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MindMap Gallery University Physics Vibrations, Waves, Electromagnetic Waves and Wave Optics
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University Physics Vibrations, Waves, Electromagnetic Waves and Wave Optics
This is a mind map about vibrations, waves, electromagnetic waves and wave optics in university physics. The introduction is detailed and the knowledge is comprehensive. I hope it can be helpful to everyone!
Edited at 2024-01-17 09:44:10
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University Physics Vibrations, Waves, Electromagnetic Waves and Wave Optics
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- Outline
Vibration and Waves
vibration
If any physical quantity changes repeatedly near a certain value, it means that the physical quantity is vibrating.
Simple harmonic motion kinematics
simple harmonic motion
The displacement of an object relative to its equilibrium position changes with time according to the cosine or sine law.
When the spring is at free length, the position of the ball is the equilibrium position
A is the amplitude. The number of times an object completes reciprocating motion per unit time is called the vibration frequency. The reciprocal of the frequency is the period.
Circular frequency (natural frequency of vibration), v is the vibration frequency
Analytical method, curve method, rotation vector method
phase difference
In phase
reverse phase
Simple harmonic oscillation dynamics
It is only determined by the inherent properties of the oscillator
elastic recovery coefficient
Elastic recovery
The magnitude is proportional to the displacement from the equilibrium position
If the resultant force on the object is an elastic restoring force, the amplitude and initial phase can be solved from the initial conditions.
Simple harmonic vibration energy
kinetic energy
potential energy
Kinetic energy and potential energy in the vibration process can be converted into each other, but the total mechanical energy is conserved.
Simple harmonic motion example
simple pendulum
Damped vibration, forced vibration, resonance
Damped vibration
overdamping, critical damping
forced vibration
Resonance
When the damping force is very small and the driving force frequency is approximately equal to the natural frequency of the vibration system, the system amplitude reaches the maximum.
Vibration synthesis spectrum analysis along the same direction
Along the same straight line, the frequency is the same
two
n amplitudes are the same
Along the same straight line, different frequencies
Vibration that sometimes gets stronger and sometimes gets weaker is called beat
Spectrum analysis
Determine the frequency components contained in a vibration and the amplitude of each frequency
The resulting set of frequencies and corresponding amplitudes is called a spectrum
The lowest frequency is the fundamental frequency
Other frequencies are called harmonics
Vibration synthesis along the vertical direction
Along vertical lines, the frequencies are the same
Along a vertical line, the frequencies are different
Lissajous figure
mechanical wave
Generation and propagation of mechanical waves
To generate mechanical waves, a mechanical vibrating object is required - the wave source.
The propagation of mechanical waves in media is mechanical waves
Mechanical waves that rely on internal elastic force to propagate are called elastic media. At this time, mechanical waves are also called elastic waves.
transverse wave
The vibration direction of the mass element is perpendicular to the direction of wave propagation
Gas, liquid and solid have compressive elasticity
Longitudinal wave
The vibration direction of the mass element is parallel to the direction of wave propagation
Solids are shear elastic
What is propagated is only the vibrational state or form of motion of the matter
Energy is transferred from the upstream mass element to the downstream mass element
Wave Propagation Geometric Representation
A straight line or curve in the direction of propagation is a wave line
Points with the same phase form an isophase surface
The front of the wave is called the wave front or wave surface
Plane waves, spherical waves, cylindrical waves
Wave speed
Gas-liquid propagation elastic longitudinal wave
Wave speed of transverse waves in solids
The wave speed of a longitudinal wave propagating in a thin rod
The velocity of a longitudinal wave propagating along a thin rod
Plane simple harmonics
Wavelength, frequency and wave number
Angular wave number k, when k is a vector, it is called wave vector, circular frequency
Plane simple harmonic wave function
The function that describes the relationship between the relative equilibrium position displacement of each mass element in the wave field and time is the wave function
significance
given time
Given space coordinates
The wave function describes the propagation of states of motion
vp is the phase velocity of the wave
Plane wave wave equation
Any physical quantity, as long as it satisfies this equation for coordinates and time, this physical quantity must propagate in the form of a plane wave
Derivation of elastic transverse waves in solids
Energy density and energy flow of mechanical waves
Kinetic energy and potential energy of matter elements in wave field
Mechanical energy
Energy density and wave intensity in the wave field
Energy Density
energy flow density
The time-averaged energy flow density is the wave intensity
The energy of the wave passing through any surface in the wave field per unit time is called the energy flow of the wave pair on this surface.
