Let There Be Light

The following sections are included:

• Preface to the First Edition

• Preface to the Second Edition

• Acknowledgements

• Contents

Light plays a central role in our lives. It is the universal messenger which enables us to be aware of the objects around us and of the rest of the universe. Without light we would not receive the lifegiving energy from the sun. Much more than that, light or electromagnetic radiation is at the centre of the physical laws. Without it the universe, as we have come to know it, would simply not exist!…

The following sections are included:

• The quickest route

• Fermat’s principle
  • Light takes the quickest route
  • The path in empty space
  • The quickest path via a reflection
  • The law of reflection

• Mirrors
  • A plane mirror
  • Reversal from left to right
  • Reflection from a curved and uneven surface
  • A spherical concave mirror
  • Applications of concave mirrors
  • Reflecting telescope
  • The ‘death rays’ of Archimedes

The following sections are included:

• Providing more than one quickest route

• Making visible things we cannot see

• Refraction
  • The refractive index
  • The lifeguard problem
  • Snell’s law
  • The reverse journey
  • Apparent depth
  • The dilemma faced by light trying to leave glass
  • Practical applications of total internal reflection
  • Light pipes and optical fibres
  • Freedom of choice when a ray meets a boundary
  • The ‘shop window effect’
  • The mystery
  • ‘The photon decides’
  • A practical puzzle – two-way mirrors

• Lenses
  • The function of a lens
  • Converging lenses
  • Diverging lenses
  • Fermat’s principle applied to lenses

• Objects and images: converging lenses
  • Ray tracing through a thin lens
  • Principal rays (thin lenses)
  • The lens equation
  • Symmetry
  • Breaking the symmetry
  • An intuitive approach – the task of a lens
  • Masking a lens

• Objects and images: diverging lenses

• Lens combinations
  • Lenses in contact
  • The power of a lens

• The eye
  • The structure of the eye
  • Accommodation
  • Common eye defects

• Making visible what the eye cannot see
  • Distant objects
  • Nearer but not clearer
  • Angular magnification

• Combinations of lenses
  • Compound microscopes
  • Telescopes

• A final note on Fermat’s principle
  • The pioneers of generalized classical mechanics

The following sections are included:

• When light reaches us after a long, long journey

• The earth
  • Is the earth round?
  • Philosophical reasons why the earth should be round
  • General intuition – Zhang-Heng (Chinese astronomer, 78–139)
  • Experimental evidence that the earth is round

• The moon
  • The phases of the moon
  • A lunar eclipse
  • A solar eclipse

• Sizes and distances
  • Relative sizes of the sun and the moon
  • The shadow of the earth on the moon
  • Shrinking shadows
  • Comparing shadows
  • The distance to the moon
  • The distance to the sun
  • A practical problem
  • A summary concerning the earth, moon and sun
  • Astronomical distances

• The planets
  • The ‘wanderers’
  • Ptolemy’s geocentric model

• The Copernican revolution
  • Frames of reference
  • Copernicus and the heliocentric model
  • Where did the epicycles come from?

• After Copernicus
  • Looking back with hindsight: why Brahe did not see any parallax
  • Kepler’s discovery
  • Galileo Galilei (1564–1642)

• The solar system in perspective

When Isaac Newton discovered the law of gravity, and that it applies equally to matter, whether on the earth, the moon or anywhere else in the universe, a completely new chapter was opened. It became possible to calculate the orbits of planets, even to predict the existence and motion of hitherto unseen planets. The science of astrophysics was born…

What is a wave? Waves are so diverse that we might tend to regard different types of waves as separate entities, unrelated to one another. Do events such as the devastation of a region by an earthquake and the melodic tones of a musical instrument have anything in common? In this chapter we explore the common ground between these and many other phenomena…

No account of waves and their properties can be complete without the inclusion of a discussion of sound waves. Sounds in the frequency range of 20–20,000 Hz are associated with human hearing. Many animals and birds can produce and detect sounds above and below this frequency range, providing them with a means of communication and an aid to survival…

We have spent some time looking at waves – and by now should be able to recognize a wave when we see one! In this chapter we look at evidence that a light beam behaves like a train of waves…

Now, we come to the making of images. We follow developments from the days of the early Greeks through to modern imaging. A photograph, although it may be truly a work of art, is just a two-dimensional image; there is no change in perspective when we look at it from different angles.

