Light is a form of energy visible to the human eye that is radiated by moving charged particles. There are many unanswered questions about light. Light is very hard to study due to its high speed. One major question about light is the uncertainty of whether light is a wave or whether it is a particle. There is some evidence pointing in both directions but no conclusive proof confirms that it can be classified as either one. Scientists have learned through experimentation that light behaves like a particle at times, and like a wave at other times. Whenever light acts like a particle, we called the particles that make up the light either a photon or quantum. In 1900, Max Planck proposed the existence of a light quantum, a finite packet of energy which is a photon.

Photons may be described as tiny packets of light energy. Photons are unlike conventional particles, such as specks of dust, because photons do not have to have a specific volume in space. Photons are always arranged in an electromagnetic wave of a definite frequency which indicates that photons are part of a wave. The frequency of the photon forms a single spectrum line that represents a particular wavelength or colour. In 1900, a German physicist named Max Planck discovered that light energy is carried by photons. He found that the energy of a photon is equal to the frequency of its electromagnetic wave multiplied by a constant called “h”, which stands for Planck’s constant. However, this constant is very small because each photon carries little energy. Using the Joule as the unit of energy, Planck's constant is 6.626 x 10^(-20) joules per second in scientific notation. Photons are different from particles of matter in that they have no mass and always move at the constant speed of light which is 300,000 km/sec (186,000 mi/sec). Sir Isaac Newton was for the idea that light is a particle (photon), although, Newton had a hard time explaining the effect of interference on the moving photons.

Another way light is thought of as travelling is in the form of a wave. It is thought this because light also shows wavelike characteristics. When light diffracts, or bends slightly as it passes around a corner, it shows wavelike behavior. If it were a particle, it would not bend around a corner. The waves are called “matter waves”. Matter waves have a specific wavelength and the wavelength is inversely proportional to the particle’s momentum. Matter waves also explain the arrangement of electrons in separate orbits. The waves associated with light are called electromagnetic waves because they consist of changing electric and magnetic fields. A wave is a continuous phenomenon, which means that when it travels, its electromagnetic field must move at each of the infinite number of points in every small part of space. When we add heat to any system to raise its temperature, the energy is shared equally among all the parts of the system that can move. When this idea is applied to light as a wave, with an infinite number of moving parts, it would require an infinite amount of heat to give all the parts equal energy. But thermal radiation, the process in which heated objects emit electromagnetic waves, occurs in nature without having to add an infinite amount of heat. The wave theory of atomic particles has given scientists a greater understanding of the structure of atoms and their nuclei.

A debate arises: “Is light a wave or a particle?” It can’t be both because the models of waves and particles are very different. The way they behave when travelling and when passing through mediums is very different. It seems that your conclusion depends on what type of experiment you are doing. In 1905, Einstein said that a ray of light travels in the path of the photon. The traveling photons are in great number and travel in straight lines. To understand the nature of light, and how it is normally created, it is necessary to study matter at its atomic level. The motion of electrons, leads to the emission of light in most sources.

The first successful theory of light wave motion in three dimensions was proposed by the Dutch scientist Christiaan Huygens in 1678. Huygens suggested that light wave peaks form surfaces like the layers of an onion. In a vacuum, or a uniform material, the surfaces are spherical. These wave surfaces advance, or spread out, through space at the speed of light. Huygens also suggested that each point on a wave surface can act like a new source of smaller spherical waves, which may be called wavelets, that are in step with the wave at that point. The envelope of all the wavelets is a wave surface. An envelope is a curve or surface that touches a whole family of other curves or surfaces like the wavelets. This construction explains how light seems to spread away from a pinhole rather than going in one straight line through the hole. The same effect blurs the edges of shadows. Huygens's principle, with minor modifications, accurately describes all forms of wave motion.

There is also a theory which light is said to travel in both a wavelike manner and a particle-like manner. This is called the wave-particle duality and was proposed in 1924 by de Broglie, who also developed the idea of the “matter wave” which is a basic part of the wave-particle duality theory. The wave-particle duality theory says that photons do have a mass and travel along on a wave. This was a combination of the wave and particle theories of light and now is the generally accepted explanation of the way light travels. Heisenberg showed that the wave-particle duality leads to the uncertainty principle. The uncertainty principle states that the position and velocity of a particle cannot simultaneously be measured with exactness. This principle is valid because a particle has certain wave properties. The wave-particle duality theory made since after Einstein connected matter and energy.

Einstein taught us that matter is just another form of very, very condensed energy. Albert Einstein's theory into the equivalence of matter and energy, expressed as the famous equation: E=mc2, has been confirmed countless times. At the time, it was much easier to demonstrate light as a wave. The process also occurs naturally when a star shines because the atoms in its core fuse, transforming a very small sliver of matter into light. And when particles of matter and antimatter meet, they annihilate each other in a burst of energy. But like any equation, E=mc2 works both ways. Meaning that it should be possible to convert massive amounts of energy into small amounts of matter. A team of physicists has now transformed light into matter. “We're able to turn optical photons into matter,” says Princeton physicist Kirk McDonald, leader of the team. And physicists who smash atoms together have witnessed the conversion of energy into matter in virtual photons that flit in and out of existence just long enough to spawn the particles of exotic matter which can be observed in particle accelerators. But the photons formed like this are not under the direct control of physicists. The photons arise as part of a complex chain of events starting with just a collision of two particles of matter. Until now, no one had directly created matter from light. The key piece was a laser capable of packing a tremendous amount of energy into a small space. By focusing this pulse on an area of just 16-millionths of a square inch, the physicists bathe a spot with an incredibly intense electromagnetic field. But even with this crowd of high-power photons squeezed together, the energy is still only about a millionth of what's needed to make matter. The problem is that the laser's greenlight photons don’t provide enough force. Photons, which are massless, can sometimes siphon off part of the energy of a high-speed particle with mass. This occurs because the total energy of the particle, which includes its mass, may exceed that of the photon. The point of trying to make matter by combining energy in the form of photons is to prove that the light traveling as photons have a “mass”. Even though the mass is very small, it was made by just light.

