Refraction, Dispersion and Resonance

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Formal Metadata

Title
Refraction, Dispersion and Resonance
Author
Leitner, Alfred
License
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
DOI
Publisher
Rensselaer Polytechnic Institute
Release Date
1975
Language
English
Producer
Rensselaer Polytechnic Institute, Office of Instructional Media
Production Year
1973

Content Metadata

Subject Area
Abstract
Animation and scientific instruments are used to demonstrate the principles of refraction, dispersion and resonance.
Keywords
refraction
dispersion
resonance
Computer animation Arc lamp Order and disorder (physics) Single (music) Optics Hitzeschild Source (album) Resonance (chemistry) Light
Speckle imaging Black hole Band gap Wavelength Colorfulness Sensor Camera lens Narrow gauge railway Screen printing Light
Glass Angle of attack Screen printing
Gaussian beam Speed of light Transmission line Year Electromagnetic radiation Relative articulation Light Glass Metre Fahrgeschwindigkeit Audio frequency Turning Volumetric flow rate Gas turbine Material
Proof test Effects unit Dielectric Day Force Magnetspule Display device Force Negativer Widerstand Dipole Light Concentrator Glass Phase (matter) Computer animation Atomism Halbwellendipol Spare part Electric charge Material
Typesetting Bestrahlungsstärke Blow torch Gruppensteuerung Composite material Negativer Widerstand Light Group delay and phase delay Glass Phase (matter) Kleinsignalverhalten Compound engine Turning Direct current Signal (electrical engineering) Cartridge (firearms) Alcohol proof Halbwellendipol Orbital period Microwave
DVD player Pager Light
Effects unit Particle displacement Scattering Force Electromagnetic radiation Backscatter Thermodynamic equilibrium Light Particle Halbwellendipol Spring (device) Radiation Electrical conductor Spaceport Electric charge Material Microwave
Spare part Radiation Steering wheel Experiment indoor Linkage (mechanical) Force Negativer Widerstand Fundamental frequency
Bird vocalization Phase (matter) Audio frequency Device driver Frequenzumrichter Steering wheel Friction Fahrzeugachse Force Negativer Widerstand Barque Fundamental frequency
Audio frequency Device driver Steering wheel Pager Fundamental frequency
Alternator Device driver Amplitude Force Negativer Widerstand Heat Resonance (chemistry) Amplitude
Audio frequency Alcohol proof Device driver Steering wheel Negativer Widerstand
Analog signal Transmission line Schubvektorsteuerung Amplitude Elektrisches Dipolmoment Negativer Widerstand Cosmic distance ladder Telescopic sight Light Dipole Phase (matter) Bird vocalization Microwave Alcohol proof Barrel Radiation Material Electromagnetic spectrum Electromagnetic radiation FACTS (newspaper) Resonance Finger protocol Audio frequency Autumn Signal (electrical engineering) Fahrgeschwindigkeit Halbwellendipol Radiation Resonance (chemistry) Microwave
Analog signal Hot working DVD player Electronic component Amplitude Audio frequency Dipole Phase (matter) Turning Computer animation Alcohol proof Signal (electrical engineering) Halbwellendipol Radiation Radiation Resonance (chemistry)
Speed of light Ballpoint pen Gruppensteuerung Vakuumphysik Light Ultraviolett B Glass Fahrgeschwindigkeit Phase (matter) Audio frequency Turning Phase (matter) Computer animation Fahrgeschwindigkeit Ship class Signal (electrical engineering) Optics Noise figure Material
Phase (matter) Audio frequency Turning Phase (matter) Vakuumphysik
Fahrgeschwindigkeit Turning Phase (matter) Absorption (electromagnetic radiation) Material Light
Audio frequency Alcohol proof Halbwellendipol Force Negativer Widerstand Microwave
Fahrgeschwindigkeit Phase (matter) Audio frequency Phase (matter) Signal (electrical engineering) Halbwellendipol Low-pressure area Amplitude Negativer Widerstand Absorption (electromagnetic radiation) Material Microwave
Interstellar medium Light Fahrgeschwindigkeit Phase (matter) Audio frequency Turning Wavelength Phase (matter) Atomism Fahrgeschwindigkeit Signal (electrical engineering) Halbwellendipol Absorption (electromagnetic radiation) Material Resonance (chemistry) Microwave
Yellow Visible spectrum Gruppensteuerung Light FACTS (newspaper) Metal Audio frequency Carburetor Wavelength Computer animation Fahrgeschwindigkeit Material Fundamental frequency
Automobile platform
Glass Carburetor Radiation Visible spectrum Arc lamp Light
Direct current Series and parallel circuits Bahnelement Ground station Automobile platform Light
Spectral line Speckle imaging Band gap Wavelength Colorfulness Narrow gauge railway Visible spectrum Orbital period Light
Visible spectrum White Light Electric arc Black hole Carburetor Audio frequency Shadow Computer animation Perturbation theory Atomism Spare part Plane (tool) Hitzeschild Fundamental frequency
Effects unit Piping Transmission line Vacuum tube Gruppensteuerung Bending (metalworking) Access network Light Cogeneration Bird vocalization Carburetor Density Lecture/Conference Steel Water vapor
Schlicker Lecture/Conference Experiment indoor Telescopic sight Light
Schlicker Spare part Plane (tool) Arc lamp
Basis (linear algebra) Carburetor Speed of light Visible spectrum Spare part Remotely operated underwater vehicle Model building Absorption (electromagnetic radiation)
