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}.
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Date Modified: 2022.0225