absorption of waves
The medium generally absorbs part of the wave energy
Sound waves, ultrasonic waves and infrasound waves
The mechanical longitudinal waves that cause human hearing are called sound waves, 20hz~20000hz
ultrasound
High frequency, small diffraction, strong penetration ability, detection, flaw detection, investigation, machining, welding, cleaning
infrasound
Mainly generated by large-scale movements of the earth's crust, sea water, and atmosphere, and can be transmitted over long distances
Huygens' Principle, Diffraction, Reflection and Refraction of Waves
Huygens' principle
When waves encounter obstacles, they will undergo diffraction and will be reflected and refracted at the interface between the two media.
Each mass element in the medium to which the wave propagates can be regarded as a wave source emitting wavelets, and the envelopes of these wavelet wave surfaces at any subsequent time are new wave surfaces.
diffraction of waves
Encountering obstacles during the propagation process, changing the straight line propagation direction, and propagating into the obstacle blocking area is called diffraction of waves.
Laws of Wave Reflection and Refraction
The relationship between reflected wave, refracted wave and incident wave amplitude
A medium with large wave resistance is called wave-dense medium, and a medium with small wave resistance is called wave-rare medium.
Boundary conditions
Available
Reflection coefficient
Transmission coefficient
Amplitude relationship conclusion
The sum of the reflection coefficient and transmission coefficient is 1, and energy is conserved
Reflection and transmission are only related to the two medium surfaces and have nothing to do with which side is incident
If the wave resistance of the two media is equal, the wave will be completely transmitted
At the interface between two media surfaces with significantly unequal wave resistance, the wave is close to total radiation.
half wave loss
When a wave is incident from a wave-dense medium to a wave-dense medium, the phase of the reflected wave at the reflection point changes by π.
Coherent superposition of waves Standing waves
wave superposition principle
Wave propagation is independent
The vibration of each mass element is the synthesis of the vibrations of the mass element caused by each series of waves.
Linear superposition of waves, also called the principle of wave superposition
Need to satisfy the linear relationship between deformation and stress
interference of waves
In the overlapping area of the two waves after passing through the narrow slit, the vibration is strengthened in some places and weakened in some places, and does not change with time. This is called interference of waves.
Two waves that can interfere are called coherent waves
The wave source that excites coherent waves is called a coherent wave source
The vibration direction is the same, the frequency is the same, and the phase difference does not change with time is called the coherence condition of the wave.
Interference and mutual benefit
Interference weakens
Standing waves (special case of wave interference)
Interference of two columns of coherent waves in the same medium along the same straight line with opposite propagation directions and the same amplitude.
There is no propagation of energy, vibrational state or phase, so it is called a standing wave
antinode,node
The same segment of a standing wave has the same phase, and two adjacent segments have opposite phases.
Eigen frequency normal mode
The corresponding frequency is the eigenfrequency
The lowest frequency is the fundamental frequency, and the rest are harmonic frequencies
Simple harmonic vibration at the fundamental frequency or harmonic frequency is the simplest possible vibration mode on a string, and is called the normal mode of the string.
The pitch is determined by the eigenfrequency of the string. The fundamental frequency corresponds to the fundamental tone, and the harmonic frequency corresponds to the overtone.
Doppler effect
The source is stationary and the receiver is moving.
