Unit 2 - Nature of Light Lessons Back to Physics 11

                                                                                                                                                                                     

Lesson 1: The Nature of Light and Newton's Corpuscular Theory

Lesson 2: Determining the Speed of Light

Lesson 3: The Wave Theory of Light

Lesson 4: Young's Experiment

Lesson 5: The Photoelectric Effect and the Wave-Particle Duality

Lesson 1: The Nature of Light and Newton's Corpuscular Theory

Introduction

In this first lesson we outline several historical models to explain the nature of light. For centuries there has existed a debate about whether the properties of light could best be explained using a particle model of light or a wave model. We will begin with theories proposed by the early Greeks, then those proposed in the 17th century, and finally the debate of the 19th century. We will focus mainly on Newton’s corpuscular theory of light and at the end of the lesson reflect on the cautions we must take in accepting the theories of eminent scientists.

The Nature of Light: Early Greece to 20th Century

Early models of light were concerned with the source of light. Did light originate in the eyes or did objects emit light? The earliest views on the nature of light came to us from the Greeks. Plato thought that light consisted of “streamers” or filaments, emitted by the eye, and that when these streamers came in contact with an object, it was possible to see the object. Euclid agreed with Plato with the argument “How else can we explain that we do not see a needle on the floor until our eyes fall on it?” Plato’s theory can be referred to as a tactile theory based on the ability of the eye to “touch objects.”

Not all Greeks agreed with Plato. The Pythagoreans believed that light travelled as a stream of fast-moving particles. According to this emission theory, objects sent out

light beams or particles that would ricochet off objects and enter the eye. One Greek, Empedocles believed that light travelled as a wave-like disturbance. So as early as ancient Greece we see a debate between a particle theory of light and a wave theory.

By the 17th century, these apparently contradictory views of the nature of light placed scientists in two camps. Newton was the principal advocate of the particle, or corpuscular theory. He was supported by the French mathematician, physicist, and astronomer La Place. Newton’s theory stated that light consisted of particles that travelled in straight lines. The wave theory, which supports the idea that light has wave-like properties, was supported principally by Christiaan Huygens of Holland, also a mathematician, physicist, and astronomer. He, in turn, was supported by Robert Hooke of England, president of the Royal Society and a vigorous personal opponent of Newton. Because of the plausibility of both theories, a scientific debate developed between the followers of Newton and the followers of Huygens that continued for more than a century. By the late 19th century, however, there appeared to be overwhelming evidence that the nature of light could be explained much better using the wave model.

At the end of the 19th century, James Clerk Maxwell combined electricity, magnetism, and light into one theory. He called his theory the electromagnetic theory of light. According to Maxwell, light was an electromagnetic wave with the same properties as other electromagnetic waves. Maxwell’s theory, however, was not able to explain all the properties of light including one called the photoelectric effect. In 1900 Max Planck, proposed the quantum hypothesis suggesting that light was transmitted and absorbed in small bundles of energy called “quanta.” Albert Einstein agreed with Planck’s theory and explained the photoelectric effect using the particle model of light. The theory of quantum mechanics, developed over several years in the early 1900s, combines the two major theories of light suggesting that light does not always behave as a particle and light does not always behave as a wave.

Recall in the previous module the discussion of scientific models and theories. Their function is to explain the known properties of a phenomenon, and to predict new behaviour or new properties. As we study the theories of light, keep in mind these characteristics of theories and how they are illustrated in this history.

Newton's Corpuscular Theory and Rectilinear Propagation

Newton built on an earlier theory proposed by Descartes that imagined light consisting of streams of tiny particles called “corpuscles.” These particles shot out like bullets from the light source. This theory is referred to as the corpuscular theory of light. There were various arguments that could be used to support the particle theory.

One argument was the rectilinear propagation of light, that is, light travels in straight lines. We can see this effect when sunlight passes through clouds forming straight “rays.” We can also see sharp shadows cast by sunlight when large objects such as buildings intercept the sunlight. Newton also commented on the fact that the speed of light must be very large. When a ball is thrown at some angle, we can clearly see that it follows a curved path. If a cannon ball or bullet is fired at the same angle, there is less of a curve over the same distance because it is moving faster. Since the path of light has no noticeable curve, Newton argued that the speed of light must be extremely high. He also argued that since light does not exert any noticeable pressure, the mass of the particles must be extremely small.

