Lecture 6: Light and Electromagnetic Radiation (EMR)

Don't Panic

Sections

Introduction

We can see light (in the sense of visible light), of course---in fact, it is all we do see.

But we don't directly perceive light in either of the two categories in which its nature is understood in modern physics: i.e.,

as a wave.
as a particle which we call a PHOTON.

So, of course, light takes some explanation.

The term light can be used for either visible light or electromagnetic radiation (EMR). The latter it the general class into which visible light falls.

EMR is a traveling, self-propagating electromagnetic field that is independent of source or sink---we'll go into this further below.

It can also be described as a traveling form of electromagnetic energy.

Thus, it can be made from or converted into any other kind of energy via the electromagnetic or some other force???.

The dual nature of the EMR (wave and particle) is a result of our human descriptive limitations, not of nature. EMR is really one thing.

The Importance of Electromagnetic Radiation

EMR is important because it is the means that nature has to send information and energy over large distances.

EMR brings us energy from the Sun to heat the Earth and power the whole biosphere.

EMR carries information from distant stars and galaxies and from the Big Bang.

We can see across thousands of megaparsecs, and so learn about the universe.

Something like infinity and eternity from our small platform.

Maybe there is still a larger universe that we can't see, but it is amazing that we see as much as we do.

The Ultimate Physical Speed

Einstein's theory of SPECIAL RELATIVITY is a valid theory of motion and electromagnetism within certain limitations we will not go into here---but those limitations are dealt with by Einstein's GENERAL RELATIVITY (GR) (which is essentially a theory of gravity) and quantum mechanics---but completely adequately to date---and we won't go into those theories here.

Question:

SPECIAL RELATIVITY

the highest possible physical speed.
equal to the speed of SOUND in air.

Answer 1 is right.

It is the highest possible physical speed and it is inertial-frame invariant: all inertial-frame observers measure the same vacuum speed for light.

Question: At firework displays, the sight and sound of an explosion are:

simultaneous.
in order sight then sound.
in order sound then sight.

Answer 2 is right. Light is faster than sound.

You-all should remember those endless 4th of July firework displays---John Philip Sousa, etc.

It seems as if you are watching a film with the picture and sound not synchronized properly.

The VACUUM SPEED OF LIGHT is the ultimate physical speed. It is much faster than the speed of sound: sound speed in air at sea level at 20 degrees C is about 343 m/s.

The speed of light.

We emphasize that the VACUUM SPEED OF LIGHT is the ultimate physical speed.

By this we mean that no physical information or effect can propagate faster than this.

Purely geometrical speeds can be as fast as you can imagine.

For example, if you take the Earth to be at rest, then distant astronomical bodies must circle the Earth at enormous speeds every day.

If the vacuum speed of light is inertial-frame invariant, observers in any relative motion must measure the same vacuum speed for a light beam.

But this conflicts with our ordinary sense of RELATIVITY.

The speed of sound for instance depends on your speed relative to the sound medium. In fact, you can move at the speed of sound in air in a jet and watch a SOUND WAVE at rest.

Watching a WATER WAVE at rest is even easier.

RELATIVITY PARADOX

SPECIAL RELATIVITY

We never notice lengths, masses, and time doing this in everyday life, because it only becomes noticeable at speeds approaching the VACUUM SPEED OF LIGHT, except for very sensitive measurements.

But those measurements have been done. Special relativity is valid within its range of applicability so far as we know.

The subject of special relativity is taken up in more detail in IAWL Lecture 25: Black Holes.

Electric and Magnetic Fields

What is EMR made of?

Coupled electric and magnetic fields which is why we call EMR EMR. They must be coupled to self-propagate: they perpetually give rise to each other.

Electric and magnetic fields are, respectively, the causes of the electric and magnetic forces.

Gravity can be described by a field too which is the cause of the gravitational force.

In mathematics, FIELDS are quantities that are defined at every point in space or at least some region of space.

Electric, magnetic, and gravity fields are physical realizations of MATHEMATCIAL FIELDS.

They are in fact vector fields: at every point in space they have a magnitude and a direction.

One can think of little arrows attached to every point in space.

ELECTRIC CHARGE gives rise to both fields: static charge causes electric fields and moving charge causes magnetic fields.

And the fields in turn give rise to electric and magnetic forces on other charge.

