Nature of Light
Light
Light is a small, but important part of the electromagnetic (EM)
spectrum. The EM spectrum ranges from cosmic gamma rays at short
wavelengths (3×10-15 m) to electromagnets at long
wavelengths (3×108 m), with light at the shorter
side (5×10-9 m) on a logarithmic scale.
The response of the human eye roughly matches that of the Sun viewed
from Earth. What we call light depends on the overall sensitivity
of the eye, ranging in wavelength from 380 nm to 760 nm.
What we identify as colour depends on the wavelength sensitivity
of different receptors in the eye and the way this information is
processed in the brain. For further discussion on colour, click here.
Light and all EM radiation are composed of small parcels called
photons. Photons are now thought to be carriers of EM force. They
are called parcels (or packets) rather than particles or waves because,
depending on their interactions with other matter, they have either
particle or wavelike behaviour. This duality in the nature of photons
is a key aspect of Quantum theory. For further discussion on the
nature of light (and photons), click here.
The speed of light (and other
EM radiation) in a vacuum, usually given the symbol c, is
3×108 m/s. This speed does not depend on the observer
(the observer's frame of reference); in this, light is different
from normal human experience where objects appear faster or slower
depending on our own speed. This special behaviour of light is the
basis for the Special Theory of Relativity.
Someone
once said, "Time is what prevents everything happening at once".
The finite, fixed speed of light in vacuum marks this Time.
The amount of energy E carried by a photon is given by E=hn
where h is Planck's constant and n (pronounced nu) is frequency. Frequency (the number of oscillations
per second) is speed divided by wavelength.
The speed of light is not constant in different materials. It is
always slower in a gas, liquid or solid than in a vacuum. Since
the photon's energy doesn't change, its frequency also cannot change,
and therefore its wavelength changes. The wavelength decreases as
the speed decreases.
The speed of light in air changes with the temperature and pressure
and humidity of the air, not enough perhaps for our eyes to detect,
but enough to upset sensitive optical instruments. If you want to
calculate wavelengths in air, click here.
For a discussion of
- shadows and reflections
- refraction in a pool
- mirages
- double images of sun and moon
- seeing underwater
- how a rainbow works
- why the sky is blue
- colours of sunrise and sunset
- twilight
- luminous plants, animals and stones
- and many other fascinating things about the light
we see
including some truly beautiful pictures, see Marcel
Minnaert, Light and Color in the Outdoors, Springer (1974).
For an entertaining history of light and the many
inventions that accompany it
- spectacles
- cameras
- electric lights
- television
see The Light Fantastic, Penguin (1981),
by the sadly missed Peter Mason.
First published on the web: 15 December 1999.
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Colour of Crystals
Many crystals are clear and many have brilliant colours. Many of
these crystals are insulators. To have colour they must absorb light,
i.e. they must have electronic or vibrational transitions with energies
equivalent to visible wavelengths, i.e. between 1.7 eV and
3.5 eV. Cadmium sulphide is yellow-orange because it has an
energy gap at 2.42 eV, corresponding to 512 nm so that
blue-green is absorbed.
Insulators generally do not have such transitions and so are clear,
i.e. light can travel through them because they do not absorb energy
in the visible region. Perfect diamonds are clear.
Colour in crystals is therefore often caused by impurities. Pure
alumina Al2O3 is clear, but with small amounts
of Cr3+ it becomes a dark red ruby, or with a
small amounts of Ti3+ a blue sapphire.
Glass can be coloured by including fine particles to cause scattering
of light at selected wavelengths, e.g. classic ruby glass is formed
by the fine precipitation of gold in the glass.
For more information, see: C Kittel, Introduction
to Solid State Physics, John Wiley & Sons, New York (1966),
pp 537-8.
Colour on the Computer Screen
Natural colour is formed by the selective absorption of sunlight,
i.e. an object appears blue because green and red are absorbed by
the object and only blue is reflected by the object to our eyes.
Such colour is called 'subtractive' colour.
Screen colour is formed by the mixing of pure colours: red, green
and blue (RGB), in varying amounts in tiny regions of the screen.
Such colour is called 'additive' colour. Natural colour and screen
colour are therefore produced in different ways. This difference
is important in understanding the difficulties of reproducing 'true'
colour on a computer screen.
It isn't simply a matter of placing coloured dots close
together, this can be done with paints as Georges Seurat and others
did so beautifully during 19th century. The colour of the dots is
formed differently, on the screen a red dot is formed by emitting
red, in paint a red dot is formed by absorbing blue and green.