The diagram below represents a light bulb in the centre. Newton imagined tiny particles shooting out from the source. The particles spread out evenly in all directions, and all are moving at the same very fast speed.

It is because light moves in straight lines that Newton rejected the wave theory of

light. Newton was of the opinion that a wave should spread out a great deal as it passes through an opening, filling almost the whole region beyond the opening. He felt that waves could not possibly produce a narrow beam. Yet we know that it is possible to produce narrow beams made up of waves. In our earlier studies with waves, we saw that when the opening is large compared to the wavelength, that the diffraction is not great and the beam is relatively straight. Unfortunately, neither Newton nor anyone else knew very much about waves at that time.

Newton's Corpuscular Theory and Reflection

When light falls on the smooth surface of a mirror, it reflects in such a way that the angle the incoming light beam makes with the surface (the angle of incidence, θi) is equal to the angle the reflected beam makes with the surface (the angle of reflection,

θr). Newton demonstrated that very hard spheres collide with very hard surfaces in a similar manner. He was also able to show that under ideal conditions, the speed of the sphere when it reflects from the surface (vf) is equal to the speed it had when it approached the surface (vi). This kind of a collision is called an elastic collision and will be studied later in our course. Thus Newton’s corpuscular theory was able to explain reflection.

Newton's Corpuscular Theory and Refraction

When light passes from air into water, it bends, or refracts, towards the normal. Light beams will always refract towards the normal when they pass from a less dense to a more dense material.

Newton was able to explain this effect using the corpuscular theory. We can imagine a ball rolling down a ramp from a raised horizontal surface to a lower horizontal surface. When this happens, the ball also bends towards the normal.

Newton believed that water attracts approaching particles of light in much the same way that gravity attracts a rolling ball on an incline. The rolling ball model implies that light particles accelerate as they pass from air into a denser medium (one with a higher index of refraction) such as glass or water. Newton predicted that the speed of light in water would be greater than the speed of light in air. At the time of Newton, the speed of light in water was not known. It was not until 123 years later after Newton’s death, in 1850, that the French physicist, Jean Foucault (1819-1868),

demonstrated experimentally that the speed of light in water is actually less than the speed of light in air, the reverse of that predicted by the particle theory.

 

Newton's Corpuscular Theory and Dispersion

When white light passes through a prism, the light is refracted by different amounts, and the colours of the spectrum result. This is called dispersion. This phenomenon has been known since the time of the ancient Egyptians. It wasn’t until 1666 that Newton investigated this phenomenon systematically.

           

 

To explain dispersion using the corpuscular theory, Newton hypothesized that each particle of the spectrum had a different mass. Since violet particles are refracted more than blue, Newton argued that the violet particles must have a smaller mass than the blue. This is so because smaller masses are diverted more easily. So for example, the blue particles would be diverted more than the green because the green are more massive than the blue, and so on, to red light. The particles that correspond to the red light have the largest mass in the visible spectrum.

Newton’s corpuscular theory provided a satisfactory explanation for four properties of light: rectilinear (straight line) propagation, reflection, refraction, and dispersion. It was weak in its explanation of other effects such as diffraction, partial reflection, and partial refraction. Considering the evidence available to Newton, his hypothesis was

valid. In its day, it was superior to the competing wave theory of light because it used the laws of mechanics that had been proven to be valid in other areas of physics. When new evidence became available that could not be explained using Newton’s corpuscular theory, this was bound to give stronger support to the wave theory. However, Newton’s stature and authority was so great that the corpuscular theory of light dominated for over a century. In fact, Newton’s successors adhered to the corpuscular theory of light more strongly than Newton ever did himself.

Newton recognized that the experimental evidence was not strong enough for either particles or waves. Although he preferred the particle theory, he was not dogmatic about it. He considered both theories to be hypotheses, that is, they required further testing.

The lesson to be learned from Newton’s example is that theories, or any pronouncements, of esteemed, famous people should be evaluated on the basis of the supporting evidence. A theory should not be accepted simply because it is put forward by an eminent person.

