SECTION D-WAVES AND LIGHT By: Danielle Girod. A wave is a pulse of energy which is carried away from a central transmitter. It is a repetitive disturbance.

SECTION D-WAVES AND SECTION D-WAVES AND LIGHTLIGHT

By: Danielle GirodBy: Danielle Girod

A wave is a pulse of energy which is A wave is a pulse of energy which is carried away from a central carried away from a central transmitter. It is a repetitive transmitter. It is a repetitive disturbance which moves through a disturbance which moves through a medium, causing particles to medium, causing particles to oscillate.oscillate.

A Pulse is a single disturbance which A Pulse is a single disturbance which moves through a medium.moves through a medium.

WAVE MOTIONWAVE MOTION(1.1) TYPES OF WAVES(1.1) TYPES OF WAVES

There are three types of waves:There are three types of waves: 1. Mechanical waves- require a material 1. Mechanical waves- require a material

medium to travel (air, water, ropes). These medium to travel (air, water, ropes). These waves are divided into three different types.waves are divided into three different types.

Transverse waves- cause the medium to move Transverse waves- cause the medium to move perpendicular to the direction of the wave.perpendicular to the direction of the wave.

Longitudinal waves- cause the medium to Longitudinal waves- cause the medium to move parallel to the direction of the wave.move parallel to the direction of the wave.

Surface waves- are both transverse waves and Surface waves- are both transverse waves and longitudinal waves mixed in one medium.longitudinal waves mixed in one medium.

Diagram showing the differences between a Diagram showing the differences between a transverse and longitudinal wave in a slinky springtransverse and longitudinal wave in a slinky spring

2. Electromagnetic waves- do not 2. Electromagnetic waves- do not require a medium to travel (light, radio). require a medium to travel (light, radio). They can travel in a vacuum.They can travel in a vacuum.

Diagram showing an electromagnetic wave

3. Matter waves- are produced by 3. Matter waves- are produced by electrons and particles.electrons and particles.

Comparison and contrast between Comparison and contrast between Progressive Waves and Stationary Progressive Waves and Stationary WavesWaves

1. Each point along a progressive wave 1. Each point along a progressive wave has equal amplitude, but for a has equal amplitude, but for a stationary wave the amplitude varies.stationary wave the amplitude varies.

2.Adjacent points on progressive waves 2.Adjacent points on progressive waves vibrate with different phases but all vibrate with different phases but all particles between nodes in stationary particles between nodes in stationary waves vibrate in phase.waves vibrate in phase.

3. Energy is transferred through space 3. Energy is transferred through space in progressive waves but not in the in progressive waves but not in the case of stationary waves.case of stationary waves.

WAVE PARAMETERSWAVE PARAMETERS(1.2)(1.2)

Frequency, code f, has the unit hertz (Hz), Frequency, code f, has the unit hertz (Hz), and is the number of waves passing a given and is the number of waves passing a given point every second.point every second.

Wavelength is defined as the distance Wavelength is defined as the distance between any two points on adjacent cycles between any two points on adjacent cycles that are in phase, in other words the distance that are in phase, in other words the distance between adjacent peaks or troughs. The between adjacent peaks or troughs. The code for wavelength is l (lambda).The units code for wavelength is l (lambda).The units for wavelength are metre (m). for wavelength are metre (m).

Period is the time taken for one complete Period is the time taken for one complete oscillation. The code is T and the units oscillation. The code is T and the units seconds (s). Frequency is the reciprocal of seconds (s). Frequency is the reciprocal of period and is related to period by the simple period and is related to period by the simple equation: equation:

f = 1/Tf = 1/T

Amplitude of a wave, code A or r, units metres Amplitude of a wave, code A or r, units metres (m), is the maximum displacement of a (m), is the maximum displacement of a particle from its equilibrium position. In other particle from its equilibrium position. In other words it is the height of the wave from the words it is the height of the wave from the average level. It is NOT the height from crest average level. It is NOT the height from crest to trough.to trough.

The phase of a particle is the fraction of the The phase of a particle is the fraction of the cycle a particle has passed through relative cycle a particle has passed through relative to a given starting point. We describe the to a given starting point. We describe the difference in the motion of particles in terms difference in the motion of particles in terms of the phase difference. This is the fraction of the phase difference. This is the fraction of a wavelength by which their motions are of a wavelength by which their motions are different. different.