 

Newton vs Huygens: a big controversy

http://www.studyphysics.ca/20/unit4/wavemodel/particlevwave/note.htm

 

During the later part of his life Newton got caught up in a very big debate… is light a particle or a wave.

Newton believed very strongly that it was a particle, and given that he was such an important scientist many people though he was right.

 

Newton would offer several pieces of evidence that light was a particle:

    1. Light travels in straight lines. When you throw something like a baseball, it doesn’t suddenly make a right turn and start going in another direction. Particles always move in straight lines, and light seems to move in straight lines.
    2. Light can travel through a vacuum. Waves need a substance, a medium, to move through. Sound travels through air, waves travel through water, etc. By Newton’s time they had a pretty good idea that the space between the earth and the sun was a vacuum, so how could light reach earth if it was a wave? If light is a particle it would have no trouble moving through a vacuum.

 

On the other side of the argument you had people like Christian Huygens, who although he was basically unknown, had a lot of carefully thought out physics to back up his claims that light was a wave.

Huygens had a tough job, since not only does he have to disprove Newton’s two main points, he also has to overcome the power that Newton has in the world of science.

  • Huygens focused most of his attack on the first point outlined above. He had to be able to show that light would diffract when it passed through openings or around obstacles.
    • He looked at the work of Francesco Grimaldi, who had shown the edges of shadows are not perfectly sharp. If light was a particle they should be. If light is a wave, we can explain that fuzziness as the diffraction of the waves partly around the object.

 

Huygens developed this idea further in order to explain the diffraction of waves around obstacles or through openings.

  • He said we should imagine the crest of a wave as being made up of an infinite number of tiny waves, which he called wavelets.
  • As these wavelets pass through an opening or an obstacle they will begin to spread out again… this is what leads to diffraction.
  • Latter, when Thomas Young showed that light does diffract and interfere when it passes through openings (which we will study shortly), Huygens had the proof he needed. Light was a wave.

 

There was still resistance to Huygen’s theories, mostly because Newton was such a famous scientist.

  • Huygens came up with a separate argument that would seem to indicate that the particle model is simply wrong.
  • When light hits the boundary between two media (like air and water) part of the light is transmitted (and refracts), while part of it is reflected.

  • Using a wave model of light Huygens was able to show that waves could do this. If you measure the amount of light reflected and the amount that was refracted, it adds up to the original wave.
  • When Newton was asked to explain this using his particle model of light, he came up with an… odd answer.
    • He said that when light particles reach the surface, they have “fits” (just like when you had a fit when you were 3 years old and you didn’t get what you wanted). Some of the particles “decide” to go into the water, while the rest “decide” to bounce off.
    • Given that this is such a pathetic response, Newton basically lost any remaining support that he had for his particle model of light.
  • In the end the wave model of light became the accepted model!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Early Greek ideas

In 55 BC Lucretius, continuing the ideas of earlier atomists, wrote that light and heat from the Sun were composed of minute particles.

10th century optical theory

The scientist Abu Ali al-Hasan ibn al-Haytham (965-c.1040), also known as Alhazen, developed a broad theory that explained vision, using geometry and anatomy, which stated that each point on an illuminated area or object radiates light rays in every direction, but that only one ray from each point, which strikes the eye perpendicularly, can be seen. The other rays strike at different angles and are not seen. He used the example of the pinhole camera, which produces an inverted image, to support his argument. Alhazen held light rays to be streams of minute particles that travelled at a finite speed. He improved Ptolemy's theory of the refraction of light. Alhazen's work did not become known in Europe until the late 16th century.

Particle theory

Pierre Gassendi, an atomist, proposed a particle theory of light which was published posthumously in the 1660s. Isaac Newton studied Gassendi's work at an early age, and preferred his view to Descartes' theory of the 'plenum'. He stated in his Hypothesis of Light of 1675 that light was composed of corpuscles (particles of matter) which were emitted in all directions from a source. One of Newton's arguments against the wave nature of light was that waves were known to bend around obstacles, while light travelled only in straight lines. He did, however, explain the phenomenon of the diffraction of light (which had been observed by Francesco Grimaldi) by allowing that a light particle could create a localised wave in the aether.

Newton's theory could be used to predict the reflection of light, but could only explain refraction by incorrectly assuming that light accelerated upon entering a denser medium because the gravitational pull was greater. Newton published the final version of his theory in his Opticks of 1704. His reputation helped the particle theory of light to dominate physics during the 18th century.

The 'plenum'

Descartes held that light was a disturbance of the 'plenum', the continuous substance of which the universe was composed. In 1637 he published a theory of the refraction of light which wrongly assumed that light travelled faster in a denser medium, by analogy with the behaviour of sound waves. Descartes' theory is often regarded as the forerunner of the wave theory of light.

Wave theory

In the 1660s Robert Hooke published a wave theory of light. Christian Huygens worked out his own wave theory of light in 1678, and published it in his Treatise on light in 1690. He proposed that light was emitted in all directions as a series of waves in a medium called the 'aether'. As waves are not affected by gravity, it was assumed that they slowed down upon entering a denser medium. The wave theory predicted that light waves could interfere with each other like sound waves (as noted in the 18th century by Thomas Young), and that light could be polarized. Young showed by means of a diffraction experiment that light behaved as waves. He also proposed that different colours were caused by different wavelengths of light, and explained colour vision in terms of three-coloured receptors in the eye.