Difficulties with Newton's Corpuscular Theory

Newton’s corpuscular theory had difficulty explaining some of the properties of light. We learned in our earlier work that waves undergo diffraction, that is the bending of waves as they pass around a barrier or through an opening. Newton believed that light travels in straight lines and does not travel “around a corner.” In making this statement, Newton discounted the work of Francesco Grimaldi (1618-1663) who showed that a beam of light passing through two successive narrow slits produced on a screen a band of light slightly larger than the width of the slits. Grimaldi believed that the beam had been bent slightly outward at the edges of the second aperture. It was Newton’s position that this effect resulted from the interactions and collisions between the light particles at the edges of the slit.

When light refracts (bends as it passes into a different medium), some of the light is reflected. Newton had difficulty explaining the phenomenon of partial reflection and partial refraction using the corpuscular theory. Newton’s explanation was the so-called “theory of fits”: particles of light arrived at the surface sometimes in a “fit” of

easy reflection and sometimes in a “fit” of easy refraction. This was obviously a weak explanation, as Newton himself recognized.

We have already seen Newton’s explanation of refraction using the corpuscular theory. As mentioned earlier, Newton predicted that the speed of light would be greater in water than in air. We know today that this in fact is not the case.

Thus, Newton’s corpuscular theory did not accurately explain diffraction, partial reflection and partial refraction, and the speed of light in a denser medium after it refracts.

Lesson 2: Determining the Speed of Light

Introduction

Measuring the speed of light has always been a challenge. In this lesson, we will review the methods used starting with that attempted by Galileo. Then in the 1600s Roemer and Huygens used similar approaches by looking at the eclipses and orbits of Jupiter and one of its moons, Io. Then in the 1800s Fizeau and Foucault used rotating wheels and mirrors to measure the speed of light. In the 1900s, Michelson improved on Foucault’s technique and obtained a very accurate measurement of the speed of light.

Measuring the Speed of Light: Galileo, Roemer, and Huygens

Galileo Galilei (1564-1642) carried out experiments to try measure the speed of light. He attempted to do this by measuring the time for light to travel a known distance between two hilltops. He stationed an assistant on one hilltop and himself on another and ordered the assistant to lift the cover from a lamp the instant he saw a flash from Galileo’s lamp. Repeated experiments failed to accurately measure any time interval between when the first and second lanterns were uncovered. They could only say that light travel at least ten times faster than sound.

The Danish astronomer, Olaus Roemer (1644 – 1710) made the first accurate

measurements of the speed of light using Jupiter’s moons. He published his results in 1676. Roemer made a detailed study of the frequent eclipses of Io by Jupiter. From this work he was able to predict when the next eclipses would occur. Over a period of months, Roemer’s predictions were steadily off by longer and longer intervals of time. His predictions were eventually off by eight minutes. Even stranger was the fact that these predictions then became more accurate till they were correct again. This strange cycle repeated itself over and over again with great regularity.Roemer realized that this time difference was caused by the difference between the distance between the earth and Jupiter. When Jupiter was closest to earth, the eclipses happened on time. The further Jupiter was away from the earth, the later the eclipses became. This was because light had a longer distance to travel to earth and this took longer. The size of the earth's orbit and Jupiter's orbit around the sun were calculated at that time. Roemer used these figures to determine the distance between the earth and Jupiter for all his observations. Roemer used these somewhat inaccurate distances (as it was known in 1675) to calculate the speed of light to be about 200 000 km/s or 2.0 x 108 m/s.

In 1677, Huygens (1629-1695) in Holland read about Roemer’s work on calculating the speed of light. He immediately sent a letter to Roemer asking for more information. In 1678, Huygens presented his “Traite de lumiere” for the Academie des Sciences. He used the earth’s orbit and the time delay presented by Roemer to calculate the speed of light. He was the first to give the speed in terrestrial units as 16 2/3 earth diameters per second. This was about 2/3 the present value of the speed of light.