Spectral line Carburetor Audio frequency Yellow Wavelength Fahrgeschwindigkeit Remotely operated underwater vehicle Light
we're putting together a single optical system in order to produce a parallel beam of light there is a certain that during this like shield the prompted Georgia's placing a carbon arc behind it the art approximating a point source of light ssh in all
resolution in this blast and shows divergent been but as I told you we want a parallel George is introducing a color making them a 2nd
lens focuses the light on the little screen it's the image
of the brightly lit circular holes In the light to you have
between here and here is still parallel this is a red filter it passes only a narrow band of red wavelengths the red image
on the screen is of course far less intense between
these 2 points for these monochromatic unwitting
glass prism into the being read by his peers because it had been retracted by the president it is that the way
through quite a large angle they we are now looking
at a price of the being from above the light beam is refracted as a dentist glass it is bent toward the line which is normal to the
glasses we hope that you have heard before snails law which governs this phenomenon and how this war can be derived from 2 important assumption these are the 1st that like the wave motion and 2nd that it be used less inside the glass men outside In this film we're not concerned with the simple derivation of the lot retraction rather we asked the question Why is the speed of light less in glass than outside In light of the glass prisms flow red red-light down the current added there will continue to assume that like the way to the precise and electromagnetic waves so I want you to think of a single monochromatic light beams I finally found a way of giving Craig by the I mean the speed with which it has advances that is the so-called the philosophy In previous it had a value of 3 times that of the year meters per 2nd and it usually denoted by the letters asking the speed of light increase face is that thing called President it true you know when light passes through matter the velocity of light emitted material can be different for different frequencies and what's more it can even be larger than the for some something all is
possible because of the way the atoms and molecules of the material reacted the light at the pact is over show To begin our classical theory of refraction let us think 1st of empty space then over light waves coming at us through the end of day will be we plan to fill the outline part of space with a material such as glass or another dielectric we should think of it in successive molecular layers and have indicated the 1st later let's concentrate on display the incident electromagnetic field off today as the light wave passes over the later the vertical oscillating is the electric field it causes the electric charges in the molecules to oscillate up and down the positive charges 1 way the negative charges competently but 2 kind of charge are separated the electric field creates alternating molecular dipole moment no the magnetic field which oscillates horizontally here also exert a force on the moving charges in the molecules but this force is small because the speed the of the moving charges is very small compared to we can neglect its effect in our discussion notice that we chose to let the molecular dipole oscillate in pace with the incident with we don't really know why they should be in at this point
let's just assume that the molecular oscillators responding fate will prove to to you that this leads to a slowing down of the light which will explain the bending of red light toward the normal as it enters glass what is important to
us now is to realize that the arsenic and IPOs will radiate each will send out its own little electromagnetic dipole which will spread from it in all directions we want to know the effective at forward .period any .period such as the 1 marked P. will receive a small signals from each of these type of In addition of course the incident wave will get through for instance considered away from the dipole atop right a signal logo from a torch .period also in the sea but this dipole isn't outlined IPO it is further from the than the dipole on the axis he indicated here the signal takes longer to reach people on the outlying IPOs than from those near the exit so the signal arriving at the from on outlined dipole at any given instant Will lagging phase behind the signal reaching peace from the died along the axis at the same instant it will also like the phase of the incident wave reaching 1 can calculate the resultant face today in the composite waved from all the polls perhaps surprisingly this phase delay turns out to be exactly 90 degrees the composite dipole wave reaches .period P 90 degrees behind in favor compared to the incident wave this happens to be true for any forward .period not just the 1 we originally trouble the phase that will be 90 degrees even if lies in the next layer so the 2 signals go on to the next layer the incident 1 undulating paid and the compound 1 from all these guys which like the the 1st by by 90 degrees clearly the superposition of these 2 signals will have a face delays no less than 90 degrees so the total signal is delayed compared to what would be the case if there were no molecules that the