Another supporter of the wave theory was Euler. He argued in Nova theoria lucis et colorum (1746) that diffraction could more easily be explained by a wave theory.

Later, Fresnel independently worked out his own wave theory of light, and presented it to the Académie des Sciences in 1817. Poisson added to Fresnel's mathematical work to produce a convincing argument in favour of the wave theory, helping to overturn Newton's corpuscular theory.

The weakness of the wave theory was that light waves, like sound waves, would need a medium for transmission. A hypothetical substance called the luminiferous aether was proposed, but its existence was later disproved.

Foucault's result in favour of the wave theory

Newton's corpuscular theory implied that light would travel faster in a denser medium, while the wave theory of Huygens and others implied the opposite. At that time, the speed of light could not be measured accurately enough to decide which theory was correct. The first to make a sufficiently accurate measurement was Léon Foucault, in 1850. His result supported the wave theory, and the classical particle theory was finally abandoned.

 

►Young Two-Slit Experiment

One of the most important experiments of wave theory is that of Young's double slits. It is a clear example of the diffraction of light conducted with essentially basic scientific equipment.

Thomas Young was a not only a physicist but also a physician and and Egyptologist, who was responsible for deciphering the Rosetta stone. He devised an experiment in the early 1800's that proved that light is a wave. The experiment has been used subsequently to show that wave behaviour exists in many other areas of nature and therefore it is worth spending a little time going into the experiment in detail.

When two light beams interact they create interference which can be constructive or destructive as we have discussed earlier. The places where constructive and destructive interference occur are subject to constant change, since em waves emitted are capable of varying phase. Using one light source and splitting it into two beams you can create two coherent sources, meaning they are of identical frequencies and have a constant phase difference (the distance between a peak of wave 1 and wave 2 is always the same) It is also important to use monochromatic light for this experiment as the location of interference occurs is wavelength dependent.

The apparatus consists of a source matching the above requirements, a screen with two very thin identical slits or the order of a wavelength in width, and a screen to view the interference on.

In principle, a light bulb, or lamp can be used, but the light must be reduced to a monochromtic source with filters. It can also be done by splitting the light into its various frequencies using a prism, a frequency can be selcted by channeling the light with a further screen with only a pin prick in it to allow the light out. These days lasers are used to provide the light source.

When the light is switched on, it travels up to the first screen and is split into two beams by the slits, we have seen that when this happens waves are diffracted and bulge outwards causing two curved wavefronts to propagate the other side of the slits, at many places between the slits and the viewing screen there are areas of constructive interference and by moving the viewing screen it is possible to get a picture of where they are occuring.

The two slit experiment is key to understand the microscopic world. The wave-like properties of light were demonstrated by the famous experiment first performed by Thomas Young in the early nineteenth century. In original experiment, a point source of light illuminates two narrow adjacent slits in a screen, and the image of the light that passes through the slits is observed on a second screen.

 

Electromagnetic theory

In 1845 Faraday discovered that the angle of polarisation of a beam of light as it passed through a polarising material could be altered by a magnetic field. This was the first evidence that light was related to electromagnetism. Faraday proposed in 1847 that light was a high-frequency electromagnetic vibration, which could propagate even in the absence of a medium such as the aether.

Faraday's work inspired James Clerk Maxwell to study electromagnetic radiation and light. Maxwell discovered that self-propagating electromagnetic waves would travel through space at a constant speed, which happened to be equal to the previously measured speed of light. From this, Maxwell concluded that light was a form of electromagnetic radiation. He first stated this in 1862 in On Physical Lines of Force. In 1873 he published Electricity and Magnetism, which contained a full mathematical description of the behaviour of electric and magnetic fields, still known as Maxwell's equations. The technology of radio transmission was, and still is, based on this theory.

The constant speed of light predicted by Maxwell's equations contradicted the mechanical laws of motion that had been unchallenged since the time of Galileo, which stated that all speeds were relative to the speed of the observer. A solution to this contradiction would later be found by Albert Einstein.

Quantum theory

This theory, described by Max Planck in 1900, described light as a particle that could exist in discrete amounts of energy only. These packets were called quanta, and the particle of light was given the name photon, to correspond with other particles being described around this time, such as the electron and proton. As it originally stood, this theory did not explain the simultaneous wave-like nature of light, though Planck would later work on theories that did. The Nobel Committee awarded Planck the Physics Prize in 1918 for his part in the founding of quantum theory.

 

E = hf= hc/l

 

Particle theory revisited

The wave theory was accepted until the late 19th century, when Albert Einstein described the photoelectric effect, by which light striking a surface caused elecrons to change their momentum, which indicated a particle-like nature of light. This clearly contradicted the wave theory, and for years physicists tried to rectify this contradiction without success.

 

► The Photoelectric Effect

Hertz Finds Maxwell's Waves: and Something Else

The most dramatic prediction of Maxwell's theory of electromagnetism, published in 1865, was the existence of electromagnetic waves moving at the speed of light, and the conclusion that light itself was just such a wave. This challenged experimentalists to generate and detect electromagnetic radiation using some form of electrical apparatus. The first clearly successful attempt was by Heinrich Hertz in 1886. He used a high voltage induction coil to cause a spark discharge between two pieces of brass, to quote him, "Imagine a cylindrical brass body, 3 cm in diameter and 26 cm long, interrupted midway along its length by a spark gap whose poles on either side are formed by spheres of 2 cm radius." The idea was that once a spark formed a conducting path between the two brass conductors, charge would rapidly oscillate back and forth, emitting electromagnetic radiation of a wavelength similar to the size of the conductors themselves.