The fields are usually represented by field lines which schematically trace out the fields: at every point along a field line one has field vectors tangent to the line and pointing in the line direction.

A cartoon of electric and magnetic fields.

Stationary charges feel the electric force.

Only moving charges feel the electric and magnetic force.

This is a fundamental reason why electric and magnetic fields can be regarded as two aspects of the same thing: the electromagnetic field.

For example, electric generators and electric motors use them both.

Then there are those things you stick on your fridge.

At the microscopic level, electric fields in atoms and molecules and between them give materials their structure: e.g., they hold us together.

Electromagnetic Radiation: Creation and Destruction

How do you create EMR?

If you accelerate a charge or make it undergo a TRANSITION in an atom or molecule or solid, the charge will emit EMR.

[We'll discuss TRANSITIONS later in

IAWL Lecture 7: Spectra

TRANSITION

For example, an alternating current in a conductor will generate radio EMR.

This emission process is just a BASIC PROCESS of nature.

The reverse process happens too: EMR can be absorbed by charges causing the charges to accelerate or make transitions in an atom or molecule or solid.

EMR is a traveling electromagnetic field in the sense that it is independent of source and sink.

EMR can self-propagate across this room, from the Sun to the Earth, and across the observable universe.

But if an electromagnetic field can propagate across the universe and travel long after it's source is destroyed and long before its sink is created, then one has to conclude that electromagnetic fields are as real as anything is real.]

A cartoon of the propagation of EMR.

Electromagnetic Radiation Wavelength and Frequency

Like all wave phenomena, EMR can be characterized by wavelength or frequency.

They convey the same information (at least for vacuum), but in two different forms.

EMR wavelength and frequency.

Just to reiterate:


    If N waves pass a point in N periods, the frequency
    of the waves is

              N            1
       f =  ______    = _______  which is the reciprocal of the period.
                           
              NP           P

Of course, you must use the right units in calculating frequency.

Although, one often quotes visible light in nanometers and microns, I usually convert to meters in order to calculate frequency since I remember the speed of light in meters per second.

    Example

    wavelength = 400 nm = 400 x 10**(-9) m

    frequency = c/wavelength = 3 x 10**8 /( 4 x 10**(-7) )

              = 7.5 x 10**14 Hz .

Heinrich Hertz (1857--1894)

It is little known, but true, that Hertz also invented talk radio and country and western stations. Not all ideas are good ideas.]

Electromagnetic Radiation Wave Nature Manifested

Energy propagation in a wave process exhibits DIFFRACTION. This process is very loosely describable as the bending of waves around obstacles or spreading out from apertures (i.e., openings of any kind).

With water waves we can literally see DIFFRACTION of waves.

Now we don't see SOUND WAVES: we merely hear them.

But one aspect of their wave nature is evident---sound bends around obstactles and spreads out from apertures (e.g., doors and windows).

DIFFRACTION is one of the main wave nature effects of EMR.

Question:

spreads out to illuminate the whole room equally.
is just beam that causes a bright square on the floor.

Answer 2 is right.

Well you can often see the beam because dust particles reflect light to you, but light not headed toward your eyes is not seen.

A laser pointer demonstrates this: you see the reflection of laser light from where the beam hits, but not the beam itself.

In the old days, I'd have a student who was a smoker breathe smoke into the laser light beam to demonstrate the reflection by smoke particles---but we can't do that any more.

The upshot of the question is that visible light doesn't diffract noticeably to the eye under most circumstances.

$light_005_diffraction.png$ Diffraction and visible light.

Now AM radio has wavelengths of order 300 meters (HRW-802), and so has no problem diffracting around large obstacles. Of course, AM radio also can pass through a fair about of stuff like walls.

But for visible light DIFFRACTION is not readily noticeable, and so we don't readily notice light as wave phenomenon.

In fact we can usually just treat visible light as coming in beams.

But many useful optical effects and devices depend on DIFFRACTION. For example, DIFFRACTION in from a diffraction grating is used to cause DISPERSION (see below).

The Electromagnetic Spectrum

There is no theoretical limit on EMR wavelength above zero.

Thus, the wavelength can extend form next to nothing to next door to infinity.

Similarly with frequency---but, of course, zero wavelength corresponds to infinite frequency and infinite wavelength to zero frequency.

There are no boundaries or gaps in EMR in the wavelength dimension: there are a CONTINUUM of wavelengths as far as we can tell.