result will likely be delayed by the 1st player In return the next layer will delay the light waves and so on it states proceed more slowly than cool that the speed of the page is less than eh and like beans which are obliquely incident on the dielectric I've been
taught the normal as we saw before the explanation we
have given is oversimplified it is based on the forward radiation of a single layer actually each dipole they also radiates backward the backscatter dipole waves from the interior layers such as this 1 a static forward again and so on an exact theory must take such multiple scattering into account it turned out however that our simplified explanation reaches the same qualitative conclusions as does the exact theory To summarize we've been treating the incident light as an electromagnetic waves its effect on the molecules of the optically transmitting materials used to convert them into oscillating died polls I think these materials are not conductors the alternating electric charges in their molecules will remain bound to each other when you stretched bounds charged particles away from their equilibrium position they will experience a restoring force pulling them back together Port equilibrium that has made another bold assumption namely that the restoring force is which means it is proportional to the amount of displacement as for example In a man connected to a spring this
system In oscillate on its own with the natural frequency it is weakly damped mostly by the wheel bearings similarly the oscillating polls experience standing but here are a good part of the energy they use will go office radiation an eccentric
linkage creates an oscillating force it
drives the other end of the Coral Springs the other end is attached to the wheels axles keep your
eye on the 2 pointers 1 is attached to the driving bark and the other to the wheel they allow us to compare the response of the wheel the driving force the frequency is small and lies far below the natural frequency of this I notice that the we'll follow at the same frequency and if it weren't for static friction temporarily freezing the bearing Of the wheel at the attitude position the wheel would follow the driver exactly in Spain as well similarly our molecular oscillating died calls will follow exactly in phase if are driven by incidents like whose frequency lies sufficiently below their natural frequency static friction does not occur inside individual molecules Georgia's
rating the driver frequently for the natural frequency but it is still below the wheel again
follows this new and larger free to move things had to changed the attitude has grown and the wheel lagged behind the pace of the driver you can keep this page leg increases as the driver approaches natural thing the driver frequencies now
that the natural responding
to the growing quite Norwich we call this
condition resonant notice that the alternator is that extreme heat amplitude position just starting back at the same time that the driver passes the
alternator lagged the driving force by one-quarter oscillation at present the laggards 90 and the amplitude has maximum value the
base continues to increase as the driving frequencies range Beyond resident reaches 180 degrees as limiting that
noted that the oscillators and down again and that he like the driver by half oscillation for example the driver is at the extreme right when the wheel that extreme left the thing that is 180
what keeping Mindy properties of harmonic oscillators regarding amplitude respondents indicated that they apply to the electric dipole oscillators written by an electromagnetic wave of course but I polls resonant frequency is much higher than for our mechanical analog it might like anywhere in the electromagnetic spectrum as a matter of fact there may be many different residences for anyone material we
returned to the molecular layer driven by an incident like remember that we chose the dipole response to being faced with the oscillations of the incident you we now understand the significance of this choice but dipole oscillators have their own resonant frequency but the frequency of the incident light is far below his resonant even so the later delays the resultant signal as I explained earlier because the radiation from the various titles of the layer I have to cover large distances to reach a forward .period such a at frequencies below that IPOs residents that face velocity of likened the material is smaller than seen consider the oscillating electric field in a wave arriving peace this matter can be defined as the projection of a uniformly rotating vector a fixed length called obtained or it goes around 1 for each fall oscillation of the field vector its length in both the field amplitude To make our construction simpler we've made out the oscillating field vector we just agreed that the projection of this upon a vertical line from the is the electric field arriving at let's suppose that this beta corresponds to the incident field which has gotten through the molecular layer no In addition the dipole in the layer radiate forward and as we told you earlier accounts way from all the dipole lags behind the incident wave by