In the case of a wave, the speed is the In the case of a wave, the speed is the distance traveled by a given point on the distance traveled by a given point on the wave (such as a crest) in a given interval of wave (such as a crest) in a given interval of time. In equation form,time. In equation form,

Wave Speed (v)= wavelength (distance)/ period Wave Speed (v)= wavelength (distance)/ period (time)(time)

• Since Period= 1/ frequencySince Period= 1/ frequency ThenThen

Wave Speed= frequency * wavelengthWave Speed= frequency * wavelength

(1.3)/(1.4)(1.3)/(1.4)DISPLACEMENT-DISTANCE DISPLACEMENT-DISTANCE

GRAPHGRAPH A displacement-distance graph is also A displacement-distance graph is also

called a displacement-position graph. It called a displacement-position graph. It shows the displacement of the particles shows the displacement of the particles at various positions at a certain time. at various positions at a certain time. Although it looks like a photograph of a Although it looks like a photograph of a transverse wave, it can be used to transverse wave, it can be used to describe BOTH a transverse and a describe BOTH a transverse and a longitudinal wavelongitudinal wave

displacement-distance graph of a longitudinal wave displacement-distance graph of a longitudinal wave

displacement- distance graph of a transverse wave displacement- distance graph of a transverse wave

From a displacement-distance graph, we can From a displacement-distance graph, we can

directly read the following information: directly read the following information: amplitude of the wave amplitude of the wave wavelength of the wave wavelength of the wave locations of crests and troughs (for a locations of crests and troughs (for a

transverse wave), or compressions and transverse wave), or compressions and rarefactions (for a longitudinal wave) rarefactions (for a longitudinal wave)

The displacement-distance graph is especially The displacement-distance graph is especially useful to study a longitudinal wave. For useful to study a longitudinal wave. For example, look at the displacement of example, look at the displacement of compression: it is zero unlike the crest. This compression: it is zero unlike the crest. This is easy to notice on the graphs.is easy to notice on the graphs.

Fig c. Time series of displacement-distance Fig c. Time series of displacement-distance graphs of a wavegraphs of a wave

Using a series of displacement-Using a series of displacement-distance graphs at various time, we can distance graphs at various time, we can see the motion of the wave (Figure c). see the motion of the wave (Figure c). By comparing the changes in these By comparing the changes in these graphs, we can deduce the travelling graphs, we can deduce the travelling speed and direction of the wave, as speed and direction of the wave, as well as the time-varying directions of well as the time-varying directions of the motion of the vibrating particles.the motion of the vibrating particles.

DISPLACEMENT-TIME GRAPHDISPLACEMENT-TIME GRAPH

Unlike a displacement-position graph, a Unlike a displacement-position graph, a displacement-time graph describes the displacement-time graph describes the displacement of ONE particle at various displacement of ONE particle at various time at a certain position. Figure d time at a certain position. Figure d shows how the displacements of shows how the displacements of particles P, Q, and R in Figure c vary particles P, Q, and R in Figure c vary with time. Each particle has its own with time. Each particle has its own displacement-time graph.displacement-time graph.

Fig d. Displacement-time graphs for particles at Fig d. Displacement-time graphs for particles at different positions. different positions.

On the contrary, using a number of On the contrary, using a number of

displacement-time graphs at various displacement-time graphs at various position, we can construct back the position, we can construct back the displacement-distance graph of the wave at a displacement-distance graph of the wave at a certain time. certain time.

From a displacement-time graph, we can From a displacement-time graph, we can directly read the following information:directly read the following information:

amplitude of the wave amplitude of the wave period of the wave (and hence, the period of the wave (and hence, the

frequency) frequency) direction of motion of the particle at various direction of motion of the particle at various

timetime

If we have a snapshot of the wave too, If we have a snapshot of the wave too,

we can deduce from them the motion of we can deduce from them the motion of the wave: its travelling speed and the wave: its travelling speed and direction.direction.

NOTENOTE: a progressive wave varies in : a progressive wave varies in both time and space simultaneously. To both time and space simultaneously. To represent it on paper, either time or represent it on paper, either time or position must be held constant.position must be held constant.

WAVE PHENOMENAWAVE PHENOMENAREFLECTION, REFRACTION, DIFFRACTIONREFLECTION, REFRACTION, DIFFRACTION

(2.1)-(2.5)(2.1)-(2.5)

Reflection, refraction and diffraction are all Reflection, refraction and diffraction are all boundary behaviors of waves associated boundary behaviors of waves associated with the bending of the path of a wave.with the bending of the path of a wave.