Holography, or three-dimensional imaging, was invented by the Hungarian physicist Dennis Gabor. We discuss what information the photograph lacks, its third dimension, and how we can encode that information to make a complete picture. We see that holography is a technique which has been rapidly incorporated as an art form and a scientific tool with practical and commercial applications…

In our universe there exist certain phenomena which involve a mysterious ‘action at a distance’. The best-known of these is gravitation, which Isaac Newton showed to be governed by one universal law of attraction…

The following sections are included:

• The light from hot soot …

• Emission of energy by radiation
  • How does matter emit electromagnetic energy?
  • Experimental results – the blackbody radiation spectrum
  • The Stefan–Boltzmann law
  • Wien’s displacement law
  • Putting theory into practice – optical pyrometers

• Classical theories of blackbody radiation
  • Cavity radiation
  • Thermodynamics of the cavity model
  • Wien’s spectral distribution law
  • A cavity model based on the wave nature of light
  • A technical advance
  • How can the theoretical models be ‘half right’?

• Max Planck enters the scene
  • The formula – but not the explanation
  • Trying to crack the code
  • Nature’s secret
  • The cause of the ultraviolet catastrophe

• Planck’s ‘act of despair’
  • The quantum hypothesis
  • The birthday of quantum theory
  • Quantum discrimination
  • The distribution of energy among the oscillators
  • The average energy
  • What does the quantum do after it is emitted?
  • A new philosophy

Planck’s quantum hypothesis was only the beginning of a new and fascinating story. In 1913, Niels Bohr extended the idea of quantization to the orbits of electrons in the planetary model of the atom. Light played a central role in that model, in that it was postulated to be created by the energy loss of atomic electrons as they dropped from higher to lower orbits, and thus gave information on the orbits themselves. As a result, Bohr, in his acceptance speech at the Nobel Prize ceremony in Oslo in 1922, was able to say ‘…we not only believe the existence of atoms to be proved beyond doubt, but also we even believe that we have an intimate knowledge of the constituents of the individual atoms’…

The energy of light comes in quantum units of value hf. In this chapter we go a step further, and look at evidence that it comes as a bundle, concentrated at a point, and behaves just like a particle. We will describe experiments that show that the photon has not only energy but also momentum…

We have established that light has the properties of a wave and discussed the evidence in detail. Light spreads out like a wave, it can bend around corners like a wave, and exhibits the properties of diffraction and interference. It must be a wave…

The following sections are included:

• Empty space is the same everywhere and for everyone …

• Space and time
  • Space and the ancient philosophers
  • Space – the intuitive view
  • Space and time – according to Isaac Newton

• ‘Dogmatic rigidity’
  • Starting with a clean slate
  • Frames of reference – defining a point of view
  • Specifying the prejudices

• Looking for the ether
  • The Michelson–Morley experiment
  • Timing the ferry
  • Details of the experiment
  • A powerful conclusion

• Symmetry
  • Space is uniform
  • The new model

• The special theory of relativity
  • Postulates of special relativity
  • Einstein’s first postulate
  • Galileo had the right idea!
  • The Galilean transformation
  • Galileo’s first step
  • Einstein’s second postulate
  • An imaginary experiment with light
  • A paradox* – how can they possibly get the same result?
  • Einstein puts the facts together
  • ‘The impossible’ in mathematical form
  • The Lorentz transformation
  • The gamma factor
  • Fact or fiction?

• Pythagoras re-visited
  • Displacement on a map
  • Moving on to three dimensions

• The fourth dimension
  • Invariant interval in space–time
  • The smoking astronaut

• A philosophical interlude
  • What is the meaning of ‘simultaneous’?

The theory of relativity was developed at a time when there was no means of experimental verification. The concepts are so foreign to the ‘everyday world’ that it is easy to be sceptical. Perhaps the basic postulates are wrong, or there is a flaw somewhere in the logic of the argument…

The following sections are included:

• Then there was light …

• Making matter out of energy
  • Collisions make particles
  • Prediction and discovery of the π meson
  • The forces between the particles
  • The laws of the world of elementary particles
  • Quarks
  • The return of photographic emulsion
  • More quarks
  • The innermost shell of the nuclear onion

• A unified theory of weak and electromagnetic forces
  • The role of light as the carrier of the electromagnetic force
  • Unification – the long hard road
  • The heavy photon
  • The Higgs boson
  • The full circle

The following sections are included:

• Index

• About the Authors