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Electromagnetic Waves (option G)
1. The nature of electromagnetic (EM) and light sources
The origin and creating of electromagnetic wave
EM Waves are produced by the accelerated electric charges (when they change speed or direction) .
Charged object produces electric field. Accelerating charge produces changing electric field. James Maxwell theory
(later confirmed by experiment) found that the changing electric field generate magnetic field. ⇒ Accelerating
charge creates both magnetic and electric field.
Examples:
1. radio waves
antenna: an alternating current
produces a radio wave
2. light
Light waves have a much higher frequency than radio waves. However, it is not possible to produce light by simply
moving a charge up and down very fast (antenna), as it is not possible to change the direction of charge quickly
enough.
Atoms contain electrons that can exist in different energy levels. When an electron changes from a high energy
level to a low one it emits electromagnetic radiation/photon. Energy of the photon equals the electron’s change in
energy ΔE. The frequency of the light, f is related to the change in energy ΔE by the equation:
where h is Planck’s constant 6.63x 10-34 Js
ΔE = hf
Light emitted when electron changes from high energy orbit (E3)
to low energy orbit (E2)
Since there are many electron energy levels in an atom this leads
to the emission of light with many different frequencies, each
frequency corresponding to a different colour
3. Even higher frequencies
Electron energy levels are in the order of 10 eV. This is 10 x 1.6 x10-19 J.
Using the formula ΔE = hf an energy change of 10 eV will give rise to light with a frequency of 2.42 x10 15 Hz.
However, EM radiation with much higher frequency, over 1020 Hz, does exist. This would need an energy change in
the order of MeV, much greater than electron energies. Radiation with such high energy comes from the nucleus.
Characteristics of EM waves
EM wave is a transverse wave, the electric and magnetic fields oscillate perpendicular
to each other and the electromagnetic wave moves in a direction perpendicular to both of the fields.
Any electromagnetic wave made up of changing electric and magnetic fields travel
through vacuum with the SAME SPEED! speed of light c ≈ 3 x 108 m/s
The speed of EM waves is INDEPENDENT of the motion of the source.
EM waves are waves, so:
c = λf
(in vacuum: independent of the frequency of the wave)
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EM waves carry energy (as any wave does) – example: warmth on the skin while walking outside
The energy of a wave is directly proportional to its frequency, but inversely proportional to its wavelength. Short
wavelengths are more energetic than long wavelengths. On the other hand energy (and intensity) of a wave is
proportional to its amplitude2.
The electromagnetic spectrum (EM spectrum)
Waves can be classified in terms of their wavelength. Each range of wavelength has a different name, different
mode of production and different uses.
The regions are not clearly separated, For example, there is considerable overlap between X-rays and gamma rays.
Some you can see (visible part), some you can feel - sense (infrared – heat) , some can do damage (ultraviolet), and
some could do a lot of harm or could save your life (x-rays, gamma rays). Some will make your life comfortable and
very dependent on (microwave oven – radio , TV, cell phones...),...
Some animals can “see” light that we can not. Yellow eyelash viper can “see” (sensors) infrared radiation.
EM spectrum – the whole range of possible wavelengths ( or frequencies).
You should be familiar with the order of magnitude of the frequencies (and wavelengths) of the different regions.
Radio waves
Radio waves have the longest wavelengths, and lie in the frequency range from 30 Hz to greater than 3000 MHz.
Radio waves are produced (among other ways) from an alternating current in a tuned electrical circuit. They are
also produced as a piece of adhesive is slowly peeled from a surface, as you can confirm by holding a transistor
radio near the tape and listening for pops and snaps coming from the speaker.
As they do not penetrate solid materials, radio waves are relatively easily reflected off surfaces and this makes
them ideal for communication technology: AM (amplitude modulated) and FM (frequency modulated) radio,
television, CB radio, radio microphones and scanning devices in MRI (magnetic resonance imaging). Because of
their many uses governments must regulate the bandwidth that can be used in communication devices in order to
avoid congestion of the airwaves.
Long and medium wavelength radio waves easily diffract around obstacles such as small mountains and buildings,
and they can be reflected by the earth’s ionosphere. Therefore, there does not have to be a direct line of sight
between the antenna and the receiver and they can be broadcasted over large distances provided the transmitter
used is powerful. Short wavelength radio waves are not reflected off the ionosphere in the upper atmosphere but
rather pass into space. For this reason, these bands of radio waves are used for outer space and satellite
communications. These outer bands are overlapping in the microwave region of the EM spectrum.