Reflection involves a change in direction of Reflection involves a change in direction of waves when they bounce off a barrier; waves when they bounce off a barrier; refraction of waves involves a change in the refraction of waves involves a change in the direction of waves as they pass from one direction of waves as they pass from one medium to another.medium to another.

Water waves are reflected from hard flat

surfaces as shown below.

Diagram showing reflection at a plane surface

NoteNote: that the total length of the line : that the total length of the line representing the wave peak stays the representing the wave peak stays the same where it is being reflected.same where it is being reflected.

The red part of the incident wave plus The red part of the incident wave plus the blue part of the reflected wave is the the blue part of the reflected wave is the same as the original line.same as the original line.

After reflection, a wave has the same After reflection, a wave has the same speed, frequency and wavelength, it is speed, frequency and wavelength, it is only the direction of the wave that has only the direction of the wave that has changed.changed.

Reflection using plane wavesReflection using plane waves If a plane barrier is placed at an angle i If a plane barrier is placed at an angle i

to the path of plane waves, the waves to the path of plane waves, the waves are reflected at an angle r, where i=r. It are reflected at an angle r, where i=r. It follows the Law of reflection which is follows the Law of reflection which is such that the waves will always reflect such that the waves will always reflect in such a way that the angle at which in such a way that the angle at which they approach the barrier equals the they approach the barrier equals the angle at which they reflect off the angle at which they reflect off the barrier.barrier.

Diagram showing the law of reflectionDiagram showing the law of reflection

Reflection using circular wavesReflection using circular waves Here the reflected waves behave as Here the reflected waves behave as

they originated as a point behind the they originated as a point behind the plane surface. It results in the plane surface. It results in the convergence of the waves at a focal convergence of the waves at a focal point.point.

Diagram showing reflection off of curved surfaces Diagram showing reflection off of curved surfaces

Refraction of waves involves a change Refraction of waves involves a change in the direction of waves as they pass in the direction of waves as they pass from one medium to another. from one medium to another. Refraction, or the bending of the path Refraction, or the bending of the path of the waves, is accompanied by a of the waves, is accompanied by a change in speed and wavelength of the change in speed and wavelength of the waves.waves.

Refraction is accompanied by changes Refraction is accompanied by changes of wavelength and wave speed. of wavelength and wave speed. Frequency (which depends on the Frequency (which depends on the source) remains unaffected.source) remains unaffected.

Angle of refraction decreases the less Angle of refraction decreases the less dense the object and thus bends dense the object and thus bends toward the normal. Angle of refraction toward the normal. Angle of refraction hence increases as density increases hence increases as density increases and bends away from the normal.and bends away from the normal.

Water waves travel faster on the Water waves travel faster on the surface of deep water than they do on surface of deep water than they do on shallow water.shallow water.

The change in speed of the wave will The change in speed of the wave will cause refraction.cause refraction.

Diagram showing refraction of water wavesDiagram showing refraction of water waves

As you can see, the change in speed As you can see, the change in speed has changed the direction of the wave.has changed the direction of the wave.

The slower wave in the shallow water The slower wave in the shallow water has a smaller wavelength.has a smaller wavelength.

The amount of refraction increases as The amount of refraction increases as the change in speed increases.the change in speed increases.

CalculationsCalculations To solve problems on refraction:To solve problems on refraction:

because and because and ff remains remains constant.constant.

For a specific change in medium, the For a specific change in medium, the ratioratio has a constant value.has a constant value.

diffraction involves a change in diffraction involves a change in direction of waves as they pass direction of waves as they pass through an opening or around a barrier through an opening or around a barrier in their path. The amount of diffraction in their path. The amount of diffraction (the sharpness of the bending) (the sharpness of the bending) increases with increasing wavelength increases with increasing wavelength and decreases with decreasing and decreases with decreasing wavelength. In fact, when the wavelength. In fact, when the wavelength of the waves are smaller wavelength of the waves are smaller than the obstacle, no noticeable than the obstacle, no noticeable diffraction occurs.diffraction occurs.

The wavelength of water waves may be The wavelength of water waves may be several metres.several metres.