For more information, see: M E Holzschlag,
"Chapter 5: Achieving High-End Color", in HTML Complete,
Sybex, San Francisco (1999), pp 191-219.
First published on the web: 15 December 1999.
Author: Richard Payling
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Rainbow
Rainbows are formed by light reflecting from rain drops.
Often we see only one rainbow, called the primary bow, but
sometimes we can see a second, outer rainbow, called the secondary
bow.
Primary Bow
When sunlight strikes a raindrop, some of the light
is refracted at the first surface, internally reflected from the back surface, and refracted again on exiting the rain drop.
For each colour there is a maximum angle of deviation of the light. So, in rain drops there is a minimum angle, for each
colour, between the incident and exit rays. For red, this is 42°
and for violet it is 40°. The nature of internal reflection is such
that many rays will emerge near this minimum angle.
Hence the sunlight will appear to be concentrated
over a small region of the sky in a narrow range of angles from
40° to 42° and separated into colours, from blue to red.
Secondary Bow
Some of the sunlight is also refracted at the first
surface, but is reflected twice internally from the back
surface, and refracted again on exiting the rain drop.
Again there is the same maximum angle of deviation for each colour, but now the double internal reflection leads to
a minimum angle between the incident and exit rays of 50.5° for
red and 54° for violet. The bow is at a higher angle, and
so will appear higher in the sky. And the colours are reversed,
going from red to blue.
The amount of rainbow you see depends on the angles between you, the sun, and the raindrops. As the sun rises, less
and less of the rainbow is visible. As you climb a mountain, you
see more and more of the rainbow.
Reference: M Fogiel (Ed.), The Optics Problem Solver®, Research and Education
Association, NJ (1990), pp 130-1.
First published on the web: 16 October 2000.
Author: Richard Payling
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Optical Transitions and light emission
If
we could solve Schrödinger's equation for all the electrons in an
atom, in its lowest energy state, we would have a detailed description
of the electron structure of the atom and its electron energy.
But
Schrödinger's equation tells us that other electron structures and
energies are possible for that atom. The atom may change to one
of these other configurations by the absorption or emission of an amount of energy equal to the difference in the energies of
the two configurations.
A
common mode for the change in atomic energy is the emission or absorption
of a photon (a parcel of electromagnetic radiation, such as light).
This process is called an 'optical transition'.
A photon is a disturbance of the electromagnetic field. The energy in a photon is
![[E=h.nu=hc/l]](images/Equations/eq_optica1.gif)
where h is Planck's constant, n is frequency, c is the speed of light in vacuum, and l is wavelength. A photon also has a momentum given by
![[p=h/l]](images/Equations/eq_optica4.gif)
Linewidth
When an atom absorbs a photon it is elevated to an excited state.
This excited state will generally last for a limited time, typically
10-8 s. The atom can de-excite by emitting a photon.
From Heisenberg's uncertainty principle, the finite lifetime Dt of the excited state means
there will be an uncertainty in the energy of the emitted
photon given by
![[delta E=h/2pi.delta t]](images/Equations/eq_optica9.gif)
Combining this with equation (1) above [don't forget to differentiate!]
gives a minimum width of
![[delta l=l2/2pi.c.delta t]](images/Equations/eq_optica8.gif)
So the finite lifetime of the excited state means that when we
measure the wavelength of the emitted photon it will have a spread
of wavelengths around the mean value l.
For a line at 450 nm and a lifetime of 10-8 s,
the minimum (or natural) linewidth is 0.01 pm.
Momentum
A spontaneous optical transition is a sudden and directional process.
It therefore involves the exchange of momentum between the atom
and the exciting photon. In absorption, the atom receives momentum
in the direction of the incoming photon. This is a fundamental aspect
of quantum mechanics, first derived by Einstein and quite different
from classical theories. The direction of emission is random, and
it is only in averaging a large number of such events that emission
appears to be non-directional with zero momentum as predicted
by classical theories.
First published on the web: 15 February 2000.
Author: Richard Payling
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Wave particle duality or is light a wave or a particle?
The apparent dual
nature of light is easily demonstrated:
Stand outside in the sun. The shadow your body makes in
sunlight suggests that light travels in straight lines from the
sun and is blocked by your body. In this, light behaves like a collection
of particles fired from the sun. Isaac Newton wrote his treatise
on Opticks: "Rays of light are very small bodies emitted from
shining substances"
Place two sheets of glass together with a little water
between them. With care, you will see fringes. These are formed by
the interference of waves. Christian Huygens (1629 - 1695) who was
a contemporary of Newton rather the wave model of light. His wavelet
construction principle has been used to explain reflection and refraction
In his work, James Clark Maxwell (1831-1879) established a clear
picture of light a form of electromagnetic energy. Following Maxwell's
equations the light can be seen as electromagnetic waves.