CONTINUUM

This CONTINUUM of EMR is called the ELECTROMAGNETIC SPECTRUM.

We divide the ELECTROMAGNETIC SPECTRUM into specific BANDS (i.e., wavelength ranges) for convenience in analysis and because these bands typically have some difference in emission and absorption processes.

The sharp boundaries sometimes given to BANDS are usually artificial and just for our convenience---there are some natural boundaries for some special cases.

The electromagnetic spectrum and visible light.

Our eyes are sensitive to EMR wavelength with in the visible band.

Of course, the eyes somehow interpret wavelength as color.

__________________________________________________________________________

Table of Visible Colors
__________________________________________________________________________

Color             Conventional Wavelength Range (microns)
__________________________________________________________________________

violet            0.390--0.450
blue              0.455--0.492
green             0.492--0.577
yellow            0.577--0.597
orange            0.597--0.622
red               0.622--0.780

__________________________________________________________________________

HZ-56

Note: There are no distinct boundaries between colors. The eye looking at white light spectrum just sees them gradually change. The boundaries given are conventional and approximate what people would ordinarily judge to be the transition points.

__________________________________________________________________________

The psycho-physical sensitivity of the average human eye.

Often we just see light of mixed wavelength (i.e., polychromatic light) and then we have a human sensitivity-weighted average response.

For example, the mixtures of colors in solar light filtered through the atmosphere gives what we call WHITE LIGHT because it looks white or white-yellow.

EMR from the UV and shortward in wavelength is dangerous to life.

It can break up (often indirectly by creating fast electrons????) organic molecules such as DNA.

We'll discuss why this is so below.

Question:

has long enough wavelengths so that they don't damage organic molecules too much.
is abundant since the Sun radiates most strongly in this band.
is abundant since the Earth's atmosphere is very transparent in this band.
has short enough wavelengths so that there isn't much diffraction in light passing through the eye openings. Diffraction would lead to inherent blurriness.
All of the above.

Birds see a bit into the UV, I believe, but I can't seem to locate in clear information???.

Some snakes (rattlesnakes and other pit vipers and boa constrictors and pythons) have loreal pits on the sides of their heads in addition to eyes.

These loreal pits are sensitive to infrared light out to perhaps 8--12 microns. This allows these snakes to see the light emitted from hot bodies and thus they can see in the dark. See the Eye Design Book.

Actually, humans can see a bit into the infrared to 0.9 microns if the source is sufficiently intense (PP-19).

There is no revelation though: it just looks deep red. It is probably not safe to look at such intense IR light.

The Dispersion of Electromagnetic Radiation

Now almost any natural or artificial source of EMR gives EMR with a mixture of wavelengths: polychromatic EMR as opposed to monochromatic EMR.

We'd often like to analyze polychromatic EMR and see what the intensity or flux of the EMR is per wavelength.

In order to analyze polychromatic EMR, we need to break it up into its constituents.

The ``breaking up'' process is called DISPERSION.

A simple disperser is a prism. Wavelength varying refraction disperses the light up.

Dispersion of light by a prism, but note the plate-glass diagram should have oblique rays for refraction.

A much less simple example of a disperser is that artifact of late 20th century life, the old compact disk (CD).

Here dispersion is caused by reflection of many finely spaced grooves and DIFFRACTION of the reflected beams: the DIFFRACTION is big because the groove spacing are comparable to the wavelength of visible light.

Question:

DISPERSION

The grooves are little prisms.
Diffraction is wavelength-dependent.
It is just so: CD behavior is a fundamental fact of nature and cannot be reduced to more elementary principles.

Answer 2 is right.

Intentional diffraction gratings are widely used.

A much older disperser of light is a cloud of water drops opposite the Sun. This gives us the rainbow.

Rainbows.

Credit: National Oceanic and Atmospheric Administration/Department of Commerce: Image ID: corp2028, NOAA Corps Collection; Photo Date: September 1992; Photographer: Commander John Bortniak, NOAA Corps.

Credit: National Oceanic and Atmospheric Administration/Department of Commerce: Image ID: line2112, America's Coastlines Collection; Photographer: Mr. David Sinson, NOAA, Office of Coast Survey

The rainbow is, of course, the spectrum of the Sun. But the water drops don't spread out (i.e., disperse) the wavelengths very much and give a rather imperfect spectrum.