If the wavelength is of a similar size to a If the wavelength is of a similar size to a gap in a harbour wall, then the wave will gap in a harbour wall, then the wave will diffract as shown below.diffract as shown below.

Diagram showing diffraction of a waveDiagram showing diffraction of a wave

If the wavelength does not match the size If the wavelength does not match the size of the gap, then only a little diffraction of the gap, then only a little diffraction will occur at the edge of the wave.will occur at the edge of the wave.

Diagram showing little diffraction of a waveDiagram showing little diffraction of a wave

The part of the wave which hits the wall The part of the wave which hits the wall in the above two pictures is reflected in the above two pictures is reflected straight back on itself.straight back on itself.

All waves undergo reflection, refraction All waves undergo reflection, refraction and diffraction when it reaches the end and diffraction when it reaches the end of the medium or when it encounters an of the medium or when it encounters an obstacle in its path.obstacle in its path.

SUPERPOSITIONSUPERPOSITION(2.6)(2.6)

In many cases (for example, in the classic In many cases (for example, in the classic wave equation), the equation describing the wave equation), the equation describing the wave is linear. When this is true, the wave is linear. When this is true, the superposition principle can be applied. That superposition principle can be applied. That means that the net amplitude caused by two means that the net amplitude caused by two or more waves traversing the same space, is or more waves traversing the same space, is the sum of the amplitudes which would have the sum of the amplitudes which would have been produced by the individual waves been produced by the individual waves separately. For example, two waves traveling separately. For example, two waves traveling towards each other will pass right through towards each other will pass right through each other without any distortion on the each other without any distortion on the other side.other side.

combinedcombined

waveform waveform

wave 1 wave 1

wave 2 wave 2 Two waves in phase Two waves 180°Two waves in phase Two waves 180°

out of phase.out of phase.

Diagram showing the superposition of two waves Diagram showing the superposition of two waves in phase and out of phasein phase and out of phase

INTERFERENCE OF WATER USING TWO INTERFERENCE OF WATER USING TWO COHERENT POINT SOURCESCOHERENT POINT SOURCES

Diagram showing two in-phase coherent point Diagram showing two in-phase coherent point sourcessources

The waves propagate outward from the point The waves propagate outward from the point

sources, forming a series of concentric circles about sources, forming a series of concentric circles about the source. In the diagram, the thick lines represent the source. In the diagram, the thick lines represent wave crests and the thin lines represent wave wave crests and the thin lines represent wave troughs. The crests and troughs from the two troughs. The crests and troughs from the two sources interfere with each other at a regular rate to sources interfere with each other at a regular rate to produce nodes (pictured in blue on the diagram) and produce nodes (pictured in blue on the diagram) and antinodes (pictured in red) along the water surface. antinodes (pictured in red) along the water surface. The nodal positions are locations where the water is The nodal positions are locations where the water is undisturbed; the antinodal positions are locations undisturbed; the antinodal positions are locations where the water is undergoing maximum where the water is undergoing maximum disturbances above and below the surrounding disturbances above and below the surrounding water level. One unique feature of the two-point water level. One unique feature of the two-point source interference pattern is that the antinodal and source interference pattern is that the antinodal and nodal positions all lie along distinct lines. Each line nodal positions all lie along distinct lines. Each line can be described as a relatively straight hyperbola. can be described as a relatively straight hyperbola. The spatial separation between the antinodal and The spatial separation between the antinodal and nodal lines in the pattern is related to the wavelength nodal lines in the pattern is related to the wavelength of the waves.of the waves.

INTERFERENCE OF SOUND WAVES INTERFERENCE OF SOUND WAVES USING TWO COHERENT POINT USING TWO COHERENT POINT

SOURCESSOURCES Shown below are two in-phase, coherent Shown below are two in-phase, coherent

sound sources. This fact that each source sound sources. This fact that each source emits the same wavelength can be verified emits the same wavelength can be verified by noting that the distance from a by noting that the distance from a crest/compression to its next crest/compression to its next crest/compression is the same for both crest/compression is the same for both sources. That the sources are coherent can sources. That the sources are coherent can be readily seen by the fact that the sources be readily seen by the fact that the sources emit their waves in unison - both release a emit their waves in unison - both release a trough, then a crest, then a trough, and so trough, then a crest, then a trough, and so on.on.