Measuring the Speed of Light: Fizeau and Foucault

The French physicist,Armand Fizeau (1819-1896), shone a light between the teeth of a rapidly rotating toothed wheel. A mirror reflected the beam back through the same gap between the teeth of the wheel. There were over a hundred teeth in the wheel. The wheel rotated at hundreds of times a second - therefore a thousandth of a second was easy to measure. Light was reflected from mirrors more than 6 kilometres apart. By varying the speed of the wheel is was possible to determine at what speed the wheel was spinning too fast for the light to pass through the gap between the teeth and back through the same gap. Fizeau calculated the speed of

light to be 3.133 00 x 108 m/s. He was able to do this because knew how short a time the light had to get through that gap and back, and he knew how far the light travelled. By dividing the distance by the time he got the speed of light.

Jean Foucault (1819-1868) bounced light from a rotating mirror back to a stationary mirror. The light from the rotating mirror bounced back at an angle slightly different from the angle it hit the mirror with - because the mirror was rotating. By measuring this angle it was possible to measure the speed of the light. Foucault continually increased the accuracy of this method. His final measurement determined that light traveled at 2.997 96 x 108 m/s.

 

Measuring the Speed of Light: Michelson

The American, Albert A. Michelson (1852-1931) was an instructor in physics at the United States Naval Academy. He had to do a lecture demonstration of how Foucault measured the speed of light. It was years since Foucault made his measurements. When Michelson was setting up his demonstration, he saw how it could be improved to give a much more accurate measurement.

Michelson used a rotating mirror apparatus for a series of high precision experiments

carried out from 1880 to the 1920s. Light from a source was directed at one face of a rotating eight-sided mirror. The reflected light traveled to a stationary mirror and back again as shown. The U.S. Coast and Geodetic Survey found the distance between the mirrors to be 35 385.5 m accurate to about one part in seven million. This was a larger distance than the 10 m or so that Foucault used. The rate at which the mirror was rotating was measured accurately using a stroboscopic comparison with an electric signal of standard frequency. If the rotating mirror was turning at just the right rate, the returning beam of light would reflect from one face of the mirror into a small telescope through which the observer looked. At a different speed of rotation, the beam would be deflected to one side and would not be seen by the observer. From the required speed of the rotating mirror and the known distance to the stationary mirror the speed of light could be calculated. Michelson set up the rotating mirror on the top of Mt. Wilson in southern California and the stationary mirror on Mt. Baldy (Mt. San Antonio) 35 km away. He determined the speed of light to be 2.997 29 x 108 m/s.

Michelson conducted similar experiments using an evacuated tube one mile (1.6 km) long to eliminate the problems of haze and variations in air density. In these investigations, he determined the speed of light to be 2.997 96 x 108 m/s which he believed to be accurate within one km/s.

Today, the accepted value for the speed of light is 2.997 924 58 x 108 m/s.

 

Lesson 3: The Wave Theory of Light

 Introduction

In this lesson, we focus on the wave theory and how it explains the behaviour of light. We will first review Huygen’s Principle and how it explains the propagation of waves. We will then use the wave theory to explain reflection, refraction, partial reflection and partial refraction, and diffraction. The wave theory provides a better explanation of partial reflection - partial refraction, and diffraction than the corpuscular theory does. It also makes a more accurate prediction of the speed of light in an optically denser medium than the corpuscular theory does. We will see why it was difficult to explain diffraction using the wave theory at the time of Newton. Throughout this discussion diagrams will be used to illustrate the principles involved.

 Huygens' Principle and Rectlinear Propagation

The wave theory of light was proposed by Robert Hooke in 1665. Twenty years later, it was improved by the Dutch scientist Christiaan Huygens. He developed a technique for predicting the future position of a wavefront based on an earlier position of the same wave. His explanation became known as Huygens’ Principle. It states that

every point on a wavefront can be considered as a point source of tiny secondary wavelets that spread out in front of the wave at the same speed as the wave itself. The surface envelope, tangent to all the wavelets, constitutes the new wavefront.

As an example of the use of Huygen’s Principle, consider the wavefront AB that is travelling away from the source S at some instant in time. The points on the wavefront represent the centres of the new wavelets, seen as a series of small circles. The common tangent to all these wavelets, the line A’B’, is the new position of the wavefront a short time later.

 

The wave theory treats light as a series of wavefronts perpendicular to the light rays. Huygens thought of the rays as simply representing the direction of motion of a wavefront. This was how the wave theory explained the rectilinear (straight line) propagation of light. Newton felt that the wave theory did not adequately explain the rectilinear propagation of light since waves emitted from a point source spread out in all directions.