![[Newton's rings]](images/REFS072.jpg)
In 1925, our understanding of light seemed to have come to an impasse.
Particle theory could explain reflection and refraction, and recent
experiments in radiation (such as the radiation from hot bodies
and the Compton experiment with X-rays). And wave theory could explain
the interference and polarization of light which particle theory
could not. Thus simple and sophisticated experiments both indicated
that light could be a particle sometimes and a wave at others.
Albert Einstein (1924) expressed the dilemma:
-
There are therefore now two theories of light, both indispensable,
and - as one must admit today in spite of twenty years of tremendous
effort on the part of theoretical physicists - without any logical
connections.(1)
The dilemma prompted Neils Bohr (1928) to offer his 'complementarity
principle': that particle theory and wave theory were equally
valid. Scientists should simply chose whichever theory worked better
in solving their problem. While it got physics out of its immediate
hole, coming from someone as important in modern physics as Bohr,
it gained a dominance in physics teaching probably never intended.
Over the succeeding years, the currently accepted solution came
in the form of the 'quantised electromagnetic field theory', i.e.
'quantum electrodynamics' (QED). The theory merges particle
and wave properties into a unified whole. Despite this, the undergraduate
physics of light is still often taught as separate chapters on particles
and waves with little or no attempt to give an overall understanding
of how this can be so. The complementarity principle is still used
in books on optics to justify the use of wave theory to explain
interference, polarization, diffraction, etc. The student is then
left with the impression either that we do not really understand
the true nature of light or that physics is simply a collection
of tools for solving problems.
Dick's Editorial
Too often as undergraduates we learn about particles and waves
as separate concepts and never get to the next level where
these concepts are brought together.
This method of teaching is not exclusive to the teaching
of the physics of light. In many fields we learn simple methods
first only to abandon them later as we learn more sophisticated
methods. In some cases this may be necessary, but as an adult I
find this method of learning frustrating and ultimately
disappointing.
An obvious example is the Special Theory of Relativity.
Here, Einstein introduced the concept of non-Euclidian space-time
to explain the constant speed of light. In this, he showed Newton
was wrong. The familiar Newtonian mechanics we see in the world
around us, in the flights of birds, in falling rocks, and speeding
cars, is still a valid approximation when speeds are much lower
than the speed of light. When speeds are less than about 10 000 km/s
Newtonian mechanics generally works very well. We should therefore
learn mechanics by starting with Relativity. Starting with Newton
simply shows a fear and lack of understanding of Modern Physics.
In the same way, the physics of light should be taught by starting
with the unified theory and showing that particle and wave
theories are approximations to this and valid under certain definable
conditions. When these conditions are met it is then acceptable
to use a particle or wave approximation as appropriate.
Reference: 1. A Einstein, "The
Compton Experiment", Appendix 3, in R S Shankland
(Ed.), Scientific Papers of Arthur Holly Compton, X-Ray and Other
Studies, University of Chicago Press, Chicago (1975).
First published on the web: 15 December 1999.
Authors: Richard Payling & Thomas
Nelis
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Quantum electrodynamics (QED)
combines the wave-particle nature of light into a
single theory. It does this chiefly by combining two concepts: uncertainty and
quanta.
Heisenberg's Uncertainty Principle
Heisenberg's uncertainty principle appears to be a defining property of nature
on an atomic level. There are several equivalent ways of stating this principle.
One of these is
![[deltax.deltap<=hbar/2]](images/Equations/eq_quanti1.gif)
which states that the product of the uncertainties in position Dx and momentum Dp of a particle in the x-direction cannot be less than ![[hbar/2]](images/Equations/eq_quanti4.gif)
where ![[hbar=h/2pi]](images/Equations/eq_quanti5.gif)
and h is Planck's constant (= 6.63x10-34 kg m2 s-1).
The consequence of this relation is that the exact location and speed of a
particle cannot be known at the same time.
To see why we are not aware of this in everyday life, consider a ball with a
mass of 100 g thrown at a speed of 100 km/hr (=27.8 m/s). Assume
we can measure its speed to an accuracy of 0.1 m/s. The uncertainty
principle then states that we are limited in how accurate we can know the
position of the ball at any moment. The uncertainty limit is 7x10-32 m,
too small to measure, considering a typical atom in the ball is about 3x10-10 m
across. But since momentum varies with the mass of an object, for a particle
like an electron with a mass 1029 smaller than that of the ball,
the uncertainty in position is 1029 larger, and no longer
insignificant.