Diagram showing two in-phase coherent sound Diagram showing two in-phase coherent sound sourcessources

"purple" wavefronts represent "purple" wavefronts represent troughs/rarefactions and "teal" wavefronts troughs/rarefactions and "teal" wavefronts represent crests/compressions.represent crests/compressions.

(2.7)(2.7) THOMAS YOUNG'S DOUBLE- SLIT THOMAS YOUNG'S DOUBLE- SLIT

EXPERIMENTEXPERIMENT The results of this experiment, first carried The results of this experiment, first carried

out by Thomas Young in 1801 , confirm that out by Thomas Young in 1801 , confirm that light has a wave-like nature.light has a wave-like nature.

The experiment is set up as follows:The experiment is set up as follows:

Diagram showing Young’s Double Slit experimentDiagram showing Young’s Double Slit experiment

There are still only two light rays that There are still only two light rays that actually go through the slits, but as actually go through the slits, but as soon as they pass through they start to soon as they pass through they start to diffract.diffract.

Remember, diffraction is when light Remember, diffraction is when light passes through a small opening and passes through a small opening and starts to spread out. This will happen starts to spread out. This will happen from both openingsfrom both openings

Diagram showing young’s waveDiagram showing young’s wave

Notice that at some points the two sets of Notice that at some points the two sets of waves will meet crest to crest, at other spots waves will meet crest to crest, at other spots crest meets trough. crest meets trough.

Where crest meets crest, there will be Where crest meets crest, there will be constructive interference and the waves will constructive interference and the waves will make it to the viewing screen as a bright make it to the viewing screen as a bright spot.spot.

Where crest meets trough there will be Where crest meets trough there will be destructive interference that cancel each destructive interference that cancel each other out… a black spot will appear on the other out… a black spot will appear on the screen. screen.

When this experiment is performed we When this experiment is performed we actually see this.actually see this.

CALCULATIONSCALCULATIONS When you set up this sort of an apparatus, there is When you set up this sort of an apparatus, there is

actually a way for you to calculate where the bright actually a way for you to calculate where the bright lines (called fringes) will appear.lines (called fringes) will appear.

There is always a middle line, which is the brightest. There is always a middle line, which is the brightest. We call it the central fringe. We call it the central fringe.

In the formula we will use, there is a variable, “n”, In the formula we will use, there is a variable, “n”, that is a count of how many bright fringes you are that is a count of how many bright fringes you are away from the central fringe. away from the central fringe.

The central fringe is n = 0. The central fringe is n = 0. The fringe to either side of the central fringe has an The fringe to either side of the central fringe has an

order of n = 1 (the first order fringe). order of n = 1 (the first order fringe). The order of the next fringe out on either side is n = The order of the next fringe out on either side is n =

2 (the second order fringe). 2 (the second order fringe). And so on.And so on.

The formula that we will use to figure out The formula that we will use to figure out problems involving double slit experiments problems involving double slit experiments is easy to mix up, so make sure you study it is easy to mix up, so make sure you study it carefully.carefully.

? = wavelength of light used (m)? = wavelength of light used (m) x = distance from central fringe (m)x = distance from central fringe (m) d = distance between the slits (m) d = distance between the slits (m) n = the order of the fringen = the order of the fringe L = length from the screen with slits to the L = length from the screen with slits to the

viewing screen (m)viewing screen (m)

Diagram shows the different things each is Diagram shows the different things each is measuring. measuring.

In changing slit spacing:In changing slit spacing: By decreasing the distance between the slits By decreasing the distance between the slits

the distance from the central fringe would the distance from the central fringe would increase.increase.

By increasing the distance between the slits By increasing the distance between the slits the distance from the central fringe would the distance from the central fringe would decrease.decrease.

In changing the wavelength of the waves:In changing the wavelength of the waves: By decreasing the wavelength of the wave, By decreasing the wavelength of the wave,

the distance from the central fringe would the distance from the central fringe would decreasedecrease

By increasing the wavelength of the wave, By increasing the wavelength of the wave, the distance from the central fringe would the distance from the central fringe would increase.increase.