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Microwaves
Short-wavelength radio waves 30 cm -1mm; frequencies from 109 Hz – 1012 Hz.
Since microwaves have a high frequency they can be used to transfer data: long distance telephone conversations,
mobile phone, satellite communication, short-range internet links.
Radar consists of short pulses of microwaves. They are used to detect the speed of vehicles by police, and to find
distances to aeroplanes and ships. It is a microwave system that guides large airliners into airports.
Microwave oven: microwaves of frequency 2450 MHz/10 cm resonate with water molecules, the molecules vibrate
and the increased kinetic energy implies an increase in temperature. The heat is therefore generated in the
substance itself rather than conducted in from the outside, and this allows food to be cooked rapidly. At short
distances from the source, microwave radiation can damage living tissue.
They are also used in the analysis of fine details concerning atomic and molecular properties of matter .
Infrared
EM waves with frequencies just below that of red light (1012 Hz – 4.3 x1014 Hz; λ: 1mm – 700 nm)
These waves can be felt as heat on our skin but cannot be seen with our eyes.
Infrared rays are often generated by the rotations and vibrations of molecules of the hot objects. In turn, when
infrared rays are absorbed by an object its molecules rotate and vibrate more vigorously, the internal energy of the
body increases resulting in an increase in the object’s temperature.
Infrared is used in TV remote controls, optical communications, and physical therapy. Most remote controls
operate on a beam of infrared light with a wavelength of about 1000 nm. This infrared light is so close to the
visible light and so low in intensity that it cannot be felt as heat. It is also used in night vision binoculars to see
warm objects in the absence of visible light.
Thermo grams – photographs made with infrared radiation.
Computer translates intensity and frequency of the radiation
into colors that we can recognize. Warmer colors indicate
higher temperatures.
Left – cat’s head – warmest red, coolest blue –
Right – Atlantic Ocean off the coast of the North America –
warmest swirling red streak is Gulf Stream.
They can also identify environmental problems. Because this radiation is scattered by small particles in the
atmosphere, they can be used in haze photography. It is also employed in the identification of the molecular
structure of many organic compounds/ vibrational spectroscopy.
Visible light
Visible light is in the range of frequencies that receptors in our eyes are sensitive to EM
Colour Wavelength
radiation between about 400 nm to 700 nm. Our brains respond to different
violet
380—450 nm
frequencies by seeing them as different colours: red is the lowest frequency and blue
blue
450—495nm
the highest. Humans have evolved with vision most sensitive to the wavelengths that
green
495—570nm
are strongest, the most intense from the Sun. In addition to that, although our Sun
yellow 570—590 nm
emits all frequencies, most of the frequencies are absorbed when the radiation passes
orange 590—620 nm
through the atmosphere.
red
620—750 nm
The eye’s sensitivity is maximum at λ ≈ 560 nm (yellow-green) Aliens from another
planets, with a Sun with different temperature would have the center of sensitivity at different wavelengths than
ours.
It’s also true that if we used radio to see then we would have to have antennae
instead of eyes and that wouldn’t look very attractive.
Use: optics and optical instruments
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Ultraviolet
EM waves with frequencies just above that of violet light— 7.5x1015 Hz to 1017 Hz (λ: 10-7 m - 10-9 m)
Ultraviolet radiation is produced by high energy electron transitions. Ultraviolet cannot be seen but does cause the
emission of visible light from some substances.
This is why white clothes glow when illuminated by ultraviolet disco lights.
Although these rays are invisible, they often make their presence known by causing sun tans with moderate
exposure. More prolonged or intense exposure can have harmful consequences, including an increased probability
of developing a skin cancer. Fortunately, most of the UV radiation that reaches Earth from the Sun is absorbed in
the atmosphere by ozone (03) and other molecules in the stratosphere. At least for now. A significant reduction in
the ozone concentration in the stratosphere could result in an unwelcome increase of UV radiation on Earth’s
surface.
UV radiation has the ability to ionise atoms and this is the reason why ozone is produced in the atmosphere. This
ozone is capable of killing bacteria and therefore it can be put to good use in the sterilisation of many objects.
