Wave Nature of Light

Anand Deo

A wave is a disturbance that travels through some material called a medium or space usually transferring energy. The disturbance produced at one end of string permeated through whole of string in form of wave. When we speak, the air molecules in front of us are disturbed and the disturbance is carried by other air molecules around it. This propagates as sound wave. Similar are the waves in water. It’s crucial to recognize is that the medium itself in each case, the string, the air, the water is not moving from one end to other. They’re simply being displaced momentarily by the energy that’s passing through and the disturbance is passed onto succeeding particles of medium while the preceding particle comes to its original place.

At the end of nineteenth century, the major branches of physics prevailing were Mechanics, Thermodynamics and Electromagnetism. In the early 1860’s James Clerk Maxwell produced a set of equations that summarized electromagnetism. Before Maxwell, electricity and magnetism were considered to be separate forces but as nineteenth century progressed, it became more and more clear that these two fundamental interactions were more and more related. As it turned out, they were both product of charge. Charge is inherent property of matter like mass. While mass produces gravitational field that interact with other masses and attracts them, charge produces electric field which interact with other charges by causing them to attract or repel. Opposite charges are attracted to each other and like charges are repelled due to the direction of lines of their field forces.

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Ampere put forward that when electric charges move, they generate magnetic field. Faraday put forth a moving magnet will produce an electric filed. Taken together, this suggests electricity and magnetism are different aspect of same force. The theory of electromagnetism involved many difficult  derivations and meticulous experiments but when the dust finally settled it became clear to all that not only magnetic and electric phenomenon are fundamentally the same force but that electric and magnetic fields could together produce a wave.

When an electric charge is shaken back and forth like a string, the electric field surrounding the charge begin to oscillate and as a result of the oscillating electric field, a magnetic field will be generated which in turn will generate an oscillating electric field and so on and on it will go. The result is an electromagnetic wave. The peculiarity is that the direction of electric field, the magnetic field and propagation of wave are all mutually perpendicular and the wave does not need any medium to propagate since it is basically a disturbance in the fields.

According to Maxwell equations, the speed with which an electromagnetic wave travels is equal to speed of light. This led him to conclude that light is an electromagnetic wave; a disturbance in electric and magnetic fields. As it turns out there are many forms of electromagnetic wave and they fundamentally differ in the wavelengths and frequency.

Long before any of these concepts of electromagnetism or light being an electromagnetic wave, there were people and there was light. Light has existed since the beginning of universe. People from ancient times to the date have noticed a shiny surface reflects light. They knew the fish is not exactly at the point where it seems under the water and everyone has seen a rainbow. But none knew why all these were happening.

Dutch astronomer Christian Huygens in mid seventeenth century put forth the wave theory of light. Huygens believed that light was a longitudinal wave, and that this wave was propagated through a material called the ‘aether’. Since light can pass through a vacuum and travels very fast he had to propose some rather strange properties for the aether: for example; it must fill all space, have zero inertia and be weightless and invisible. For this reason scientists were skeptical of his theory.

Also known as Huygens’ theory of secondary wavelets, he proposed that a point source (S) sends out waves in all directions. In time t, the waves of light would reach a distance of ct in all directions in space, where c is speed of light. All the points where the waves have reached in same time are on surface of sphere with source S as center and ct as radius. Since all the points on the surface of sphere have received the wave in same time, they’re all in same phase and this surface is called a wavefront. The wavefront would appear spherical in 3D and as circle in 2D. In order to explain how a wavefront is propagated forward through a homogeneous isotropic medium, Huygens made two assumptions:  1: Each point on wavefront acts as a fresh source of disturbance called as secondary wavelets. These wavelets spread out in the medium with the velocity of the light in the very medium. 2: The new wavefront at any time later is obtained by taking the forward envelope of the secondary wavelets at that time.