LIGHT WAVESLIGHT WAVESWAVES OR PARTICLESWAVES OR PARTICLES

(5.1)(5.1) The earliest comprehensive theory of light was The earliest comprehensive theory of light was

advanced by Christiaan Huygens, who proposed a advanced by Christiaan Huygens, who proposed a wave theory of light, and in particular demonstrated wave theory of light, and in particular demonstrated how waves might interfere to form a wave front, how waves might interfere to form a wave front, propagating in a straight line. It recognizes that each propagating in a straight line. It recognizes that each point of an advancing wave front is in fact the center point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary may be regarded as the sum of all the secondary waves arising from points in the medium already waves arising from points in the medium already traversed. This view of wave propagation helps traversed. This view of wave propagation helps better understand a variety of wave phenomena, better understand a variety of wave phenomena, such as diffraction.such as diffraction.

(5.1) continuation 1(5.1) continuation 1 However, the theory had difficulties in other matters, However, the theory had difficulties in other matters,

and was soon overshadowed by Isaac Newton's and was soon overshadowed by Isaac Newton's corpuscular theory of light. That is says that light is corpuscular theory of light. That is says that light is made up of small discrete particles called made up of small discrete particles called "corpuscles" (little particles). In its contemporary "corpuscles" (little particles). In its contemporary incarnation, the theory of photons, this idea explains incarnation, the theory of photons, this idea explains many properties of light, in particular the many properties of light, in particular the photoelectric effect. However, it fails to explain other photoelectric effect. However, it fails to explain other effects, such as interference and diffraction. It was effects, such as interference and diffraction. It was therefore superseded by the wave theory of light, therefore superseded by the wave theory of light, later understood as part of electromagnetism, and later understood as part of electromagnetism, and eventually supplanted by modern quantum eventually supplanted by modern quantum mechanics and the wave–particle duality. Newton's mechanics and the wave–particle duality. Newton's particle viewpoint went essentially unchallenged for particle viewpoint went essentially unchallenged for over a century.over a century.

(5.1) continuation 2(5.1) continuation 2 In the early 1800s, the double-slit experiments by In the early 1800s, the double-slit experiments by

Young provided evidence for Huygens' wave Young provided evidence for Huygens' wave theories. The double-slit experiment in is an theories. The double-slit experiment in is an experiment that demonstrates the inseparability of experiment that demonstrates the inseparability of the wave and particle natures of light and other the wave and particle natures of light and other quantum particles. A coherent light source quantum particles. A coherent light source illuminates a thin plate with two parallel slits cut in it, illuminates a thin plate with two parallel slits cut in it, and the light passing through the slits strikes a and the light passing through the slits strikes a screen behind them. The wave nature of light causes screen behind them. The wave nature of light causes the light waves passing through both slits to the light waves passing through both slits to interfere, creating an interference pattern of bright interfere, creating an interference pattern of bright and dark bands on the screen. However, at the and dark bands on the screen. However, at the screen, the light is always found to be absorbed as screen, the light is always found to be absorbed as discrete particles, called photons.discrete particles, called photons.

(5.1) continuation 3(5.1) continuation 3 In 1905, Albert Einstein provided an explanation of In 1905, Albert Einstein provided an explanation of

the photoelectric effect, a hitherto troubling the photoelectric effect, a hitherto troubling experiment that the wave theory of light seemed experiment that the wave theory of light seemed incapable of explaining. He did so by postulating the incapable of explaining. He did so by postulating the existence of photons, quanta of light energy with existence of photons, quanta of light energy with particulate qualities. The photoelectric effect is a particulate qualities. The photoelectric effect is a quantum electronic phenomenon in which electrons quantum electronic phenomenon in which electrons are emitted from matter after the absorption of are emitted from matter after the absorption of energy from electromagnetic radiation such as x-energy from electromagnetic radiation such as x-rays or visible light.[1] The emitted electrons can be rays or visible light.[1] The emitted electrons can be referred to as photoelectrons in this context. The referred to as photoelectrons in this context. The effect is also termed the Hertz Effect, due to its effect is also termed the Hertz Effect, due to its discovery by Heinrich Rudolf Hertz, although the discovery by Heinrich Rudolf Hertz, although the term has generally fallen out of use.term has generally fallen out of use.

Photoelectric effect takes place with photons with Photoelectric effect takes place with photons with energies of about a few eV. If the photon has energies of about a few eV. If the photon has sufficiently high energy, Compton scattering (~keV) sufficiently high energy, Compton scattering (~keV) or Pair production (~MeV) may take place.or Pair production (~MeV) may take place.