exactly 90 degrees the scope of edition of the 2 waves is the projection on the red vertical lines Of the relocating the results I notice that the resultant lags behind the incident when now that we know that these phases are supposed to be rotating vectors we can stop them and let this barrel remind us so here we have our schematic representation of conditions at a point Beyond that call later then I can be brief a delay in the radiation from the dipole their causes the resultant signal to have this phase that relative to the incident radiation reaching the point let me again remind you that this condition occurs when the IPOs in the layer respond in phase for the incident wave as it passes over the later this happens men the frequency of the incident radiation lie sufficiently far below that I IPOs residents next let us figure out what should happen if we raise this frequency toward resonance
by our mechanical analogy we know that as we do this the dipole response becomes stronger and it's phase begins for that at present the light reaches 90 degrees and the response amplitude is maximum so the dipole
radiation from the lady work forward .period such as will acquire additional face today and the phase or representing it will .period downward in this picture at resonance it will .period vertically down let's look at this again as a resident approached the amplitude of the dipole where grows toward a maximum we shall repeat this motion of her time that you look at it and concentrate on the results the players lack of the resultant signal 1st increases reaches the maximum and then decreases at present the resultant is in phase with the incident component at the same time the resultant becomes shorter and shorter by
the way we can now begin to draw qualitative graph of the face velocity of light in optical materials as a function of frequency In vacuo it has the same value frequency recorded CDs but in an optical material and I polls resonate some frequency at euro if the light incident on it as a frequency quite a bit below a 0 the resultant signal which is represented by the white phase or lags only a bit behind face compared to see the face velocity is reduced only a small amount by the material but when we use like a higher frequency the figures lag its 1st increases the speed of light in the material falls further sea when the material is class this is the frequency range from visible light glass refracts the light more than red light it has a residence in the near ultraviolet if a beam of
light light balls obliquely on a glass surface is
spent more than red as we
increased frequency further toward the residents value at 0 the baby lay reaches a maximum and then it decreases correspondingly the face be goes through a minimal finally at residents the phase lag in the total disturbance is 0 the speed rises again reaching at resonance as if we had a vacuum notice also how
small the white face there is at present very little light gets through In other words near 0 the material absorbs the light it
is opaque there or nearly so if some of these conclusions are a surprise to you when we are in for what surprises when we consider the conditions for a life of even higher frequencies as
you remember an oscillator will lag even more behind the driving force above residence sure for the higher
frequencies the dipole Callaway we lag behind even more then at 0 From residents on upward the dipole waves phase delay increases from 180 to 270 degrees above residents
the dipole oscillators respond with lower amplitude again so the phase representing the dipole wave would charter as we think of larger and larger frequencies the resultant
signal growth in amplitude the material is again transparent but even more importantly notice that the resultant wave signal which at the Redmond at Xerox was in favor the incident signal now leads it
what were the pays lagged below 0 now is the place to be about the phase of light moves faster than see through the medium they velocity can exceed the speed of light increased space keep in mind that only the resultant waves phase moves faster than C the individual dipole waves the incident where all these waves move from Adam to atoms through the intervening space at the scene no signal actually moves faster than the Our Kirby's called dispersion :colon it tells the story about what happens to live in the neighborhood of the frequency where it's medium as a resonant response below resonance the face of light moves more slowly than in vacuo and of being obliquely incident on the material will be bent toward the normal new residents the material is opaque about resonance and obliquely incident being should be dead away from the normal yes that must be true because we just shot that above resonance the wave as a phase velocity which is larger than in that still
you might be skeptical so we'll check by experiment we need to think 1st of all we need a material was adamant on molecules have arisen in some range of wavelengths
