ultra high frequency TV wave}| (UHF).
frequencies below infrared {microwave radiation}|.
Heat-ray {infrared}| frequency is 10^12 Hz, with wavelength 3 x 10^-4 meters.
Light {visible light}| can have wavelength 400 nm to 700 nm. Visible light has same wavelengths as diameters of, and energy changes in, atoms and molecules. Matching diameters allows people to focus on objects, because light is not too diffracting or too strong. Matching energy changes allows absorption, emission, and chemical reactions.
Smallest visible-light frequency {red light}| is 4 x 10^14 Hz, with wavelength 6.8 x 10^-7 meters.
Highest visible-light frequency {violet light}| is 7.5 x 10^14 Hz, with wavelength 4.1 x 10^-7 meters.
higher frequency than violet {ultraviolet}|.
Light {far ultraviolet}| {black light} can have frequency 1.5 x 10^15 Hz and wavelength 2 x 10^-7 meters.
higher frequency than far ultraviolet {X ray}| {x ray}.
Next-to-highest frequency {gamma ray, spectrum}| is 10^23 Hz, with wavelength 3 x 10^-15 meters.
Highest frequency {cosmic ray}| {primary cosmic ray} is 10^25 Hz, with wavelength 3 x 10^-17 meters. Quasars and powerful energy sources make cosmic radiation.
Light {monochromatic light}| can have one wavelength.
Light {polychromatic light}| can have many wavelengths.
Magenta, yellow, and green pigments {primary pigment}| mix to make black.
Variations {dichroism}| in absorbed-light color can depend on light-polarization direction. Dichroism indicates molecule orientation, which can be linear, circular {circular dichroism}, or elliptical. Microvilli rhabdom can lie parallel, exhibit dichroism, and detect polarized-light polarization plane.
If one photon accelerates, light-wave electric field vibrates in one plane {plane polarized wave} {polarized light}, and light-wave magnetic field vibrates in perpendicular plane {polarization, wave}|. Typically, many charges accelerate in all possible planes, so there is no polarization.
materials
Materials can allow only light with one electric-field plane to transmit. Polaroid plastic and tourmaline can polarize light.
circular
Asymmetric-molecule electric forces cause substances to rotate electric-field planes {circularly polarized wave} around light travel direction.
Optical activity can vary with light frequency {dispersion, light}|. Higher frequencies cause more rotation, because photons have more energy.
If polarized light with different wavelengths passes through asymmetric medium, shorter wavelengths rotate plane more than longer wavelengths {optical rotatory dispersion} {Cotton effect}.
Materials with asymmetric-molecule electric forces can have refractive index different for left and right circularly polarized light {optical activity}|. Carbon can bond four different atoms, in two mirror-image forms.
Light takes shortest path, and so least time, between two points {Fermat's principle} {Fermat principle}.
Action is energy times time, or momentum times distance, or angular momentum times angle. Light uses path with least action between two points {Hamilton's principle} {principle of least action, Hamilton} {least-action principle, light}|. In quantum mechanics, action has quanta, which have size Planck constant h, so photons have energy quanta h * frequency, momentum quanta h / wavelength, and angular-momentum quanta h / 2 * pi.
Lasers produce light waves {coherent light}| that have same phase.
Light passed through consecutive slits {collimate}| has many light waves in phase.
Devices {laser}| {Light Amplification by Stimulated Emission of Radiation} can emit many photons in phase [1960].
light source
Flash tube excites atom electrons into highest orbital. Below highest orbital are one or two lower-energy levels, and below them is ground-state level.
light
Electrons spontaneously fall to intermediate-energy level by vibration, rotation, or radiation.
Then previous photon causes electron to fall to next-lower level {lase}, which simultaneously makes another photon, so both photons are in phase and photon number doubles. This process repeats to make many in-phase photons. Lasers can emit light axially or transversely.
collimation
Photons conserve momentum, so they have same direction.
amplitude
Mirrors can build power by repeated lasing and reflecting, until shutter opens {Q switching} and light releases. Shutter can be rotating mirror, Pockels cell, photochemical, or exploding film. Current modulation can modify laser amplitude. Lasers can pulse or be continuous. Laser can be tunable to different light frequencies.
materials
Lasers can use helium-neon, helium-cadmium, argon, krypton, carbon dioxide, and gallium arsenide. Ruby lasers emit red light. Gallium-nitride lasers emit blue light. Zinc selenide can also make blue light.
purposes
Lasers can align exactly, measure distances by reflection from corner reflectors, attach retinas by burning them on, weld, and make holographs. Lasers can separate atom isotopes, by exciting only one isotope. Lasers can measure thickness, drill holes, and carve miniature circuit blocks. Lasers can implode pellet to start nuclear fusion in tube {hohlraum}.
fiber optics
Laser light passed down non-linear optical fiber {microstructure fiber} broadens in wavelength {supercontinuum light}. Light can alter material, which then alters light {self-phase modulation}.
timing
Lasers {mode-locked laser} can make one-femtosecond microwave or light pulses at 1-GHz. Frequencies are visible light within 150-nm wavelength interval. Superposition makes pulses have few wavelengths. Phase {offset frequency} increases slightly with each pulse. Wave-train pulses have higher net frequencies until cycling again, with equal spacing. Pulses are beats, so pulse frequency is lower-frequency frequency difference. Given reference frequency, beat frequency can determine unknown frequency.
Storing light-wave interference patterns {hologram}| on photographic plates {holograph} allows display of three-dimensional images [Gabor, 1946].
production
Coherent light can shine directly on photographic plate and can reflect from static scene onto plate. Wave-front superposition makes interference pattern that photographic plate can record.
projection
Shining coherent light on or through photographic plate can project scene wave front into space. Plate positions contribute to all image points, whereas photograph points contribute to one image point. Observer sees wave front coming from three-dimensional space, rather than from surface. Observer can view image from different points to see image from different perspectives.
Shining coherent light on part of plate makes whole image but with lower resolution, because number of contributions is less, so standard error is more. Using longer-wavelength coherent light to reconstruct image can magnify image size. Using shorter wavelength coherent-light to reconstruct image reduces image size.
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Date Modified: 2022.0225