(5.2)(5.2) Much in quantum mechanics revolves around the Much in quantum mechanics revolves around the

apparent impossibility of the wave-particle duality. It apparent impossibility of the wave-particle duality. It all started with the question whether light is a wave all started with the question whether light is a wave or a particle. Huygens started by proclaiming light is or a particle. Huygens started by proclaiming light is a wave, but years later the photoelectric effect a wave, but years later the photoelectric effect seemed to indicate light consisted of particles after seemed to indicate light consisted of particles after all. Now we know that light, as well as "particles" all. Now we know that light, as well as "particles" such as electrons, sometimes behave as particles such as electrons, sometimes behave as particles and sometimes as a wave. This is called wave-and sometimes as a wave. This is called wave-particle duality and is probably the first curiosity one particle duality and is probably the first curiosity one encounters when starting with quantum mechanics. encounters when starting with quantum mechanics.

A good way of demonstrating this duality is the A good way of demonstrating this duality is the double slit experiment.double slit experiment.

Diagram showing Double’s slit experimentDiagram showing Double’s slit experiment

Rays of light Rays of light (5.3) (5.3)

Diffraction is normally taken to refer to various Diffraction is normally taken to refer to various phenomena which occur when a wave encounters an phenomena which occur when a wave encounters an obstacle. It is described as the apparent bending of obstacle. It is described as the apparent bending of waves around small obstacles and the spreading out waves around small obstacles and the spreading out of waves past small openings. Very similar effects of waves past small openings. Very similar effects are observed when there is an alteration in the are observed when there is an alteration in the properties of the medium in which the wave is properties of the medium in which the wave is travelling, for example a variation in refractive index travelling, for example a variation in refractive index for light waves or in acoustic impedance for sound for light waves or in acoustic impedance for sound waves and these can also be referred to as waves and these can also be referred to as diffraction effects. Diffraction occurs with all waves, diffraction effects. Diffraction occurs with all waves, including sound waves, water waves, and including sound waves, water waves, and electromagnetic waves such as visible light, x-rays electromagnetic waves such as visible light, x-rays and radio waves. As physical objects have wave-like and radio waves. As physical objects have wave-like properties, diffraction also occurs with matter and properties, diffraction also occurs with matter and can be studied according to the principles of can be studied according to the principles of quantum mechanics.quantum mechanics.

While diffraction occurs whenever While diffraction occurs whenever propagating waves encounter such changes, propagating waves encounter such changes, its effects are generally most pronounced for its effects are generally most pronounced for waves where the wavelength is on the order waves where the wavelength is on the order of the size of the diffracting objects. The of the size of the diffracting objects. The complex patterns resulting from the intensity complex patterns resulting from the intensity of a diffracted wave are a result of the of a diffracted wave are a result of the superposition, or interference of different superposition, or interference of different parts of a wave that traveled to the observer parts of a wave that traveled to the observer by different paths.by different paths.

The formalism of diffraction can also The formalism of diffraction can also describe the way in which waves of finite describe the way in which waves of finite extent propagate in free space. For example, extent propagate in free space. For example, the expanding profile of a laser beam, the the expanding profile of a laser beam, the beam shape of a radar antenna and the field beam shape of a radar antenna and the field of view of an ultrasonic transducer are all of view of an ultrasonic transducer are all explained by diffraction theory.explained by diffraction theory.

(5.4)(5.4) In a material of constant refractive In a material of constant refractive

index, light travels in straight lines.  index, light travels in straight lines.  Whether you think of light as made up Whether you think of light as made up of waves or photons, the path that of waves or photons, the path that either takes is called a ray.  In either takes is called a ray.  In geometrical optics we trace rays to geometrical optics we trace rays to learn how light travels from one point learn how light travels from one point to another.  A ray is indicated by a to another.  A ray is indicated by a straight line.straight line.

Diagram showing a Pinhole cameraDiagram showing a Pinhole camera A pinhole camera is a very simple camera A pinhole camera is a very simple camera

with no lens and a single very small aperture. with no lens and a single very small aperture. Simply explained, it is a light-proof box with Simply explained, it is a light-proof box with a single hole in one side. Light from a scene a single hole in one side. Light from a scene passes through this single point and projects passes through this single point and projects an inverted image on the opposite side of the an inverted image on the opposite side of the box. Cameras using small apertures, and the box. Cameras using small apertures, and the human eye in bright light both act like a human eye in bright light both act like a pinhole camera.pinhole camera.

Diagram showing where the light enters in to Diagram showing where the light enters in to the camerathe camera