To prove there really was radiation emitted, it had to be detected. Hertz used a piece of copper wire 1 mm thick bent into a circle of diameter 7.5 cm, with a small brass sphere on one end, and the other end of the wire was pointed, with the point near the sphere. He added a screw mechanism so that the point could be moved very close to the sphere in a controlled fashion. This "receiver" was designed so that current oscillating back and forth in the wire would have a natural period close to that of the "transmitter" described above. The presence of oscillating charge in the receiver would be signalled by a spark across the (tiny) gap between the point and the sphere (typically, this gap was hundredths of a millimetre). (It was suggested to Hertz that this spark gap could be replaced as a detector by a suitably prepared frog's leg, but that apparently didn't work.)

The experiment was very successful - Hertz was able to detect the radiation up to fifty feet away, and in a series of ingenious experiments established that the radiation was reflected and refracted as expected, and that it was polarized. The main problem - the limiting factor in detection -- was being able to see the tiny spark in the receiver. In trying to improve the spark's visibility, he came upon something very mysterious. To quote from Hertz again (he called the transmitter spark A, the receiver B): "I occasionally enclosed the spark B in a dark case so as to more easily make the observations; and in so doing I observed that the maximum spark-length became decidedly smaller in the case than it was before. On removing in succession the various parts of the case, it was seen that the only portion of it which exercised this prejudicial effect was that which screened the spark B from the spark A. The partition on that side exhibited this effect, not only when it was in the immediate neighbourhood of the spark B, but also when it was interposed at greater distances from B between A and B. A phenomenon so remarkable called for closer investigation."

Hertz then embarked on a very thorough investigation. He found that the small receiver spark was more vigorous if it was exposed to ultraviolet light from the transmitter spark. It took a long time to figure this out - he first checked for some kind of electromagnetic effect, but found a sheet of glass effectively shielded the spark. He then found a slab of quartz did not shield the spark, whereupon he used a quartz prism to break up the light from the big spark into its components, and discovered that the wavelength which made the little spark more powerful was beyond the visible, in the ultraviolet.

In 1887, Hertz concluded what must have been months of investigation: "… I confine myself at present to communicating the results obtained, without attempting any theory respecting the manner in which the observed phenomena are brought about."

Hallwachs' Simpler Approach

The next year, 1888, another German physicist, Wilhelm Hallwachs, in Dresden, wrote:

"In a recent publication Hertz has described investigations on the dependence of the maximum length of an induction spark on the radiation received by it from another induction spark. He proved that the phenomenon observed is an action of the ultraviolet light. No further light on the nature of the phenomenon could be obtained, because of the complicated conditions of the research in which it appeared. I have endeavored to obtain related phenomena which would occur under simpler conditions, in order to make the explanation of the phenomena easier. Success was obtained by investigating the action of the electric light on electrically charged bodies."

He then describes his very simple experiment: a clean circular plate of zinc was mounted on an insulating stand and attached by a wire to a gold leaf electroscope, which was then charged negatively. The electroscope lost its charge very slowly. However, if the zinc plate was exposed to ultraviolet light from an arc lamp, or from burning magnesium, charge leaked away quickly. If the plate was positively charged, there was no fast charge leakage. (We showed this as a lecture demo, using a UV lamp as source.)

Questions for the reader: Could it be that the ultraviolet light somehow spoiled the insulating properties of the stand the zinc plate was on? Could it be that electric or magnetic effects from the large current in the arc lamp somehow caused the charge leakage?

Although Hallwach's experiment certainly clarified the situation, he did not offer any theory of what was going on.

J.J. Thomson Identifies the Particles

In fact, the situation remained unclear until 1899, when Thomson established that the ultraviolet light caused electrons to be emitted, the same particles found in cathode rays. His method was to enclose the metallic surface to be exposed to radiation in a vacuum tube, in other words to make it the cathode in a cathode ray tube. The new feature was that electrons were to be ejected from the cathode by the radiation, rather than by the strong electric field used previously.

By this time, there was a plausible picture of what was going on. Atoms in the cathode contained electrons, which were shaken and caused to vibrate by the oscillating electric field of the incident radiation. Eventually some of them would be shaken loose, and would be ejected from the cathode. It is worthwhile considering carefully how the number and speed of electrons emitted would be expected to vary with the intensity and color of the incident radiation. Increasing the intensity of radiation would shake the electrons more violently, so one would expect more to be emitted, and they would shoot out at greater speed, on average. Increasing the frequency of the radiation would shake the electrons faster, so might cause the electrons to come out faster. For very dim light, it would take some time for an electron to work up to a sufficient amplitude of vibration to shake loose.

Lenard Finds Some Surprises

In 1902, Lenard studied how the energy of the emitted photoelectrons varied with the intensity of the light. He used a carbon arc light, and could increase the intensity a thousand-fold. The ejected electrons hit another metal plate, the collector, which was connected to the cathode by a wire with a sensitive ammeter, to measure the current produced by the illumination. To measure the energy of the ejected electrons, Lenard charged the collector plate negatively, to repel the electrons coming towards it. Thus, only electrons ejected with enough kinetic energy to get up this potential hill would contribute to the current. Lenard discovered that there was a well defined minimum voltage that stopped any electrons getting through, we'll call it Vstop. To his surprise, he found that Vstop did not depend at all on the intensity of the light! Doubling the light intensity doubled the number of electrons emitted, but did not affect the energies of the emitted electrons. The more powerful oscillating field ejected more electrons, but the maximum individual energy of the ejected electrons was the same as for the weaker field.

