Light and Duality: Newton vs Huygens

Dilip Angom

Theoretical Physics and Complex Systems Division

Light Through the ages: ancient

500 BC Empedocles postulated objects consists of fire, water, air and earth. Aphrodite made human eye out of the four elements and light emanating from eye gave sight.

300 BC Euclid wrote Optica. Postulated light travel in straight lines and studied reflection. He gave mathematical description.

55 BC Light and heat of the sun consist of minute atoms, these travel in straight lines wrote Lucretius in On the nature of the

Universe. No one believed him.

140 AD Ptolemy made accurate observations of stars and realized light is refracted by the atmosphere.

1000 AD al-Haytham believed rays of light from sun make sight possible. Light consists of small particles and travels in

straight lines. Among his supporting arguments, camera obscura is the most convincing.

Light Through the ages: middle

1220 AD Grosseteste emphasized the importance of studying light in natural philosophy and advocated use of geometry to study properties of light.

1270 AD Roger Bacon concluded light has finite velocity. He advanced the idea of using convex lenses to correct defective eyesights.

1270 AD Witelo wrote Perspective after studying mirrors and refraction of light. This book was the textbook on optics for several centuries following its publication.

1590 AD Zacharius Jensen made a microscope with compound lenses. This followed from better understanding of lenses and properties of light.

1611 AD Kepler gave the correct mathematical theory of camera obscura. He published Dioptrice, an important book in optics.

Snell’s law of refractionWillebrord Snell discovered the sine law of refraction of light in 1621. However, the first published work on sine law of refraction is Descartes’ La Dioptrique in 1937. Interestingly, the law was discovered even earlier.

Thomas Harriot discovered the sine law of refrraction in 1604.

Light Through the ages: seventeen century

Major advances in our understanding of light occurred during the seventeen century.

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Lense maker’s formulaIn 1647 Cavalieri gave the relationship between the curvature of a thin lens and its focal length. This gave insight to fine tune construction of optical instruments.

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These developments were related to construction of better optical instruments.All branches of sciences experienced several breakthroughs during the seventeenth century. It marked the end of Aristotelian view, all objects are made of fire, water, air and earth.

Light Through the ages: seventeen century

Sir Isaac Newton (1642–1727)

Wrote and published several papers on properties of light and colors. He advocated corpuscular theory of light and published Opticks in 1709.

Christiaan Huygens (1629–1695)

Studied the properties of light and proposed the wave theory of light in his book Traite de la lumiere in 1678.

Christiaan Huygens and Isaac Newton

Christiaan Huygens:Traite de la Lumiere

In 1678 Huygens published Traite de la Lumiere. The book has the following chapters:

•On rays propagated in straight lines.

•On reflexion.

•On refraxion.

•On the refraxion of the air.

•On the strange refraxion of iceland crystal.

•On the figure of the transparent bodies.

The first chapter of the book formulates the wave theory of light. The book also mention’s Hook’s and father Pardies work on wave theory of light.

Traite de la Lumiere: Finite velocity of light

Huygens explains the finite velocity of light and wave theory in the first chapter. He uses the time variation of ecplise of satelites of Jupiter.

Finite velocity of light

Huygens estimated the velocity of light as 2,282 toises,which is

…..more than six hundred thousand times greater than that of Sound.

Christiaan Huygens

In 1676 two years before Huygens published Traite de la Lumiere, Römer calculated the velocity of light using the data of the eclipses of Jupiter’s moon. His result was 225,000 km per second (the correct value is 299,792 km).

Traite de la Lumiere: Wave theory

Wave theory

Huygens postulated light propagates successively by spherical waves. Each little region of luminous object creates its own waves.

Thus in the flame of a candle, having distinguished the points A, B, C, concentric circles described about each of these points represent the waves which come from them.

Christiaan Huygens

Light propagates in ether, a substance possessing near perfect hardness and springiness as prompt as we choose. Ether particles allow light waves propagating in different direction to cross each other without mutual disturbance.

Traite de la Lumiere: Wave fronts

Wave front

Each particle of ether propagates the wave to all the other particles touching it, propagation is not confined to the direction of the propagation. About the boundary

….. a wave ought to spread in such a way that its extremities lie always between the same straight lines drawn from the luminous point. Thus the portion BG of the wave, having the luminous point A as its centre, will spread into the arc CE bounded by the straight lines ABC, AGE

Christiaan Huygens

This precondition or restriction on the secondary wave front ensures light travels in straight line and follows the law of reflection.