The Wave Theory and Reflection

Light reflects from surfaces in such a way that the angle of incidence is equal to the angle of reflection. In our studies of waves in two dimensions, we learned that water waves also reflect from surfaces so that the angle of incidence is equal to the angle of reflection. The diagram below shows one incident wavefront approaching a barrier. The arrow is the incident wave ray showing the direction that the wavefront is moving. A wavelet is shown at one edge of the wavefront.

When the wavefronts reflect, they do so in such a way that the angle of incidence ( i

) is equal to the angle of reflection ( r ) for the wave rays. The diagram below shows only one of the incident wavefronts at the point when one edge is making contact with the barrier.

The diagram below shows how several reflected wavefronts would move. Note that

the wavefronts are drawn perpendicular to the wave rays. One reflected wavelet is shown.

 

The Wave Theory and Refraction

Using his wavelet concept, Huygens predicted that light is bent towards the normal as it passes into an optically denser medium such a glass, because its velocity is slower in the second medium. In our work in the unit waves in two dimensions, we studied a diagram similar to the one shown below.

 

The diagram shows incident wavefronts in deep water. This corresponds to light moving in a low density material like air. The direction of the wavefronts is indicated by the incident wave ray. One of the wavelets is included on this ray. Note that the wavefront is tangent to the wavelet.

After the wavefronts move into the shallow water, they refract in such a way that the angle of refraction is less than the angle of incidence. The wave ray in the shallow water corresponds of light moving in a higher density material like water. A wavelet is drawn on the refracted wave ray.

The distance between the wavefronts (wavelength) in the shallow water (denser material), is less than the wavelength in the deeper water. This corresponds to a decrease in speed of the wavefronts in the shallow water. Thus the wave theory predicts a decrease in speed of light as it moves into a denser material. Newton’s corpuscular theory predicted the reverse, that is the speed of light in the denser material was greater.

Snell’s Law applies to light waves as it does for water waves. The direction of the refracted wave can be determined using the ratio of the two velocities in the two media.

The Wave Theory and Partial Reflection and Partial Refraction

Waves partially reflect and partially refract whenever there is a change in velocity. The amount of partial reflection varies with the angle of incidence. Also partial reflection is much more apparent when there is an increase in velocity than when there is a decrease. This is just how light behaves.

The diagram below shows incident wavefronts in a slow medium approaching a boundary. This slow medium could represent shallow water, or it could represent an optically dense medium that light waves travel through.

Part of the incident wavefronts are reflected. These are shown by dashed lines. Part of the incident wavefronts are also refracted. The corresponding wave rays are

shown. One wavelet is also shown on each of the three types of avefronts.

The lower diagram shows the angle of incidence ( i ) equal to the angle of reflection ( r ), and the angle of incidence is less than the angle of refraction ( R ) for this kind of a wave moving from a slow medium to a fast medium. The wave theory is an excellent model for explaining the behaviour of light for partial reflection and partial refraction.

The Wave Theory and Diffraction

At the time of Newton, Grimaldi observed the diffraction of light when a ray was directed through two successive narrow slits. Newton criticized Grimaldi’s work by saying that if light was a wave, then light waves should bend much more than was observed by Grimaldi.

In our earlier work in diffraction of water waves, we observed that there is considerable diffraction only when the size of the aperture is of approximately the same size as the wavelength of the waves. For example, in the left diagram below, the size of the opening is large compared to the wavelength and there is little diffraction. In the right diagram, the opening size is small and therefore there is a great deal of diffraction. 

The diagrams below also show that diffraction around a sharp barrier is less for shorter wavelengths.

 

At the time of Huygens and Newton, the wavelength of visible light was not known. We know today that because the wavelength of visible light is so small, that diffraction effects are also very small for the relatively large openings we regularly experience. The wave theory provided a much better explanation of diffraction than did the corpuscular theory.

Lesson 4: Young's Experiment

 Introduction

The research by Thomas Young (1773 – 1829) into the interference of light was critical in demonstrating that light has wave like properties. His famous experiment has become known as “Young’s Experiment.” In this lesson, we will review what we learned about the interference of two dimensional waves from our work in an earlier module. We will then extend this knowledge to an understanding of the interference of light waves. This will lead us to a mathematical equation that will allow us to determine the wavelength of light based on measurements taken from the interference of light.