The atoms of many elements emit UV radiations that are characteristic of those elements, and this quality allows
many unknown substances to be identified. UV radiation can be detected by photography and the photo-electric
effect. Furthermore, certain crystals fluoresce when they absorb UV radiation, and this is put to use in washing
powders to make the “whites look whiter”.
X-rays
f: between about 1017 Hz to 1020 Hz,
It can be generated by the rapid deceleration (stopping) or deflection of fast-moving electrons when
they strike a metal target or other hard objects.
X-rays can penetrate different materials to different degrees, depending on the frequency/energy and the material
itself. For example, X-rays can easily penetrate skin and flesh containing mainly the lighter atoms carbon, hydrogen
and oxygen, but are less able to penetrate dense material such as bone containing the heavier element calcium.
Because X-rays are detected by photography, the photographic plate placed beneath the body can be used to
identify possible bone fractures.
X-rays are ideal for identifying flaws in metals. They are also used in CAT scans (computerised axial tomography).
Because tissues absorb X-rays differently, when a body is scanned, the internal organs and tissues can be
identified from the analysis of the images produced by the computer.
X-radiation can ionise gases and cause fluorescence.
Because X-rays produce interference patterns when they interact with crystals in rocks and salts, the structure of
these regular patterns of atoms and molecules can be determined by this process of X-ray diffraction.
X-rays can damage living cells and continued use and exposure to X-rays is discouraged. Radiologists who work in
X-ray departments always stand behind lead-lined walls when an X-ray is being taken. On the other hand, some
types of diseased cells are damaged more easily than are healthy cells. Therefore, if X-rays are carefully controlled,
they can be used to destroy cancerous cells, as is the case with the use of certain lasers in radiation therapy.
Gamma radiation (γ)
The gamma radiation region of the EM spectrum overlaps with the X-ray region and their use in cancer
therapy overlaps with the last statement made about X ray use in radiotherapy. These high frequency rays are
highly penetrating and are produced by natural and artificial radioactive materials. As such, gamma rays will
pass through metres of air and need large thicknesses of concrete or lead to absorb them in order to protect
humans from danger. Gamma radiation can be detected by an ionisation chamber as found in a Geiger-Müller
counter.
More recently they are used to kill microorganisms in food. If you see a label in the grocery store that tells
”irradiated food” you will now know that it has been exposed to γ rays from cobalt-60 from 20 to 30 min. NASA
has irradiated astronauts’ food since the 1960s.
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EM radiation and health
When electromagnetic radiation is absorbed by human tissue the effect is dependent on the wavelength.
Radio — microwave
When radio waves are absorbed by the body, they cause a slight heating, but do not change the structure of the
cells. There seems to be no physical reason why they should cause illness, but cases of illness have been attributed
to closeness to a powerful source of radio waves such as a radio antenna. The higher frequency of microwaves
used in mobile phone communication means that the heating effects are greater but the power of the signal is
weak. There is some evidence that a mobile phone held close to the brain for a long period of time might cause
some damage. There is however, significant risk for people dependent on electronic devices such as pacemakers,
that interference from strong sources of radio signals can result in malfunction.
IR
The heating effect caused by infrared radiation is significant: exposure to JR can result in burns but low levels of IR
cause no harm.
Light
High powered sources of visible light, such as lasers, can damage the eyes and burn the skin.
UV
Exposure to ultraviolet radiation triggers the release of chemicals in the skin that cause redness and swelling. The
effect is rather like a burn, hence the name sunburn. UV radiation can also change the structure of the skin’s DNA
leading to skin cancer.
X-ray and γ ray
Both X-rays and y (gamma) rays have enough energy to remove electrons from atoms; this is called ionization.
When radiation ionizes atoms that are part of a living cell it can affect the ability of the cell to carry out its function
or even cause the cell wall to be ruptured. If a large number of cells that are part of a vital organ are affected then
this can lead to death. To prevent this there are strict limits to the exposure of individuals to these forms of
radiation.
The interaction of EM radiation with matter
When EM radiation is produced, changing electric and magnetic fields
spread out in three dimensions from the source: we say that the wave
is transmitted through the medium. The intensity of a wave is the
power per unit area, as the wave becomes more spread out its
intensity becomes less.
If the power (of the source) in the whole wave is P then at a distance r
this power is spread over a sphere of area 4πr2 . The intensity, I, at a
distance, r, is therefore
I=
P
4πr2
So, there is an inverse square relationship
Radio waves spread out in a sphere
centred on the source.