Astronomers can do better.

The spectrum is spread out on a wrap-around line.

The spectrum is basically a Planck spectrum of temperature 5800 K (Se-147) with absorption lines from the Sun and Earth's atmosphere superimposed.

Credit: N.A.Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF.

IAWL Lecture 7: Spectra

The analysis of dispersed EMR is called spectroscopy.

Spectroscopy is the most useful and important of all chemical analysis tools. In IAWL Lecture 7: Spectra we'll go into spectra and spectroscopy more deeply.

Photons

Photon is the name that is given to the EMR particle.

Now when does EMR act as a particle and when does it act as a wave?

For short wavelength EMR, one can usually treat, EMR as a beam of energy without worrying about wave or particle.

At deeper level (which we won't go to), it is often a useful rule of thumb is to say that EMR acts as a wave in propagation and as a particle in emission and absorption.

[Note this rule is not strictly true. But it is a useful way of thinking about EMR behavior.]

It certainly is true that EMR is emitted and absorbed in photons: distinct packets of EMR energy.

The energy of an individual photon is


E = 1.99*10**(-25) J-m / (wavelength of photon)  ,

    where wavelength is measured in meters

    and the joule (symbol J) is the MKS unit of energy.

        (Note  1 Watt-second = 1 J and  1 KW-hour = 3,600,000 J.)

    The smaller the wavelength, the bigger the photon energy.

    The higher the frequency, the bigger the photon energy.

Even for gamma-rays with wavelengths less than 10**(-11) m (HRW-802), the energy of a single photon is miniscule: i.e., of order and greater than 10**(-14) J.

Now I know what you are thinking.

How big is a photon? Well a photon doesn't really have a fixed size.

It has probability of being found over some region of space. And when it is found it is absorbed or otherwise modified at that point.

But before then it exists nowhere in particular---such is the quantum mechanical theory.

Why we don't notice the particulate nature of EMR?

Any macroscopic amount of EMR contains so many photons that the particulate nature is washed out.

Similarly one doesn't notice that water is made of molecules of H_2O.

The intensity of light (energy per unit time per unit area) depends both on the rate of photons and on their individual energies.

But that doesn't mean that NUMBER OF and ENERGY OF photons are exactly compensatory quantities: they are for just amount of energy, of course.

Many reactions with matter are sensitive to the energy of the individual photons.

For example, chemical bonds and electron-atom bonds can be broken by EMR. But only a single photon breaks such bonds (except in rare cases).

Bonds require a minimum energy before they will break. Thus to break a certain bond, you must have a photon of sufficient energy.

No matter how many photons you bombard the matter with, the bond will not break if none of them individually have enough energy.

Photons from the UV and shorter can break organic chemical bonds (including DNA bonds), and so are destructive of organic material.

Often this breaking up is indirect by means of fast electrons created by the high energy photons which eject the electrons from atoms????. Slow electrons are not dangerous: there everywhere; an ordinary constituent of ordinary matter.

Lower energy photons can, of course, be absorbed as heat energy and if biological entities get too hot that is dangerous too. But individually lower energy photons are usually not dangerous.

Photon Propagation

Photons are useful for thinking about how EMR propagates through a gas of atoms.

An example important for our course, is for thinking about how EMR propagates through the Sun and stars.

[Note my rule about wave and particle behavior given above was not strict and this is one of those places where one uses a different rule.]

One can think of the photon as a particle scattering off the atoms and/or electrons and executing RANDOM WALK.

In a RANDOM WALK photons do NOT NOT move: they wander away from their place of origin slowly and in particular wander preferentially into lower density regions because they take longer steps in those directions.

Star density falls outward from the center, and so this biases a RANDOM WALK direction toward the surface of a star.

A photon executing a random walk.

It takes a long time for an imagined photon to go from the center to the surface of the Sun by this process.

A rough estimate is of order 10,000 years (Shu-90).

But one really can't think of a single photon doing this. Photons are created and destroyed as energy is propagates outward.

Nevertheless, the 10,000 years estimate shows it takes a long time for certain kinds of changes in the Sun's center to effect the surface.

The direct flight time for a photon from the Sun's center to surface can be easily calculated:


      t = R_Sun/c = 6.96*10**8 m / ( 3*10**8 m/s )
       
        = approximately 2 seconds  .

random walk