 

Attempts to Produce and Interference Pattern in Light

In our studies of waves in two dimensions, we learned that waves generated by two point sources in a ripple tank interfere with each other to produce areas of constructive and destructive interference as shown below.

In the diagram below, the nodal lines are grey in colour. They represent areas of destructive interference where troughs and crests meet. The areas with the shaded in circles represent areas of constructive interference. The line joining the shaded in dots would appear to have bright and dark areas on a ripple tank screen.

If light has wave properties, then two sources of light waves should produce a result similar to that for waves in a ripple tank. In Newton’s time, many scientists attempted to observe the interference of light. In most cases, they placed two sources of light side by side. The light from the two sources, falling on a nearby screen, was carefully examined, but no interference was observed. The scientists conducting these experiments did not know that the wavelength of light is extremely small. We can see in a ripple tank that when the frequency of the vibrating sources is high, so that the wavelength is small, that the distance between two adjacent nodal lines is small. In the early experiments with light, the distance between the nodal lines was so small that no nodal lines could be observed.

There was also a second more basic problem. In a ripple tank, the nodal line pattern is most easily observed when the two vibrating sources are in phase, that is vibrating at the same time. If the phase of the vibrating sources is altered, the interference pattern will shift. When two incandescent light sources are used side by side, the light is emitted randomly by the atoms in each source, in bursts, not necessarily in phase. When light strikes the screen, a constantly varying interference pattern is produced and no single pattern is observed.

Young's Experiment 

In the years 1802 to 1804, Thomas Young (1773-1829) performed a number of experiments. Instead of using two sources, he used only one source of light directing it through two pinholes placed very close together. The light was diffracted through each pinhole so that each acted as a point source of light. Since the sources were close together, the spacing between the nodal lines was great enough that the pattern could be seen. Because the light from the two pinholes came from the same source, the two interfering beams of light were always in phase and a single, fixed interference pattern could be created on the screen.

The two major problems in observing the interference of light were solved. In Young’s experiment, the two sources were in phase, and the distance between sources was small enough that a series of bright and dark bands, called interference fringes, were created on a screen placed in the path of the light. This experiment, now commonly called Young’s Experiment, provided very strong evidence for the wave theory of light.

Young's Experiment: Interference at Three Angles

 We will look at interference in Young’s Experiment at three different angles. In the diagrams below, light waves in phase are passing through the slits S1 and S2 which are a distance d apart. The waves spread out in all directions through the slits.

In the left diagram below, both waves that reach the centre of the screen are in phase because they travel the same distance. Constructive interference occurs and there is a bright spot on the screen.

In the right diagram below, the waves from S2 travel an extra 1/2 to reach the screen. When they do so, they are exactly out of phase. This means that the crest from the wave of S1 meets the trough from the wave of S2. Destructive interference occurs and the screen is dark at this point. This corresponds to nodal point 1. 

 

Young's Experiment and Deriving a Useful Equation

From our work on wave interference in water, we learned that the difference in path length from the point P on a nodal line (destructive interference)to the two sources S1

and S2 is equal to     From the diagram below showing

destructive interference, it can be shown that the difference in path length, , is

also equal to d . Therefore we can write     The diagram below shows the two triangles from the diagrams above. In this diagram, x is the distance of the nodal line from the centre line on the screen, and L is the distance from the midpoint between the two slits S1 and S2 to the screen. In the two triangles,

the angle  is identical. For very long distances, the distance L is almost identical to

the length of the hypotenuse. Therefore, another way to write sin is . In place of x we can write xn which is the distance to the nth nodal line measured from

the right bisector. Our new equation becomes .

The distance from the centre line to the first nodal line (x1) can be given by

.

The distance x2 is given by . The distance between x2 and x1 is

. In general, we can say that where x is the distance between adjacent nodal lines on a screen, d is the separation between the slits, and L is the perpendicular distance from the slits to the screen.