I 
1
r2
As the wave spreads out it interacts with atoms of the medium.
First, let's look at the general properties of light interacting with
matter. When light strikes an object it will react in one or more of the
following ways depending on whether the object is transparent,
translucent, opaque, smooth, rough, or glossy:
It will be wholly or partly transmitted .
It will be wholly or partly reflected.
It will be wholly or partly absorbed.
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How a receiving material responds when light is incident upon it depends on the frequency of the light and the natural
frequency of electrons in the material and vibrational natural frequencies of the molecules.
If the frequency of light matches one of the natural frequencies of the material light will be absorbed and converted
into vibrational energy of the electrons/molecules - thermal energy.
If the frequency of light waves do not match natural freq., the electrons in the atoms of the object still begin vibrating
but not with great amplitudes. If the object is transparent for particular frequency vibrations of the electrons are
passed on to neighboring atoms through the bulk of the material and reemitted on the opposite side of the object. If
the object is opaque, the electrons of atoms on the material's surface vibrate for short periods of time and then
reemit the energy as a reflected light wave. Such frequencies of light are said to be reflected.
This is why microwaves are absorbed by water molecules; IR radiation is absorbed by atoms in solids; and UV
radiation is absorbed by the ozone layer. However, the energy in an X-ray is too high to excite an atomic electron
and it can pass through most solids.
Transmission
Transmission takes place when light passes through an object; the object, in this case, is said to be transparent.
Light striking the surface of an object straight on (that is, at normal incidence) will pass through without refraction.
But light striking at any other angle will be refracted as well as partially reflected: Transparent materials are clear
(can be seen through).
Reflection
The colour of objects can be explained in terms of reflection and absorption
of different wavelengths of light. If a mixture of red, blue and green light
is shone onto a blue object the red and green is absorbed but the blue is reflected.
Law of reflection: r = i
Refraction
EM radiation travels at different speeds in different mediums. When
a wave passes from one medium to another the change in speed
causes its direction to change. This explains why a ray of light bends
when it passes through a block of glass.
When the light passes from one material into other at an
angle, the light beam is refracted according to Snell's law
n1 sin1 = n2 sin2
Refractive index n of a medium (substance) is defined as the ratio of the speed in a vacuum, c, to the speed of
light in a material through witch it passes, v: n = c/v
As v can never be greater than c, refractive index is always greater than 1.00.
The refractive index of air is usually taken as 1.0, although its true value is 1.0003.
The frequency, f, of the wave remains constant when the light passes through substance. Thus, if the velocity, c, is
reduced on passage through a substance, the wavelength, λ, must also decrease.
Dispersion (Chromatic dispersion)
the speed of light through a material varies slightly with the frequency of the light.
Each wavelength is refracted at a slightly different angle when passing through a
material at an angle. The longer the wavelength, the smaller index of refraction.
nred < nblue , red light is refracted less than blue light This is why rainbows are
produced when white light passes through a prism.
Synthesis of white light: the spectra are combined
together and they appear as white colour.
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Scattering
Scattering takes place when light is scattered in all directions
while passing through material. The object is said to be
translucent. Translucent materials allow light to pass through
them only diffusely giving diffuse images (frosted glass).
The colours of our world
If the Earth had no atmosphere, what color would the sky be?
If the Earth had no atmosphere, the sun’s light would travel directly from the Sun in a straight line towards our
eyes and we would see the Sun as a very bright star (white) in sea of blackness.
With atmosphere? Why is the sky blue?
When the white light hits a molecule in the air that has the resonant (natural) frequency equal to the some
frequency in the white light, the resonance occur. If the molecule that was hit was in the solid or liquid it would
make many collisions with other molecules and give up its energy in the form of heat. There is nothing to hit in the
atmosphere. So the molecule will reemit in different direction.
Scattering is the process of absorption of a light wave by an atom followed by radiation in different direction.
The reemitted light is sent in all directions. It is scattered.
Tiny particles (The nitrogen and oxygen molecules...) in the air scatter high frequencies and large particles (CO 2 ...)
scatter low frequencies of light.
Scattering of violet and blue frequencies of sunlight in all directions is what gives the sky its blue color.
A clear cloudless day-time sky is blue because molecules in the air (the nitrogen and oxygen molecules...) scatter blue
light from the sun more than they scatter red light.