But Lenard did something else. With his very powerful arc lamp, there was sufficient intensity to separate out the colors and check the photoelectric effect using light of different colors. He found that the maximum energy of the ejected electrons did depend on the color --- the shorter wavelength, higher frequency light caused electrons to be ejected with more energy. This was, however, a fairly qualitative conclusion --- the energy measurements were not very reproducible, because they were extremely sensitive to the condition of the surface, in particular its state of partial oxidation. In the best vacua available at that time, significant oxidation of a fresh surface took place in tens of minutes. (The details of the surface are crucial because the fastest electrons emitted are those from right at the surface, and their binding to the solid depends strongly on the nature of the surface --- is it pure metal or a mixture of metal and oxygen atoms?)

Question: In the above figure, the battery represents the potential Lenard used to charge the collector plate negatively, which would actually be a variable voltage source. Since the electrons ejected by the blue light are getting to the collector plate, evidently the potential supplied by the battery is less than Vstop for blue light. Show with an arrow on the wire the direction of the electric current in the wire.

 

Einstein Suggests an Explanation

In 1905 Einstein gave a very simple interpretation of Lenard's results. He just assumed that the incoming radiation should be thought of as quanta of frequency hf, with f the frequency. In photoemission, one such quantum is absorbed by one electron. If the electron is some distance into the material of the cathode, some energy will be lost as it moves towards the surface. There will always be some electrostatic cost as the electron leaves the surface, this is usually called the work function, W. The most energetic electrons emitted will be those very close to the surface, and they will leave the cathode with kinetic energy

E = hf - W.

On cranking up the negative voltage on the collector plate until the current just stops, that is, to Vstop, the highest kinetic energy electrons must have had energy eVstop on leaving the cathode. Thus,

eVstop = hf - W

Thus Einstein's theory makes a very definite quantitative prediction: if the frequency of the incident light is varied, and Vstop plotted as a function of frequency, the slope of the line should be h/e.

It is also clear that there is a minimum light frequency for a given metal, that for which the quantum of energy is equal to the work function. Light below that frequency , no matter how bright, will not cause photoemission.

Millikan's Attempts to Disprove Einstein's Theory

If we accept Einstein's theory, then, this is a completely different way to measure Planck's constant. The American experimental physicist Robert Millikan, who did not accept Einstein's theory, which he saw as an attack on the wave theory of light, worked for ten years, until 1916, on the photoelectric effect. He even devised techniques for scraping clean the metal surfaces inside the vacuum tube. For all his efforts he found disappointing results: he confirmed Einstein's theory, measuring Planck's constant to within 0.5% by this method. One consolation was that he did get a Nobel prize for this series of experiments.

► The Compton Effect

As learned on the preceding pages, Einstein proposed the hypothesis of light quanta and succeeded in the explanation of the photoelectric effect. As a result, it has been established that light exists in the space as grains (or corpuscles or particles) with energy hf. The particle nature or corpuscular nature of light was more firmly established by the discovery of the Compton effect.
In 1923, A. H. Compton (USA, 1892 - 1962) discovered that the scattering of X rays by a crystal can be explained well on the basis of the particle nature of light. (Of course, the phenomenon that X rays are scattered by crystals had been well-known before.)

The scattering of X rays by a particle (an electron at present) is sometimes called Compton scattering. Compton found that, if we consider that X rays collide with the electrons in a crystal as if they were balls of billiard, Compton scattering could be explained well. To formulate this process, we have to define the momentum of a light quantum.

Momentum of a Light Quantum

It has been discussed that a light quantum is a "particle" with energy hf. This "particle" is considered to carry a momentum at the same time, because we know that light gives a pressure on the surrounding wall. How large is the amount of the momentum? Let us study this below.

Consider a container filled with light of frequency f. Let the pressure given on the wall of the container by the light be P and the energy of the light per unit volume be U. We have a relation

which is proved by experiment. (This relation can also be derived from the classical theory.) From this relation, we see that the momentum p of a light quantum is given as p=hn/c=h/l
Namely, we can say that the momentum of a light quantum is given by dividing the energy by the light speed.

This result can be obtained by a method similar to that through which we derived the relation between the molecular motion in a gas and its pressure.

The Compton Effect by the Hypothesis of Light Quanta

 Compton found that, when the monochromatic X rays are illuminated on a graphite (a kind of carbon crystal), the wavelength of the scattered X rays would be longer as the scattering angle becomes larger. This cannot be explained with the classical theory.

In the classical theory consisting of Newtonian mechanics and Maxwellian electromagnetism, the incident X rays oscillate the charged particle (electron at present) and the oscillating charged particle radiates around the same frequency of electromagnetic waves (X rays). Accordingly, the frequency of the radiated (scattered) X rays must be the same as that of the incident X rays.
Compton analyzed Compton scattering as follows. He thought that the incident X rays collide against the electron in the graphite as a "particle" with the energy hn. and the momentum hn/c. Suppose that the energy and the momentum of the X rays scattered in the scattering angle are and , respectively.
The electron (the mass = m ) recoils with a momentum mv. The energies and momenta in Compton scattering are shown in the following figure (A), and the relation of the momentum conservation is in the following figure (B).

 
The momentum conservation relation is written

 

Since , we have

 
Inserting this into the above momentum conservation relation, we get

 

On the other hand, the energy conservation is written

 

Therefore, the difference between the the wavelength of the incident and scattered X rays becomes

 

Accordingly, the wavelength of the scattered X rays becomes longer as the scattering angle increases.
Compton's results at the scattering angles, and , are shown in the following figure. Each graph represents the intensity of X rays (ordinate) as a function of wavelength (abscissa).

As the scattering angle increases in the above figure, the intensity of X rays separates into two peaks; the right one of the longer wavelength shifts to longer region. This wavelength is well fit to the formula presented above.

The wavelength of another peak is just the same as that of the incident X-ray beam. This is that scattered by the whole atom whose mass is quite large, so that the wavelength seems not to be varied.
Thus the particle nature of X rays was completely confirmed.