secondly we have to make a Prizm out of this material now let's suppose the materials residents lies in the Yellow region of the visible spectrum the wavelengths of red lights are longer than yellow so the Red frequencies lie below the residents in the yellow Red Light will be refracted downward by the presence the frequencies of light on the blue side of yellow lie above the resonant green light will be refracted upward by a prison with material resonates in the yellow it's phase velocity is larger than C In the material so this is the fact we should look for I plan
to make our prism out the behind labor of sodium metal sodium vapor can be made to radiate strongly at a natural frequency in the yellow region of the spectrum that show you I'm cutting some
small pieces of sodium
let me put 1 on a little platform about this burner when sufficiently he
sodium vapor will blow
exactly the same radiation it produces in sodium lamps by an
electric discharge In our next experiment will take a look but the spectrum of the light and he did so you make the purpose I'm fed up a glass president benefits go over here Our sodium lamp is the light source and with the help other continental and in here it
illuminates a vertical slit
the light from this is aided by another and beyond that I have a little platform on which all amount this president
actually it's a series of 3 prisons together they form of good disburses element for visible light but the disbursed like this and generally forward which a single prison would not do a so-called direct view prison it's quite convenient I'll make a movie
of sodium spectrum with this camera the light from the narrow wavelength bands we see 2 images in different colors the brightest spectral lines is yellow
period Chiara spectacle began but this time the light source is the carbon market in all of the women
the spectrum the white light from the arc is continuous this
shield has holes in it could permit like to pass through inside it is the sodium burner we used before I'm
putting it in the path of the white light from the art it said it had at the time of his arrest our and the occasional figuring extending over the entire spectrum range it due to smoke from the plane curling a shadow on the streets as hot sodium that performs it absorbs light in in a narrow region of the yellow part of the spectrum we may think of sodium atoms in the vapor as oscillating died polls driven by white light that means light waves of different frequencies that sodium has a natural frequency in the yellow show there is a resident in the yellow and light is absorbed there In sodium vapor resident is very sharp and narrow
knowledge go onto the prism of sodium vapor will produce it in this device it's basically a steel too glass windows have been sealed to regions with Blanchard there already is some sort you mentally in the 2 this
access by which has a valve in a move to the area has been evacuated from the 2 at each side of copper pipe is bound around 2 and started doing a stray piece connects the corals along the top cold water is running through the copper pipes a gas burner will lead the bottom from a line of playing with the bottom half of the top and sides called sodium vapor will be most then near bottom center it will be in the stands along the top and each end because the vapor will condense on the call to action altogether this density variations will form what is in effect the vapor prison oriented this way it will retract red lights down and green light I put up a
simple spectra scope for this president Our light source is a common market right
from the Arctic is focused on a slip this
lady's horizontal because it must be parallel to the refracting surfaces of the prisons which are oriented in this way the
President it is only the 1st part of a double victory go the 2nd factions involved in the blasts direct you present mounted as before it is perceived the light rays from the carbon arc in a horizontal plane Red going there green and blue this way the 2nd slip this vertical it's
perpendicular to to the person that
let's check what the camera if I keep the sodium too cold and just turned the Argonne all the sodium produces no up-and-down dispersion because it is called the blast prison disburses horizontally rated less like green at right and I'm
not I
mean under which Estonian President Benjamin nightgown side and not on the green refraction is part of the normal on the red tide because on this side of the speed of light through the vapor is less than and refraction is away from the normal on the greenside because it is more than the notice the qualitative resemblance between the spectrum of the 2 crossed presence and the dispersion curves we derive on basis of our classical the reason why the spectrum does not reflect the curve continuously it is also clear from our model there's absorption at the residence In high
dispersion the Yellow Sorghum light is found to be a Dublin 2 spectral lines separated by 6 banks dreams as to wavelength so there are really 2 residents we need to dispersion curves next to each other Our experiment with the sodium vapor prison proved that above residents the light rays are bent away from the normal In other words the experiment proved that they velocity can indeed be larger than the at some frequencies To conclude with also like to tell you that the quantum-mechanical theory of dispersion leads to the same result in almost every detail as that the classical explanation we have presented in this field
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