The receiver is stationary and the source is moving
The wave source and receiver are both moving
longitudinal doppler effect
shock wave
When the wave source speed in the medium is greater than the medium wave speed
The moving speed of the wave source is equal to the wave speed in the medium, which will cause a sound barrier
Cherenkov radiation
electromagnetic waves
Electromagnetic Wave Equation Hertz Experiment
electromagnetic wave equation
The propagation speed of electromagnetic waves in vacuum is the speed of light in vacuum
Hertz experiment
Electromagnetic wave classification and electromagnetic spectrum
Emission of electromagnetic waves Antenna Electric dipole radiation
Emission of electromagnetic waves
Various electromagnetic wave degrees are generated by Euclidean points and accelerated motion. Only the accelerated motion points can stimulate electromagnetic waves that are separated from the field source and move independently in space.
LC tank and antenna
electric dipole radiation field
Planar monochromatic electromagnetic waves
Plane monochromatic electromagnetic wave equation
Plane monochromatic electromagnetic wave wave function
Characteristics of Planar Monochromatic Electromagnetic Waves
Energy Density and Energy Flow
The polarization state of a plane wave
Reflection and refraction of electromagnetic waves on media surfaces
Fresnel formula
Application of Fresnel formula
Interference and Diffraction of Electromagnetic Waves
Coherence conditions for electromagnetic waves
interference of electromagnetic waves
Diffraction phenomenon of electromagnetic waves
The time average value of electromagnetic wave energy flux density is called light intensity
Wave optics (optics can be divided into geometric, wave, quantum)
Coherent superposition of light waves - interference
Light source - atoms emit light
energy level
The energy of an isolated atom can only take on a series of discrete values.
The lowest energy state is the ground state, and other states with higher energy are called excited states.
jump
emit photons
When an atom emits light, it actually emits a wave train or wave train with a certain frequency, a limited length, and a certain vibration direction.
light interference optical path
Two lights that meet the coherence conditions are called coherent lights, and the light source is a coherent light source.
Interference is constructive, interference is destructive
optical path in medium
Thin lenses do not cause additional optical path difference
Ways to obtain coherent light
splitting front
Young's double-slit interference
Grating multi-slit interference
Amplitude (according to whether the upper and lower surfaces are parallel)
isoclinal interference
Equal thickness interference
Wavefront interference
Young's double-slit interference
The k value is the fringe level, k=0 corresponds to x=0 central clear fringe
Young's double-slit interference pattern is a pattern of alternating light and dark stripes, which are piled up and distributed on both sides of the central light stripe.
For a given interference device and a determined light wavelength, Young's double-slit interference fringes are equally spaced
Other wavefront interference
Fresnel Biprism
Fresnel double-sided mirror
lloyd mirror
Forming a coherent light source inverse phase
spatial coherence and temporal coherence
interference fringe contrast
Limiting width of light source coherence Spatial coherence
Monochromaticity of light source Temporal coherence
thin film isoclinic interference
Principle of isoclinal interference Optical path difference
Experiments to observe isoclinic interference and analysis of interference patterns
45 degree angle half mirror
The pattern is concentric circles of alternating light and dark circles
The smaller the radius, the higher the level of the bright ring, and the center bright spot has the highest level.
The bright rings are sparser toward the middle and denser toward the outside.
The interference pattern is determined only by the angle of incidence, with the intensity increasing at the same angle of incidence.
AR coating and AR coating
Enhanced reflection film
Interference and mutual benefit
AR coating
Reflected light interference destructive
thin film equal thickness interference
Cutting edge interference
Appears on the lower surface of the upper glass plate
Destructive interference at edges
Analysis of tip interference pattern
The wavelength and refractive index of the medium are constant. The smaller the inclination angle, the larger the spacing between adjacent interference fringes. If θ is too large to a certain extent, it will not be visible.
n and e are constant, the red light stripe is wider than the purple light, and the white light will have a colored spectrum.
The tip of the chopper is filled with water, and the interference fringes become denser.