Incidentally, the recoil electron could not be detected in Compton's experiment, but, a little bit later, its picture was taken with Wilson's cloud chamber.

Photon
After Einstein proposed the hypothesis of light quanta in 1905, people have been doubtful of the idea of the particle nature of light for about 20 years. However, once they look at the experimental results of the Compton effect, they cannot help convincing themselves about the theory of light quanta. Then, the particle of light (light quantum) has been called photon, which has been admitted into the brotherhood of "particles" like electrons or protons.

Wave-particle duality

This is the modern theory that explains the nature of light, and in fact of all particles. It was described by Albert Einstein in the early 1900s, based on his work on the photoelectric effect, as well as Planck's results. Einstein determined that the energy of a photon is proportional to its frequency. More generally, the theory states that everything has both a particle nature, and a wave nature, and various experiments can be done to bring out one or the other. The particle nature is more easily discerned if an object has a large mass, so it took until an experiment by Louis de Broglie in 1924 to realise that electrons also exhibited wave-particle duality. Einstein received the Nobel Prize in 1921 for his work with the wave-particle duality on photons, and de Broglie followed in 1929 for his extension to other particles.

 

l = h/p

The propagation of light is governed by its wave properties, whereas the exchange of energy between light and matter is governed by its particle properties. This wave-particle duality is a general property of nature. For example, the propagation of electrons (and other so-called particles) is also governed by wave properties, whereas the exchange of energy between the electrons and other particles is governed by particle properties.

 

 

 

 

 

 

 

The study of light and the interaction of light and matter is termed optics. The observation and study of optical phenomena such as rainbows offers many clues as to the nature of light as well as much enjoyment.

The speed of light

See speed of light. Although some people speak of the "velocity of light", the word velocity should be reserved for vector quantities (i.e. those associated with a direction). The speed of light is a scalar quantity (i.e. it has no direction), and therefore speed is the correct term.

Speed-of-light formula

v =l f where l is the wavelength, f is the frequency, v is the speed of the light. If the light is travelling in a vacuum, then v = c, thus c =l f

where c is the speed of light. We can express v as v =c/n

where n is a constant (the refractive index) which is a property of the material through which the light is passing.

Changes in the speed of light

All light propagates at a finite speed. Even moving observers always measure the same value of c, the speed of light in vacuum, as c = 299,792,458 metres per second (186,282.397 miles per second); however, when light passes through a transparent substance such as air, water or glass, its speed is reduced, and it suffers refraction. Thus, n=1 in a vacuum and n>1 in matter.

History of the measurement of the speed of light

The speed of light has been measured many times, by many physicists. The best early measurement is Olaus Roemer's (a Danish physicist), in 1676. He had developed a method for measuring light. He observed and noted the motions of Jupiter and one of its moonss with a telescope. It was possible to time the revolution of the moon because it was eclipsed by Jupiter at regular intervalss. Roemer discovered that the moon revolved around Jupiter once every 42-1/2 hours when Earth was closest to Jupiter. The problem was that when Earth and Jupiter were not as close, the moon's revolution seemed to be more. It was clear that light took longer to reach Earth when it was farther away from Jupiter. The speed of light was calculated by analyzing the distance between the two planets at various times. Roemer reached a speed of 227,000 kilometers per second (approximately 141,050 miles per second).

Albert A. Michelson improved on Roemer's work in 1926. He used rotating mirrors to measure the time it took light to make a round trip from Mt. Wilson to Mt. San Antonio in California. The precise measurements yielded a speed of 186,285 miles/second (299,796 kilometers/second). In daily use, the figures are rounded off to 186,000 mi/s and 300,000 km/s.

Color and wavelengths

The different wavelengths are interpreted by the human brain as colors, ranging from red at the longest wavelengths (lowest frequencies) to violet at the shortest wavelengths (highest frequencies). The intervening frequencies are seen as orange, yellow, green, blue, and, conventionally, indigo. The frequencies of the spectrum immediately outside the range the human eye is able to perceive are called ultraviolet (UV) at the high frequency end and infrared (IR) at the low. Though humans cannot see IR, we do perceive it by receptors in the skin as heat. Cameras that can pick up IR and convert it to visible light are called night-vision cameras. UV radiation is not perceived by humans at all except in a very delayed fashion, as overexposure of the skin to UV light causes sunburn, or skin cancer. Some animals, such as bees, can see UV radiation while others, such as pit viper snakes, can see IR using pits in their heads.

Measurement of light

The following quantities and units are used to measure light.

  • brightness (or temperature)
  • illuminance or illumination (SI unit: lux)
  • luminous flux (SI unit: lumen)
  • luminous intensity (SI unit: candela)

 

 

 

Propagation of Light

Visible light is a narrow part of the electromagnetic spectrum and in a vacuum all electromagnetic radiation travels at the speed of light:

The above number is now accepted as a standard value and the value of the meter is defined to be consistent with it. In a material medium the effective speed of light is slower and is usually stated in terms of the index of refraction of the medium. Light propagation is affected by the phenomena refraction, reflection, diffraction, and interference.

The behaviour of light in optical systems will be characterized in terms of its vergence.

Reflection

Light incident upon a surface will in general be partially reflected and partially transmitted as a refracted ray. The angle relationships for both reflection and refraction can be derived from Fermat's principle. The fact that the angle of incidence is equal to the angle of reflection is sometimes called the "law of reflection".

 

Law of Reflection

A light ray incident upon a reflective surface will be reflected at an angle equal to the incident angle. Both angles are typically measured with respect to the normal to the surface. This law of reflection can be derived from Fermat's principle.

The law of reflection gives the familiar reflected image in a plane mirror where the image distance behind the mirror is the same as the object distance in front of the mirror.