Light as an Electromagnetic Wave

We have seen that there is strong evidence for the wave nature of light. It was James Maxwell (1831-1879) who described the nature of the vibrations transmitted by the light. He called them electromagnetic waves. To understand what is meant by electromagnetic waves, we must have some basic knowledge of electricity and

magnetism. This will come later in this course and in Physics 40S. However, we can describe the electromagnetic wave based on our knowledge of transverse waves.

The diagram below shows two transverse waves. The wave with the solid line could represent the electric field lines and the wave with the dashed lines could represent the magnetic field lines. The electric and magnetic field lines are perpendicular to each other and to the direction of motion of the waves.

In the diagram below, the electric field vibrates in an up and down way. This is equivalent to the wave vibrating along the y axis. The magnetic field vibrates into and out of the paper, along the z axis. The wave itself moves to the right along the x axis.

                           

Lesson 5: The Photoelectric Effect and the Wave-Particle Duality

Introduction

In this last lesson we discuss the photoelectric effect. The wave theory and the particle theories of light make different predictions about the effects of the frequency and the intensity of light on this effect. Albert Einstein proposed the idea that light is made up of photons and we will see that his theory explained the photoelectric effect very well. The lesson concludes with a discussion of the wave-particle duality and the Principle of Complementarity. This discussion will show that to fully explain the behaviour of light we need to use both the wave and the particle (photon) theories. Both Maxwell’s electromagnetic theory and Newton’s corpuscular theory provided

excellent models for our understanding of light, and the wave-particle model was built on the contributions of these and other great scientists.

The Photoelectric Effect and the Photocell

In 1887, the German physicist Heinrich Hertz (1857-1894) was testing Maxwell’s Theory of Electromagnetic waves. Hertz noticed that when he directed ultraviolet waves at certain metallic surfaces, they lose their negative charges. For example, a negatively charged zinc plate was discharged when ultraviolet radiation fell on it, but it remained charged when ordinary light fell on it. But a positively charged plate was never discharged. The incident light somehow caused the metal to liberate electrons. Both light and electricity are involved so the term photoelectric effect was given to this phenomenon of emitting electrons when electromagnetic radiation falls on an object.

The photoelectric effect can be studied using a photocell such as the one shown below. The cell has two metal electrodes sealed in an evacuated tube. The air has been removed to keep the metal surface clean and to keep electrons from being stopped by the air molecules. The large electrode, the cathode, is usually coated with cesium or some other alkali metal. The second electrode, the anode, is made of a thin wire so it does not block any radiation. The tube if often made of quartz to permit ultraviolet wavelengths to pass through. A power source is connected to the anode and the cathode in such a way that the that the negative side of the source is attached to the cathode and the positive side is connected to the anode. An ammeter can measure if there is a current flowing through the circuit.

When no radiation falls on the cathode, the current does not flow in the circuit. When radiation does fall on the cathode, a current is produced in the circuit and this is indicated by the ammeter. The current is a result of electrons, called photoelectrons, being ejected from the cathode by the radiation. The electrons then move to the positive electrode, the anode.

The Photoelectric Effect and the Wave Theory 

Not all radiation that falls on the cathode in a photoelectric cell results in current flow. Electrons are ejected only if the frequency of the radiation is above a certain minimum value called the threshold frequency, fo. The threshold frequency varies with the metal. For example, all wavelengths of light except red will eject electrons from cesium, but ultraviolet light must be used with zinc. Radiation of a frequency below fo does not eject any electrons from the metal no matter how bright it is. Even if it is very dim, radiation at or above the threshold frequency causes electrons to leave the metal immediately, and the greater the intensity of this radiation, the larger the flow of photoelectrons.

The electromagnetic wave theory cannot explain these effects. The wave theory says that a more intense radiation, regardless of frequency, has stronger electric and

magnetic fields. According to the wave theory, the electric field accelerates and ejects the electrons from the metal. With very faint light shining on the metal, electrons would require a very long time before they gained enough energy to be ejected.

When the photoelectric effect occurs, the light energy is absorbed by an electron instantaneously, and does not need to “accumulate” energy to a point where the electron can be liberated. The classical wave theory predicts that electrons can be ejected even for very dim light but there must be a long time for this to occur.