Another, equivalent form of the Uncertainty relation is
![[delta e.delta t>=hbar]](images/Equations/eq_quanti12.gif)
where the product of the uncertainty in the particle's energy and the time
period of the measurement cannot be less than .
Since any event must take a finite time, the particle's energy cannot
be perfectly known. Eg, if an atomic event takes 10-8 s,
then the minimum uncertainty in energy is only about 10-26 J.
Schrödinger's Equation
The ultimate assumption, in applying QED to atoms and atomic events, is that in
describing all observed phenomena we are dealing only with the interactions
between charged particles (electrons, protons) and the electromagnetic field
they generate.
The motions of particles in a field are described by a special functions called
wavefunctions, Y.
These wavefunctions are solutions of Schrödinger’s equation
where m is the reduced mass of the particle, ![[Laplace]](images/Equations/eq_quanti8.gif)
a squared second derivative operator called the Laplace Operator, V(r) the field, and E energy.
The Laplace operator is defined as
![[Laplace operator]](images/Equations/eq_quanti11.gif)
which means "the spatial rate of change in the spatial rate of
change",
and in this it is like acceleration.
The two terms inside the brackets are called the
'Hamiltonian'. The first
term of the Hamiltonian represents the kinetic energy and the second term the
potential energy.
Comment: Strictly speaking Schrödinger’s equation
is non-relativistic and we should use Dirac's relativistic equation. This has
important consequences for understanding atomic structure and spectra,
principally electron spin, but we will deal with relativistic effects separately
as most phenomena of interest can be explained with the non-relativistic
equation. For consistency, in future versions of this page, I am tempted to
begin with Dirac's equation.
The only possible wavefunctions Y that satisfy Schrödinger’s equation represent stationary waves with definite energy.
One way to imagine this is to consider a guitar string. The guitar string is
fixed at either end and can only produce standing waves (resonance notes) by
plucking the sting at fixed locations. For example, plucking the string in the centre
produces the first harmonic; plucking one-quarter way along produces the second
harmonic, etc.
Because only certain solutions (states) are possible and each has a definite energy, Schrödinger’s equation
embodies 'quantisation':
- only certain states are possible;
- only discrete (quantum) steps from one allowed state to another allowed state are
possible;
- changes of state involve a definite change in energy.
Schrödinger’s equation also embodies 'probability'. The square of the
electron wavefunction, i.e. Y2,
at a particular point is the probability that the electron will be found near
that point.
First published on the web:
15 February 2000.
Author: Richard Payling
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Speed of Light
The speed of light is a subject that has been
intensively studied over the last centuries: Today it is assumed to
be constant and is one of the basic physical constants.
Light is today understood as one from of electromagnetic energy.
We will start by considering a space free of matter, charges etc.
: the vacuum. The electromagnetic state of space is specified by
two vector fields the electrical field E and the magnetic
field H. In the static situation, when the fields do not vary
in time, the two fields are independent. However, when these two
fields are variable in time, in the dynamic situation, they influence
each other. A variation in the magnetic field will induce a change
in the electrical field and vice versa. Their interdependence has
been first properly described by James Clark Maxwell in the today
well kown Maxwell equations for the vacuum.
The two curl equation link the two vector fields and their time
derivatives. A change in the magnetic field will induce a curl of
the electric field. The equivalent is valid for a change in the
electric field. The divergence equations indicate the absence of
point charges in the vacuum. The divergence of the magnetic field
is always zero, because magnet monopoles do not exist in nature,
at least they have not been observed yet.
The constant mu is called the permeability of the vacuum. Its value
is defined to be 4pi 10-7 henry per meter (Hm-1)
The other constant epsilon is the permitivity of the vacuum is of
8.854187817... x10-12 farads per meter (Fm-1).
These values, however, depend on the units used.
The two constants, mu and epsilon, are closely linked to the speed
of light. Maxwells equation can be decoupled. Combinig the curl
and divergence equations, using a little mathematical gymnastics
we find the a classical second order differential equation, known
as the wave or Laplace equation.