Fermat's Principle:Reflection

Fermat's Principle: Light follows the path of least time. The law of reflection can be derived from this principle as follows:

The pathlength from A to B is

Since the speed is constant, the minimum time path is simply the minimum distance path. This may be found by setting the derivative of L with respect to x equal to zero.

Refraction

Refraction is the bending of a wave when it enters a medium where it's speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell's Law.

Refraction is responsible for image formation by lenses and the eye.

 

As the speed of light is reduced in the slower medium, the wavelength is shortened proportionately. The frequency is unchanged; it is a characteristic of the source of the light and unaffected by medium changes.

Fermat's Principle and Refraction

Fermat's Principle: Light follows the path of least time.

 Snell's Law can be derived from this by setting the derivative of the time =0.

 

Snell's Law

Snell's Law relates the indices of refraction n of the two media to the directions of propagation in terms of the angles to the normal. Snell's law can be derived from Fermat's Principle or from the Fresnel Equations.

If the incident medium has the larger index of refraction, then the angle with the normal is increased by refraction. The larger index medium is commonly called the "internal" medium, since air with n=1 is usually the surrounding or "external" medium. You can calculate the condition for total internal reflection by setting the refracted angle = 90° and calculating the incident angle. Since you can't refract the light by more than 90°, all of it will reflect for angles of incidence greater than the angle which gives refraction at 90°.

Total Internal Reflection

When light is incident upon a medium of lesser index of refraction, the ray is bent away from the normal, so the exit angle is greater than the incident angle. Such reflection is commonly called "internal reflection". The exit angle will then approach 90° for some critical incident angle qc , and for incident angles greater than the critical angle there will be total internal reflection.

The critical angle can be calculated from Snell's law by setting the refraction angle equal to 90°. Total internal reflection is important in fiber optics and is employed in polarizing prisms.

For any angle of incidence less than the critical angle, part of the incident light will be transmitted and part will be reflected. The normal incidence reflection coefficient can be calculated from the indices of refraction. For non-normal incidence, the transmission and reflection coefficients can be calculated from the Fresnel equations.

Index of Refraction

The index of refraction is defined as the speed of light in vacuum divided by the speed of light in the medium.

The indices of refraction of some common substances are given below with a more complete description of the indices for optical glasses given elsewhere. The values given are approximate and do not account for the small variation of index with light wavelength which is called dispersion.

Mirrors in Imaging

Mirrors are used widely in optical instruments for gathering light and forming images since they work over a wider wavelength range and do not have the problems of dispersion which are associated with lenses and other refracting elements.

Mirror Instruments

Mirrors are widely used in telescopes and telephoto lenses. They have the advantage of operating over a wider range of wavelengths, from infrared to ultraviolet and above. They avoid the chromatic aberration arising from dispersion in lenses, but are subject to other aberrations. Instruments which use only mirrors to form images are called catoptric systems, while those which use both lenses and mirrors are called catadioptric systems (dioptric systems being those with lenses only).

Mirror Geometry

Convex Mirror Image

A convex mirror forms a virtual image.

Using a ray parallel to the principal axis and one incident upon the center of the mirror, the position of the image can be constructed by back-projecting the rays which reflect from the mirror. The virtual image that is formed will appear smaller and closer to the mirror than the object.

Concave Mirror Image

If the object is outside the focal length, a concave mirror will form a real, inverted image.

Spherical Mirror Equation

The equation for image formation by rays near the optic axis (paraxial rays) of a mirror has the same form as the thin lens equation:

From the geometry of the spherical mirror, note that the focal length is half the radius of curvature:

As in the case of lenses, the cartesian sign convention is used here, and that is the origin of the negative sign above. The radius r for a concave mirror is a negative quantity (going left from the surface), and this gives a positive focal length, implying convergence.

 

Lens in Imaging

Thin Lenses

In order to understand lenses, one must first define some terms.

  • The Focal point is the location at which rays parallel to the optical axis of an ideal mirror or lens converges to a point.
  • The focal length is the distance between the focal point and the middle of the lens.  It will be represented by F.  You will also see 2F being mentioned.  2F just refers to two times the focal length.
  • The distance from the center of the lens to the object will be referred to as do.
  • The distance from the center of the lens to the image will be referred to as di.
  • A Real Image is an optical image at which rays from the object converge.  It is inverted or flipped upside down.
  • A Virtual Image is a point from which Light rays appear to converge without actually doing so.  It is upright or in the same direction as the object.
  • A concave lens is a lens thinner in center than edges and is diverging.
  • A convex lens is a lens thicker in the center than at the edges and is converging. 

Principal Focal Length

For a thin double convex lens, all parallel rays will be focused to a point referred to as the principal focal point. The distance from the lens to that point is the principal focal length f of the lens. For a double concave lens where the rays are diverged, the principal focal length is the distance at which the back-projected rays would come together and it is given a negative sign. The lens strength in diopters is defined as the inverse of the focal length in meters. For a thick lens made from spherical surfaces, the focal distance will differ for different rays, and this change is called spherical aberration. The focal length for different wavelengths will also differ slightly, and this is called chromatic aberration.

The principal focal length of a lens is determined by the index of refraction of the glass, the radii of curvature of the surfaces, and the medium in which the lens resides. It can be calculated from the lens-maker's formula for thin lenses.

Focal Length and Lens Strength

The most important characteristic of a lens is its principal focal length, or its inverse which is called the lens strength or lens "power". Optometrists usually prescribe corrective lenses in terms of the lens power in diopters. The lens power is the inverse of the focal length in meters: the physical unit for lens power is 1/meter which is called diopter.