Blue light is scattered all around the sky. Whichever direction you look, some of this scattered blue light reaches you. Since you
see the blue light from everywhere overhead, the sky looks blue. Although violet light is scattered more than blue, our eyes are
more sensitive to blue, so we see a blue sky.
If the Earth had atmosphere without small particles, what color would the sky be?
Light travels through space in a straight line as long as nothing disturbs it. As light moves through the atmosphere,
it continues to go straight until it bumps into a bit of dust or a gas molecule. Then what happens to the light
depends on its wave length and the size of the thing it hits. Let’s imagine for the moment that there are no small
particles. When light (visible) hits these large particles, it gets reflected in different directions. The different colors
of light are all reflected by the particle in the same way. The reflected light appears white because it still contains
all of the same colors. Whichever direction you look, some of this reflected light reaches you. Since you see the
white light from everywhere overhead, the sky looks white. If there were no small particle the sky would be
white!!!!!!
Why Sunsets Are Red?
As the day progresses and the sun is lower in the sky, the path of the light
through the atmosphere is longer before it gets to you; more short wavelength
violet, blue and greens are now scattered from the sunlight. As the path
through atmosphere is greater there is more chance for the blue light to scatter
multiple times, less chance to reach your eye.
When we look towards the sun at sunset, we see red and orange colours
because the blue light has been scattered out and away from the line of sight.
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Sources of light
Light is produced when atomic electrons change from a high energy level
to a low one. Electrons must first he given energy to reach the high energy
level. This can be achieved in a variety of ways.
The light bulb
A light bulb consists of a thin wire filament enclosed in a glass ball.
When an electric current flows through the filament, energy is
transferred to the filament. This causes the filament to get hot and
electrons to become excited (lifted to a higher energy level). Each
time an excited electron falls back down to its low energy level a
pulse of light is emitted, and these pulses are called photons.
The glowing filament of a light bulb.
The discharge tube
A discharge tube is a glass tube containing a low pressure gas. A high potential difference created between the
ends of the tube causes charged particles in the gas to be accelerated. When these fast moving particles interact
with the other gas atoms they excite atomic electrons into high energy levels. When the electrons become deexcited light is emitted.
The fluorescent tube
As you can see from the photograph of the discharge tube containing mercury
vapour, it does not produce much light. However, a large amount of radiation
in the UV region is emitted. This is invisible to the human eye, but if the inside
of the tube is coated with a substance that absorbs UV radiation and gives out
visible light (fluorescence) then this invisible radiation is converted to light.
The result is a much brighter light. This is the principle behind the common
strip light, properly called a fluorescent light.
The amount of light from a discharge tube containing
mercury vapour is low but the UV radiation is high.
Comparison of light from a light bulb, discharge tube and fluorescent tube
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The laser - Light Amplification by Stimulated Emission of Radiation
Spontaneous Emission: An atom in excited state can
return to the lower state spontaneously. LED, lamp…
Stimulated Emission: Stimulated emission is a very uncommon process in nature but it is central to the operation
of lasers. Suppose an electron is already in an excited state and a photon comes along with energy equal to the
difference in the energy between the excited state and the ground state of the atom or molecule. What will
happen is that the photon will stimulate the electron to fall into the lower energy state emitting a photon which is
in phase and in the same direction as original photon. This is resonance process, called stimulated emission.
One photon interacting with an excited atom results in two photons coherent photons (identical and in phase)
Such waves will constructively interfere, leading to a more intense wave.
Population inversion
The production of laser light relies on a process that promotes (or pumps) a large number of electrons to a higher
energy level. When a sizable population of electrons resides in upper levels, this condition is called a "population
inversion". It is necessary to create a population inversion for laser action to occur. Some atoms will undergo
spontaneous emission, and the resulting photons cause other atoms to undergo stimulated emission, leading to a
chain reaction. The resultant light is composed of one frequency, very intense, and coherent. To have inverse
population it is important that higher energy level is metastable state – excited state with longer lifetime, so the
electrons can remain in this state for a longer period before they decay to the ground state.
Finding substances in which a population inversion can be set up is central to the development of new kinds of
laser.
The first laser used synthetic ruby a material with chromium ions with metastable state that are able to stay excited for some
time after excitation. Electrons are first pumped up to the higher level by flash of light. Some of excited ruby atoms then start
to de-excite. This light can then interact with other chromium ions that are in the metastable levels causing them to emit
light of the same wavelength by stimulated emission. As each stimulating photon leads to the emission of two photons, the
intensity of the light emitted will build up quickly. This is a cascade process. The result is an amplification of the light, hence
the name LASER (Light Amplification by the Stimulated Emission of Radiation).