In the following tabel a non-exhaustive list of experimental determinations
of the speed of light is given to demonstrate the long history of
this scientific effort.
| Date |
Experimenter |
Experimental technique |
Result (kms-1) |
Exp. uncertainty (kms-1) |
|
| 1676 |
Römer |
eclipse of Jupiter moons |
214 459 |
*1 x 105 |
| 1727 |
Bradley |
abberation of light |
300 000* |
*1 x 105 |
| 1848 |
Fizeau |
rotating toothed wheel |
313 290 |
5 x 103 |
| 1850 |
Foucault |
rotating mirror |
298 000 |
2 x 103 |
| 1857 |
Weber & Kohlrausch |
electrical constants |
310 000 |
2 x 104 |
| 1868 |
Maxwell |
electrical constants |
288 000 |
2 x 104 |
| 1875 |
Cornu |
rotating mirror |
299 990 |
2 x 102 |
| 1880 |
Michelson |
rotating mirror |
299 910 |
1.5 x 102 |
| 1883 |
Thomson |
electrical constants |
282 000 |
2 x 104 |
| 1883 |
Newcomb |
rotating mirror |
299 880 |
3 x 101 |
| 1901 |
Perrotin |
rotating mirror |
299 777 |
3 x 101 |
| 1907 |
Rosa & Dorsey |
electrical constants |
299 784 |
1 x 101 |
| 1923 |
Mercier |
standing waves on wires |
299 782 |
3 x 101 |
| 1928 |
Mittelstaedt |
Kerr cell shutter |
299 778 |
1 x 101 |
| 1932 |
Pease & Pearson |
rotating mirror |
299 774 |
2 x 100 |
| 1940 |
Hüttel |
Kerr cell shutter |
299 768 |
1 x 101 |
| 1941 |
Anderson |
Kerr cell shutter |
299 776 |
6 x 100 |
| 1947 |
Jones & Conford |
Oboe radar |
299 782 |
2.5 x 101 |
| 1950 |
Bol |
cavity resonator |
299 789.3 |
4 x 10-1 |
| 1950 |
Essen |
cavity resonator |
299 792.5 |
2.5 x 100 |
| 1951 |
Bergstrand |
Kerr cell shutter |
299 793.1 |
3 x 10-1 |
| 1951 |
Alsakson |
Shoran radar |
299 794.2 |
2.5 x 100 |
| 1952 |
Froome |
microwave interferometry |
299 792.6 |
7 x 10-1 |
| 1972 |
Evenson & Wells |
hetrodyn laser experiment |
299 792.456 2 |
1.1 x 10-4 |
| *these values are estimated. Sources used for the
for this page did not provide the exact value.Hints to find them
are welcome! The uncertainty in determination of the speed of light
based on astromic measurements are usually linked to the uncertainty
in the distance between sun and earth |
When looking at the table one not only notices the impressive improvement
in the experimental precision that has been achieved over the years.
It is even more important that the experiments lead to the same
result independent of the technique employed for the determination.
This further supports the idea that the speed of electromagnetic
waves is independent of the type of EM radiation used for the experiment.
The last experiment in the list, by Ken M. Evenson (1932-2002)
and Joe Wells from the National Institute of Standards and Technology in Boulder,
Co, has most likely been the last in a long series of determination
of the speed of light. In fact following Ken Evenson's experiment
the standard meter had to be re-defined. The precision of time measurements
was much higher then the precision with which the meter could be
defined. Since the 17th Conférence Générale
des Poids et Mesures in 1983 the meter is defined as the distance
light travels in 1/299 792 458 s, i.e. the speed of light has turned
in to a basic constant (c=299 792 458 ms-1) and the meter
has turned into the inverse of time (scaled by c). The odd number
for the speed of light was chosen to change the definition of the
meter as little as possible from the former value.
References:
- G.R. Fowles, Introduction to Modern
Optics, 2nd Ed.; Dover publiction New York, NY, (1989).
- G.Woan, The Cambridge Handbook of Physics Formulas,
Cambridge University Press, Cambrigre, UK (2000)
- E. B. Rosa and N. E. Dorsey, A new determination of the ratio of the electromagnetic to the electrostatic unit of electricity, Bull. Bur. Stand .3, 433-604 (1907); A comparison of the various methods of determining the ratio of the electromagnetic to the electrostatic unit of electricity, Bull. Bur. Stand. 3; (1907); 605-622.
- L.Bergmann, C.Schaefer, Lehrbuch der Exp. Phys.;
Vol III, 7th edition, DeGruyter (1978)
- D. B. Sullivan in http://nvl.nist.gov/pub/nistpubs/sp958-lide/191-193.pdf
- http://www.uark.edu/ua/pirelli/html/train_PW_CW.htm
- K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, G. W. Day, R. L. Barger, and J. L. Hall, Speed of Light from Direct Frequency and Wavelength Measurements of the Methane-Stabi-lized Laser, Phys. Rev. Lett. 29, (1972); 1346-1349
First published on the web: 10.11.2006.
Author: Thomas Nelis
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