 

Image Formation

Thin Lens Equation

A common Gaussian form of the lens equation is shown below. This is the form used in most introductory textbooks. A form using the Cartesian sign convention is often used in more advanced texts because of advantages with multiple-lens systems and more complex optical instruments. Either form can be used with positive or negative lenses and predicts the formation of both real and virtual images. Does not apply to thick lenses.

If the lens equation yields a negative image distance, then the image is a virtual image on the same side of the lens as the object. If it yields a negative focal length, then the lens is a diverging lens rather than the converging lens in the illustration. The lens equation can be used to calculate the image distance for either real or virtual images and for either positive on negative lenses. The linear magnification relationship allows you to predict the size of the image.

Thin-Lens Equation:Cartesian Convention

The thin-lens equation in the Gaussian form is

 

where the Cartesian sign convention has been used. The lens equation is also sometimes expressed in the Newtonian form. The derivation of the Gaussian form proceeds from triangle geometry. For a thin lens, the lens power P is the sum of the surface powers. For thicker lenses, Gullstrand's equation can be used to get the equivalent power.

Cartesian Sign Convention

  1. All figures are drawn with light traveling from left to right.
  2. All distances are measured from a reference surface, such as a wavefont or a refracting surface. Distances to the left of the surface are negative.
  3. The refractive power of a surface that makes light rays more convergent is positive. The focal length of such a surface is positive.
  4. The distance of a real object is negative.
  5. The distance of a real image is positive.
  6. Heights above the optic axis are positive.
  7. Angles measured clockwise from the optic axis are negative.

Because the direction of light travel is consistent and there is a consistent convention to determine the sign of all distances in a calculation, this sign convention is used in many texts. It has some advantages when dealing with multilens systems and more complex optical instruments.

Magnification:Transverse &Angular

The linear magnification or transverse magnification is the ratio of the image size to the object size. If the image and object are in the same medium it is just the image distance divided by the object distance.

The negative sign is used on the linear magnification equation as a reminder that all real images are inverted. If the image is virtual, the image distance will be negative, and the magnification will therefore be positive for the erect image.

If the media are different on the two sides of the surface or lens, the magnification is not quite so straigtforward. It can be variously expressed as

In this equation V is the vergence, n is the index of refraction, and u is used for the angle.

The angular magnification of an instrument is the ratio of the angle subtended at the eye when using the instrument divided by the angular size without the instrument. An important example is the simple magnifier. The angular magnification of any optical system can be obtained from the system matrix for the system.

Real Image Formation

If a luminous object is placed at a distance greater than the focal length away from a convex lens, then it will form an inverted real image on the opposite side of the lens. The image position may be found from the lens equation or by using a ray diagram.

 

If the lens equation yields a negative image distance, then the image is a virtual image on the same side of the lens as the object. If it yields a negative focal length, then the lens is a diverging lens rather than the converging lens in the illustration. The lens equation can be used to calculate the image distance for either real or virtual images and for either positive on negative lenses. The linear magnification relationship allows you to predict the size of the image.

Virtual Image Formation

 

A virtual image is formed at the position where the paths of the principal rays cross when projected backward from their paths beyond the lens. Although a virtual image does not form a visible projection on a screen, it is no sense "imaginary", i.e., it has a definite position and size and can be "seen" or imaged by the eye, camera, or other optical instrument.

 

A reduced virtual image if formed by a single negative lens regardless of the object position. An enlarged virtual image can be formed by a positive lens by placing the object inside the principal focal point.

Diverging lenses form reduced, erect, virtual images. Using the common form of the lens equation, f, P and i are negative quantities.

The lens equation can be used to calculate the image distance for either real or virtual images and for either positive on negative lenses. The linear magnification relationship allows you to predict the size of the image.


Light Absorption

Light passing through an optical system can be attenuated by absorption and by scattering. The exponential law of absorption is the basic working relationship, but specific terms such as absorbance, absorptivity, and transmittance are widely used.

The differential absorption can be expressed as

which upon integration from 0 to x gives the exponential law of absorption:

If the absorbing medium is a solution, the concentration c is included and the law becomes

 

Optical Instruments

Prisms

A refracting prism is a convenient geometry to illustrate dispersion and the use of the angle of minimum deviation provides a good way to measure the index of refraction of a material. Reflecting prisms are used for erecting or otherwise changing the orientation of an image and make use of total internal reflection instead of refraction.

 

 

White light may be separated into its spectral colors by dispersion in a prism.

Prisms are typically characterized by their angle of minimum deviation d. This minimum deviation is achieved by adjusting the incident angle until the ray passes through theprism parallel to the bottom of the prism.

An interesting application of refraction of light in a prism occurs in atmospheric optics when tiny hexagonal ice crystals are in the air. This refraction produces the 22° halo commonly observed in northern latitudes. The fact that these ice crystals will preferentially orient themselves horizontally when falling produces a brighter part of the 22° halo horizontally to both sides of the sun; these bright spots are commonly called "sundogs".

The angle of minimum deviation for a prism may be calculated from the prism equation. Note from the illustration that this minimum deviation occurs when the path of the light inside the prism is parallel to the base of the prism. If the incident light beam is rotated in either direction, the deviation of the light from its incident path caused by refraction in the prism will be greater.

White light may be separated into its spectral colors by dispersion in a prism.

 

 

 

Double Slit Interference

Polarization by Reflection

Polarization by Scattering

The scattering of light off air molecules produces linearly polarized light in the plane perpendicular to the incident light. The scatterers can be visualized as tiny antennae which radiate perpendicular to their line of oscillation. If the charges in a molecule are oscillating along the y-axis, it will not radiate along the y-axis. Therefore, at 90° away from the beam direction, the scattered light is linearly polarized. This causes the light which undergoes Rayleigh scattering from the blue sky to be partially polarized.

 

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