The tube flashes, pumping the
ruby atoms into the high level. As
each photon passes an excited
ruby atom it de-excites and
another photon is emitted. This is
called stimulated emission of
radiation because the atoms are
being stimulated to give out
radiation by the passing photon.
MASER Microwave amplification by stimulated emission of radiation
LASER Light amplification by stimulated emission of radiation
Both apply the same principles, and only differ in the frequency range in which they operate.
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The theoretical basis of the laser was first proposed by Albert Einstein in 1915. The first design was proposed by
Townes and Schawlow in 1958, and the first working laser was produced by Maiman in 1960. Even for a time
thereafter, there was very little interest in the applications of laser beams. However, in the past 20 years their
applications have become extensive in technology, industry, medicine and communications.
Originally viewed as a curiosity, lasers now are found in a wide variety of applications, including
• surgery - malignant tissue absorbs laser radiation more strongly than does healthy tissue. Laser beams of a
specific wavelength, pulse rate, power density and energy dose are chosen to suit the absorption properties of the
particular tumour - as laser therapy to correct the optical properties of the lens of the eye
• precision cutting tools, CDROM readers, supermarket checkout stand scanners, and holograms
• In military operations - the success of laser guidance systems in weapons
• Scientists use lasers to produce a superheated gas that we call plasma. It is hoped that research in this area may
one day make nuclear fusion reactors commercially viable.
Monochromatic
A monochromatic source of radiation is one that has a extremely narrow band of frequencies or extremely small
narrow wavelength band (or colour in the case of visible light). Most sources of light emit many different
wavelengths. Laser light is monochromatic.
Light sources giving many wavelengths are white.
Unlike other light sources, each photon of laser light has the same wavelength; this means the laser is a single
colour or monochromatic.
Coherence
When a light bulb emits photons, they are emitted randomly in different directions and with different phase
because the filament atoms act independently from each other. The light emitted is incoherent.
However, in a laser, each photon of light is in phase with all the other photons.
Laser light is a coherent and monochromatic source of electromagnetic radiation.
Two sources are coherent if they
▪ have the same frequency
▪ maintain a constant phase difference with each other.
◘ Two coherent waves have a phase difference which remains constant over time.
Waves that have the same frequency, the same amplitude and constant phase relationship are
said to be coherent. As we have seen, the light from a light bulb is emitted randomly so two
light bulbs will not be coherent . However, we can make two coherent sources by splitting one
source in two, but first we must make one light source as illustrated. Different parts of a
filament give out light of different wavelength and phase, but using a narrow slit we can select
just one part of the filament. This doesn’t make the source monochromatic but all parts are in
phase.
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INTERFERENCE
Interference is the addition (superposition) of two or more waves overlapping that results in a new wave pattern.
When two waves of the same type are incident at the same place they add together to give one resultant wave,
this is called superposition. The resultant is dependent on the relative phase of the two waves
Principle of superposition: When two or more waves overlap, the resultant displacement at any point and at any
instant is the vector sum of the displacements of the individual waves at that point: y = y1 + y2

PD = path difference is the difference in distances traveled by waves from two sources to a point P: PD = d2 – d1
Constructive and distractive interference
Two coherent waves traveling along two different paths to the same point will
►
interfere constructively if there is a difference in distance traveled that is equivalent to a whole number of
wavelengths:
PD = n λ
►
n = 0, ± 1, ± 2, ± 3, …
interfere destructively if there is a difference in distance traveled that is equivalent to a half number of
wavelengths:
PD = (n + ½ ) λ
n = 0, ± 1, ± 2, ± 3, …
These principles were presented to explain the two-point source interference patterns that are characteristic of
Young's experiment and a wavelength measurement. Yet, these principles are more general in the sense that they
can explain any physical situation in which waves take two different paths from two coherent sources to the same
point. Such coherent waves will undergo interference resulting in interference pattern.
● Real-world examples of two-point source interference
So where in this world do we observe two-point source interference? Where can we experience the phenomenon
that light taking two paths from two locations to the same point in space can undergo constructive and destructive
interference?