Newton's rings
Concentric rings that are sparse on the inside and dense on the outside, with a dark pattern in the center ring
The radius of Newton's ring is proportional to the square root of the ring's order. The larger the radius, the denser it is.
Michelson interferometer (using fractional amplitude method)
device
Beam splitter
Divide the incident light into reflected light and transmitted light with similar amplitudes
Compensation board
Increase the optical path of transmitted light
principle
isoclinal interference
Every time it moves half a wavelength, one fringe emerges or is swallowed
Equal thickness interference
application
Measurement
side refractive index
Laser alarm
Laser snooping
Single-slit Fraunhofer diffraction of light
diffraction
Light can bypass obstacles and propagate into the geometric shadow area of the obstacle
When the size of the obstacle is reduced to a level comparable to the wavelength of light, diffraction will be evident.
Fresnel diffraction and Fraunhofer diffraction
Fresnel diffraction
The distance between the light source, the receiving screen (or one of the two) and the diffraction screen is finite.
Fraunhofer diffraction
The light source to the diffraction screen and the receiving screen to the diffraction screen are infinite or equivalent to infinity.
Single-slit Fraunhofer diffraction experimental device
Huygens Fresnel theorem
Each surface element on the wave front can be regarded as a wavelet source. The vibration of any point in front of the wave is the result of the coherent superposition of all wavelets at that point.
Fresnel Kirchhoff formula
Interference diffraction of light is the result of coherent superposition of light waves. However, the number of light interference sources is limited, while the number of light diffraction sources is infinite.
Fresnel half-band method
The optical path difference between the light emitted from each point of the adjacent narrow strips and reaching point p is half a wavelength.
The diffraction angle is not zero, the number of half-wave bands is an even number, the adjacent half-wave bands are an even number, and the light destructs into dark spots.
When it is an odd number, P is the bright point
For a diffraction angle of zero, the optical path difference of all wavelets is zero, and point p is the central clear fringe.
amplitude vector method
Divided into N wavebands, but not necessarily half a wavelength in length
Optical path difference between adjacent wavebands
phase difference
nature
There is a stimulation light pattern between two adjacent dark patterns, which can be obtained by using derivatives.
The width of the secondary clear pattern is half the width of the central clear pattern
At a certain wavelength, the narrower the single slit, the wider the diffraction fringes, and the more obvious the diffraction phenomenon is.
Fraunhofer Diffraction of a Circular Hole Resolving Power of Optical Instruments
Fraunhofer diffraction of a circular hole
Airebore
central bright spot surrounded by first dark ring
Central clear fringe corresponding to slit diffraction
The resolving power of optical instruments
Rayleigh criterion
When the center of one Airy disk happens to fall on the first-level dark ring of another, the two Airy disks can just be distinguished.
is called the resolution radius of the instrument
Improve discrimination ability
Increase the aperture of the objective lens
telescope
Reduce the wavelength of incident light
electron microscope
Fraunhofer diffraction of gratings Grating spectra and grating resolving power
Fraunhofer diffraction with gratings (Fraunhofer diffraction with multiple slits)
Grating is an optical element in which diffractive units are arranged repeatedly in space.
Diffraction unit characteristics
Transmission diffraction grating
Reflective diffraction grating
spatial distribution
One-dimensional grating
2D grating
3D grating
Parameter
The slit width is a (light transmission width)
The opaque width is b
d=a b is called a grating constant
Stripe position has nothing to do with the number of grating slits
As the number of grating slits increases, the stripe width becomes effective. The number of gratings is very large and the stripes are very sharp.
The brightness of the grating changes in the same way as the single-slit diffraction fringe. The larger the number of grating slits, the greater the brightness of the fringe.
multi-beam interference
adjacent phase difference
grating equation
Satisfying the grating equation is called the interference principal maximum
dark pattern
There are N-1 dark fringes between two adjacent main maxima, which are called minima, and N-2 bright fringes, and the bright fringes are called secondary maxima.