Demonstration: Propagation

Propagation

According to Huygen’s postulate, each point on the plane wave front creates a secondary wave front. These superpose to produce a plane wave front again.

The points in the picture are in the medium of light propagation. Each point creates a secondary wave front, as the wave front passes. These superpose to yield a plane wave front.

Demonstration: Reflection

Reflection

According to Huygen’s postulate, when a wave front is incident on a reflecting surface. Each point on the surface creates a secondary wave front.

The points in the picture are points on the reflecting surface. As the light is incident on the surface, secondary wave front originates from each of these.

Isaac Newton: Opticks

Newton published his theory of color in 1672. He gave evidences to prove light is composed of minute particles.

In 1703 he published Opticks after Hook’s demise. The book has

The first book of optics

•Part I: definitions and propositions.

•Part II: propositions-proved by experiments.

The second book of optics

•Part I:observations on reflection, refractions, and color of thin transparant bodies.

•Part II: remarks upon the foregoing observations.

•Part III: parmanent colors of natural bodies …

•Part IV: observations concerning reflections and colors of thick transparant bodies.

………………….

Opticks: rays of light

In the 1717 edition of Opticks Newton defines rays of light

By the rays of Light I understand its least parts, and those as well Successive in the same lines as Contemporary in Several lines.

Isaac Newton, Opticks, Book 1, Part I

Rays are straight lines connecting the source of illumination to the illuminated point. A ray of light travels in straight lines.

Rays are defined in general terms to allow infinite velocity of light as well as the finite velocity measure by Römer. (The 1717 edition doesn’t mention corpuscules)

Opticks: definitions

Reflexivity and refrangibility

The first Book of the Opticks clearly defines reflexivity and refrangibility.

Refrangibility of the rays of Light, is their disposition to be refracted or turned out of Way in passing out of one transparent Body or Medium into another.

Isaac Newton, Opticks, Book 1, part I

Reflexivity of rays, is their Disposition to be reflected or turned back into the same medium from any other Medium upon whose Surface they fall.

Isaac Newton, Opticks, Book 1, part I

The book gives definitions about colors also, there are eight definition in total. Then, eight axioms follow the definitions.

Opticks: colors and refraction

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Color of sunlight

Newton proved the white light received from the sun consists of several colors.

Whiteness and all grey colours between white and black, maybe compounded of Colours, and whiteness of the Sun’s light is compounded of all the primary colours mixe’d in a due Proportion.

Isaac Newton, Opticks, Book 1, pp-117

Newton proved this by passing sunlight through two prisms placed with their bases opposite. Prior to Newton’s publications, colors observed in refraction of white light were attributed to curruption by the medium.

Opticks: colors and refraction

All homogeneal light has Proper Colour answering to its degree of Refringibility, and that Colour cannot be changed by reflexions and refractions.

Isaac Newton, Opticks, pp-106.

Of colors

After numerous experiments, Newton concluded color of light is immutable. There are primary colors and mixture of it.

All colours in the Universe which are made by Light, and not depend on the power of Imagination, are either the colour of homogeneal Lights, or compounded of these, and that very accurately or very nearly, according to the foregoing Problem.

Isaac Newton, Opticks, pp-138. Light does not change colors while or after passing through a medium. Each color of light posses a characteristic refractive index.

The book also has detailed experiments with intereference effects in thin films.

Legacy of Huygens and Newton

Nature of lightLight is a wave which propagates in ether, a medium of perfect hardness and infinite springibility. Every point of the light source is creates a wavefront and each point in the wave front is source of secondary wave fronts. Huygens

Light consists of rays, which connect the source of illumination to the point illuminated. Newton

Of colorsThere are primary colors of lights, which does not change while passing through a medium. Mixing lights of primary colors yield light of compound colors. Each color of light has different refractive indices. Newton

Newton as well as Huygens explained reflection and refraction based on their theories.

Of reflection and refraction

Legacy of Huygens and Newton

Of velocity of light

The velocity of light extremely large but it is finite. This can be observed from the seasonal variation in the duration of eclipse of jupiters moon. Huygens

Velocity of light can be infinite but it could be finite if results from calculation from the observations of moons of of Jupiters is correct. Light travels faster in denser medium. Newton

Opinion of the other scientists

Till the end of eighteen century most of the scientist accepted Newton’s corspuscular theory. Perhaps this was due to Newton’s reputation after his remarkable contributions to physics. An exception was Eular, in 1746 he published Nova theoria lucis et colorum and strongly supported wave theory.