Another way of looking at the photoelectric effect using the classical wave theory is to consider that the light wave shakes the atom until it loses an electron. According to the wave theory, the amplitude and time duration of the wave would determine whether sufficient energy had been transferred to the atom that ejects an electron. The amplitude is related to the brightness, or intensity, of the light. Thus, more intense beams of light, even of lower frequency, should eject more electrons. But this is not the case. Higher frequency beams are necessary in most cases.

The Photoelectric Effect and Einstein

In 1905, Albert Einstein published a revolutionary theory that explained the photoelectric effect. Einstein made the radical proposal that the energy of light and other forms of electromagnetic radiation is not transmitted as a continuous wave. Rather it is concentrated in discrete bundles of energy called photons. He proposed that the amount of energy in each of these bundles was a discrete, fixed amount that depended on the frequency of the light. The higher the frequency, the greater the energy contained in the photon.

Einstein’s theory explained the existence of a threshold frequency. A photon must have a minimum energy to eject an electron from a metal. This minimum energy depends on the threshold frequency, fo, of the light. If the photon has a frequency below fo, then it does not have the energy needed to eject an electron. Light with a frequency greater than fo has more energy than needed to eject the electron. The excess energy make the electron move, and is converted to kinetic energy of the moving electron.

Einstein thus predicted why there was a threshold frequency. The electron must have a minimum amount of energy to escape the attractive force holding it to the metal. When the frequency of the incident light is too low, the photon does not give the absorbing electron sufficient energy and it remains bound to the surface. The intensity (brightness) of the light is only a measure of the rate at which the photons strike the surface, not the energy of the photon. This explains why the kinetic energy of the emitted photoelectrons and the threshold frequency do not depend on the intensity of the incident light.

Notice that an electron cannot simply accumulate photons until it has enough energy. Only one photon interacts with one electron. The photon either has enough energy to eject the electron or it does not. Thus, the photon behaves more like a particle than a wave.

The Principle of Complementarity and Light

It has become obvious that light is not just a wave and not just a particle. It has a dual nature, a property referred to by physicists as a wave-particle duality. We can come to this conclusion because both theories of light have been shown to be valid based on very strong experimental evidence. It is clear that light is a much more complex phenomenon than just a beam of particles or just a simple wave.

The great Danish physicist, Neils Bohr (1885-1962) clarified the situation by proposing the Principle of Complementarity. He stated that “To understand a specific experiment, one must use either the wave or the photon theory but not both.” Understanding both the wave and the particle properties of light is essential if one is to have a full understanding of light. In other words, the two aspects of light complement one another.

If we return to Young’s experiment and the photoelectric effect, we can illustrate how this principle is applied. To understand how light interferes after it passes through two parallel slits, we must use the wave theory, not the particle theory. To understand why the photoelectric effect occurs, we must use the photon, or particle nature of light, not the wave theory.

As a general rule, when light passes through space or through a medium, its behaviour is best explained using its wave properties. But when light interacts with matter, its behaviour is more like that of a particle.

The Wave-Particle Duality and Models

One of the reasons we have trouble understanding the dual nature of light is that it is very difficult if not impossible for us to visualize this duality. We cannot draw pictures or create images of a wave-particle combination. We are restricted to creating wave images in some applications and particle images in other applications, but never both at the same time.

Also, most of the laws and principles of physics we are familiar with are based on experiments that involve direct observations. In the study of light, particularly as it transfers energy from place to place, we base our knowledge on indirect experiments. We cannot see directly how light energy is transmitted as a wave or particle. All we can observe are the results of the interaction of light and matter. Our knowledge is limited to indirect information, and therefore, to describe light’s dual nature, we cannot use visual means. Quantum mechanics utilizes mathematical models, not visual models, but this method constitutes a part of quantum mechanics that is much beyond the scope of this course.

The wave-particle model of light that we use today is much more subtle than Newton’s corpuscular theory or Maxwell’s electromagnetic theory. Both of these theories were important in their time and contributed much to our understanding of the behaviour of light. But these models were inadequate in themselves for explaining all of the properties of light. Like all models or theories, they can be replaced by better models when new information becomes available. This is the case with the two classical models of light. They have been superseded by the wave-particle model of light, the only theory that we find acceptable today for a full understanding of the nature of light.