Light intensity distribution of grating diffraction
Single slit diffraction factor effect
Modulate the main maximum intensity at all levels so that the light energy is concentrated in the central main maximum area
The missing order phenomenon produces interference main maximum fringes. The single-slit diffraction minimum appears at the multi-beam interference maximum. When the fringes are small, the synthetic light intensity is zero.
When d/a is an integer, the positive and negative main maxima of n integer times will be missing.
Determine the distribution of main maximum and submaximal intensities and the generation of missing levels
multi-beam interference factor
Determine the positions of main maximum, dark pattern and sub-maximum
Grating spectrum and grating resolving power
A grating is a spectrometer
The spectral lines arranged by the grating according to the wavelength are called the grating spectrum.
According to the order of wavelength from short to long, spread from the center to both ends
Grating resolving power refers to the ability to distinguish two spectral lines with similar wavelengths on the grating spectrum.
defined as
Therefore, the grating resolving power is related to the total number of grating slits and the order to separate two adjacent spectral lines.
X-ray lattice diffraction
X-ray
The X-rays scattered by the crystal hit the receiving screen behind, resulting in spots
Diffraction theory explanation of Laue spots Bragg formula
The atoms (ions) in the crystal form a regular lattice structure
A cross section of a crystal is called a crystal face
Parallel crystal faces form face clusters
Interference of wavelets emitted from each grid point in the same crystal plane
d1 is the distance between two atoms (ions)
Therefore, the same crystal plane satisfies the zero-order constructive interference of wavelets, which occurs in the reflection direction of the crystal as a reflecting surface.
Interference of wavelets emitted from lattice points on different crystal faces of the same crystal face cluster
Bragg formula
For crystal face clusters with different orientations and lattice constants, as long as the grazing angle satisfies the Bragg formula, Laue spots are observed.
X-ray crystal powder diffraction experiment
Concentric rings of light and dark
Polarization state of light Obtaining polarized light
Electric field intensity vector is also called light vector
Electromagnetic waves are transverse waves, and the vibration direction of the light vector is perpendicular to the direction of light propagation.
The different vibration states of the light vector are called the polarization states of light
polarization state of light
Natural light
Emitted by ordinary light sources, with randomness and independence
The light vibrations of the wave train are symmetrically distributed in a plane perpendicular to the direction of propagation
Linearly polarized light (plane polarized light)
After natural light is reflected, refracted, and absorbed by certain substances, it may become light whose light vector only vibrates in a certain direction.
The light vector and the propagation direction of light constitute a vibration surface
partially polarized light
Between plane polarized light and natural light
Light vectors exist in all directions, but in different directions, in a plane perpendicular to the direction of light propagation
Elliptically polarized light and circularly polarized light
The light vector rotates at a certain angular velocity in a plane perpendicular to the direction of propagation. Category depends on light vector endpoint trajectory
Looking directly towards the direction of the light, clockwise is a right-hand rotation, and counterclockwise is a left-hand rotation.
Polarizers and Analyzers
Polarizer
The process of obtaining plane polarized light from natural light is called polarization
Crystals that selectively absorb light vectors in a certain direction are called dichroic crystals
The polarizer only allows light vibration in a specific direction to pass through, which is called the light direction (or polarization direction).
When a polarizing plate is used to produce plane polarized light, it is called a polarizer
Analyzer
The polarizing plate used to check the polarization state of light is called an analyzer
Marius' law
If the incident light is partially polarized, there will be no extinction phenomenon when the analyzer is rotated.
Degree of polarization
Plane polarized light has a degree of polarization of 1
Natural light, circularly polarized light with a polarization degree of 0
Partially polarized light, elliptically polarized light between 0 and 1
Changes in the polarization state of light caused by reflection and refraction
Fresnel formula
Brewster's angle (Brewster's law)
Using a stack of glass sheets can increase the intensity of reflected light and the degree of polarization of refracted light