Huygens successfully explained the phenomenon like reflection, refraction exhibited by light based on his wave theory. Many scientists even believed in the existence of aether. The theory was a promising one but it had some drawbacks that led Newton and others to reject it. The secondary waves are propagated in the forward direction only and they are assumed to destroy each other except where they form the new wavefront. Newton argued against wave theory of light saying light cannot be wave because although we can hear sound from behind the obstacle we cannot see light on the other side of obstacle i.e. light does not show diffraction. Newton did not know that in fact light does do this, but the effects are exceedingly small due to the very short wavelength of light. Huygens’ theory also failed to explain the rectilinear propagation of light. Furthermore Huygens’ wave theory could not explain polarization of light because he believed light to be a longitudinal wave and polarization is a property of transverse wave.

Along came Newton’s radical approach around 1690 to explain the observed behavior of light like reflection and refraction. He developed Corpuscular theory of light, arguably put forward for the first time by Pierre Gassendi which had to say that every source of light emit large number of tiny particles known as corpuscles in the medium surrounding the source and also these corpuscles were perfectly elastic and weightless. He also assumed the various colors of light were due to difference in size of the corpuscles of various colors of light; corpuscles of red light being larger than corpuscles of violet light.

With his corpuscles of light he tried to explain reflection akin to a bill striking a wall and bouncing back. If the ball hit the wall perpendicular to the later, the ball would bounce back the same way it traversed while going towards the wall but if it hit the wall at some other angles, the ball would bounce back traversing a different path than the original one. Light behaved the same way. The corpuscles of light were the ball and the shiny surface reflecting off the corpuscles was the wall.

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Corpuscular theory also intended to explain refraction of light by speculating that the corpuscles velocity varied with the medium and therefore it changed the direction while traversing from one medium to other. Newton assumed that there is an attraction between the molecules of a solid and the particles of light, and that this attraction acts only perpendicularly to the surface and only at very short distances from the surface. This has the effect of increasing the velocity of the light in the material. It would mean the denser the medium is, the higher the velocity of the corpuscles would be. Also, based on this attraction between particles of medium and corpuscles at shirt distances, Newton explained total internal reflection of light by saying that the perpendicular component of velocity was too small to overcome the molecular attraction.

Newton in his 44th trial successfully set up two prisms at such an angle that white light when passed through first got separated into seven colors and when it emerged from the second reconstituted as a white light. He tried to explain this in reference to differences in change in velocity of various sized corpuscles and hence change in path of the corpuscles combined with geometry of prism leading to splitting into different colors.

Corpuscular theory and Wave theory were contemporary but scientific community seemed to prefer former over later for the Newton’s eminence associated with the former one. But with time, it was more than obvious that corpuscular theory was neither satisfactorily explaining various observed phenomenon exhibited by light like diffraction, interference, polarization. Newton was unable to prove that the corpuscles had higher velocity in denser medium. Various colors of light due to difference in size of corpuscles also didn’t seem to have a solid ground. Another problem of the corpuscular theory was that temperature has no effect on the velocity of light, although on the basis of this theory we would expect the particles to be shot out at greater velocities as the temperature rises. Despite having greatest of minds working and two great theories on stand, the picture was incomplete. Both the theories had its drawbacks. Something was missing.

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Then in 1801, Thomas Young did a crucial experiment with light that came through two slits and hit a white screen. One would expect he saw two bright lines on screen in the line of slit. Common sense as well as corpuscular theory would indicate the same. Instead he saw a row of bright and dark lines on the screen. Young decided that Huygens’ wave theory of light was the only plausible explanation for this interference pattern. Since then, other properties of light like diffraction, dispersion which happen to be property exclusively of waves were also experimented with and results seemed fit to wave nature of light. Light was established as wave beyond any shadow of doubt. Thanks to Maxwell, the wave nature of light was established in later half of nineteenth century as an electromagnetic and not longitudinal as Huygens’ had assumed. Polarisation was explainable now with this new piece of information. It was just the lack of insight and technology during Huygens’ time that his wave theory was less regarded. But at the end of the day, light was electromagnetic wave and that remained the story for nineteenth century.

 

 

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