Wave theory: evidences

DiffractionAround 1671 James Gregory discovered diffraction when sunlight passes through the feather of a seabird. However, he did not published the results, but he did write

Let in the sun's rays by a small hole to a darkened house, and at the hole place a feather (…….), and it shall direct to a white wall or paper opposite to it a number of small circles and ovals (…….) whereof one is somewhat white (……) and all the rest severally coloured. I would gladly hear Mr Newton's thoughts of it. James Gregory

Interference

Newton conducted experiments on diffraction of light from a sharp edge. However, he explained in terms of refraction.

Newton did numerous experiments on interference patterns created by thin films. He gave algebraic relations of the fringes of different colours and thickness of the film. But explained the phemenon using reflection and refraction.

Wave theory: Thomas Young

Two slit experiment

Between 1797 and 1799 Thomas Young carried out a series of experiments diffraction through a single slit and double slit interference. The results were published in 1801. He explained the results using wave theory of light.

Thomas also explained the interference patterns from thin films, which Newton had observed and studied. This include Newton’s ring.

Unfortunately, these were not widely accepted. The formation of dark bands/strips when two light waves superpose was difficult to accept for scientist of that time.

Wave theory: Augustin Fresnel

Mathematical model of diffraction

This was the Grand Prix topic of Académie des Sciences in 1819. Augustin Fresnel submitted his entry and used wave theory.

The committee of judges included Arago as chairman, and Poisson, Biot and Laplace as members. Their disposition were towards corpuscular theory. However, Poisson found Fresnel’s work fascinating.

He calculated the integrals in Fresnels theory of diffraction and found light incident on a disc

The disk casts a shadow - of course - but the very centre of the shadow will be bright. Poisson

Polarization of light: Augustin Fresnel

After receiving Grand Prix Fresnel worked with Arago. They could explained polarization of light using wave theory.

Polarization of light

By 1920s the wave theory of light was accepted and diffraction was studied in detail. The other important discoveries of the era include Fraunhoffer’s theory on diffraction and Airy’s calculation of diffraction pattern produced by a circular aperture.

The predictions of Poisson was confirmed experimentally and Fresnel received the grand prix.

Wave theory of light

Properties of light: 1850

Nature of lightIt is a wave and different wavelengths posseses different colors. They also have different refractive indices. It follows laws of reflection and refraction.

Velocity of light

For the first time Fizeau measured the velocity of light without using an astronomical method in 1949. His results showed light travels with a velocity of 300,000 kilometers per second. In 1950 Foucoult showed light travels with a lower velocity in water.

Polarization of light

Light can have different polarizations. Fresnel and Arago explained it in terms of wave nature of light. However, it was not known that light is electromagnatic wave.

By 1950 the wave theory of light well established.

Light: electromagnetic wave

Faraday effect

In 1845 Faraday found that magnetic field changes the plane of polarization of light propagating through a medium. This established a connection between magnetic field and light.

Based on this observation, Faraday opined that there is a unity of forces in nature

The view which I am so bold to put forth considers radiation as a high species of vibration in the lines of force which are known to connect particles, and also masses of matter together. It endeavours to dismiss the aether but not the vibrations. Faraday 1846, Royal Society

Light: electromagnetic wave

Maxwell’s equations

James Clerk Maxwell was born at 14 India Street in Edinburgh. He unified electricity and magnetism. The famed Maxwell’s equations first appeared in it’s present form in electricity and magnetism (1873).

Around 1862 Maxwell realised that electromagnetic phenomena are related to light. He wrote in 1864

This velocity is so nearly that of light that it seems we have strong reason to conclude that light itself (…..) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.

Light: end of classical era

Perhaps it could be said that, Maxwells equations marks the last development in understanding the classical theory of light.

The other breakthroughs occurred with the advent of quantum mechanics and relativity. Two theories marking the matter-wave duality and mass-energy equivalence.

Photoelectric effect, which implies particle nature of light would later revive the particle nature of light. However, with a very different concept: wave-matter duality. Different from the classical corpuscular theory of light.

Bibliography

Selected resources•History of light: classical era http://www-history.mcs.st-andrews.ac.uk/HistTopics/Light_1.html

•Online copy of Christiaan Huygen’s treatise on light http://www.gutenberg.org/dirs/1/4/7/2/14725/14725-h/14725-h.htm

•Online copy of Newton’s Opticks http://burndy.mit.edu/Collections/Babson/Online/Opticks/

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