This is relatively common for homes located near
mountain cliffs. Waves are taking two different
paths from the source to the antenna - a direct
path and a reflected path. It might be a problem
if 2d = (n + ½ ) λ for certain frequency. It’s lost.
While the interference is momentary (the plane
does not remain in a stationary location), it is
nonetheless observable.
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A relatively common demonstration of sound wave interference can be performed
with two speakers in a large room. If both speakers are hooked up to the same
sound source producing a monotone sound, then a sound interference pattern can
be observed within the room. If one were to walk along a line parallel to the line
connecting the speakers, there would be clear locations of destructive and
constructive interference. At locations of destructive interference, the sound
intensity would become weak, perhaps even barely noticeable. At locations of
constructive interference, the sound intensity would be amplified.
constructive and destructive interference, This effect occurs when two light
beams overlap but it can only be observed if the beams are coherent.
 Why do I not observe bright and dark fringes along my living room wall from the interference of light from two
lamps?
Light from an incandescent source is emitted with a completely random phase. Although the light from two
separate sources (two light bulbs) will interfere, because of the randomly changing phase no permanent points
of constructive or destructive interference will be observed since the phase difference between the waves from
the two sources is no longer constant i.e., the sources are no longer coherent. There will be no interference
patterns.
Young ’s double slit experiment
This is one of the great classic experiments of physics and did much to reinforce the wave theory of light. The
experiment was carried out by Thomas Young in about 1830. The essential features of the experiment are shown
When the light passes through the narrow slit it spreads out due to
diffraction; this makes it possible to pass the light through two more slits.
Filament bulb S0 is turned into a single source using a narrow slit
If laser light is used it is already coherent so the first slit is not necessary.
The light from two light bulbs will not be coherent, so there will be no interference
pattern. SO, he first made one light source by allowing sunlight to fall onto a narrow
single slit which now became a point source. This didn’t make the source
monochromatic, but all parts were in phase. He got two coherent sources by splitting
one source in two.
Young observed a pattern of multi- coloured “fringes” in the screen. When he placed
a coloured filter between the single slit and double slit he obtained a pattern which
consisted of bright coloured fringes separated by darkness with the central one being
the bright.– monochromatic fringe pattern.
today: laser light is used as source S0.
Two waves from two slits will always start the journey with equal phase, so interference pattern – distribution
of constructive and destructive interference depends on their path difference
● The geometry of Young’s double slit experiment
S1 and S2 two coherent, monochromatic point sources.
D - distance from the sources to the screen ~ m
d - distance between the slits ~ mm.
The waves from the two sources will be in phase at Q
and there will be a bright fringe here.
What happens at P distance x from Q?
we drew the picture so that S1P = AP, so S2 A is path difference.
As D >> d and D >> x, θ’ is very small angle → angle S2AS1 is almost 900 so θ’ ≈ θ
13
The condition for a bright fringe at P distance x from center Q
is constructive interference. Path difference d sin θ must be
a whole number of wavelengths:
►
d sin θ = nλ
n = 0, ± 1, ± 2, ± 3, …
for small angles θ, tan θ = sin θ
tan  = x/D sin  = n λ /d
x
nλ
=
D
d
● Spacing s between the fringes:
s = xn+1 - xn =  n+1 λD - nλD
d
λD
d
s=
d
Young actually use this expression to measure the wavelength of the light he used
and it is a method still used today.
The condition for a dark fringe at P distance x from center Q
is destructive interference. Path difference d sin θ must be
an odd number of half wavelengths:
►
d sin θ = (n + ½ ) λ

n = 0, ± 1, ± 2, ± 3, …

x
λ
= n +1
2 d
D
intensity
● intensity distribution of the fringes on the screen
when the separation of the slits is large compared
to their width. The fringes are of equal intensity
and of equal separation.
If the slit separation is decreased, the pattern
will spread out.
light sensor can measure intensity of light
This equal intensity and equal separation pattern
breaks down when the separation between slits is
not large compared to their with – fortunately we
do not investigate that case
14
● Diffraction grating - increasing the number of slits
The intensity of double slit interference patterns is very low but can be increased by using more than two slits.
A diffraction gratings is a series of very fine parallel slits mounted on a glass plate. Additional slits at the same
separation will not affect the condition for constructive interference. In other words, the angle at which the light
from slits adds constructively will he unaffected by the number of slits.
When light is incident on the grating it is diffracted at each slit. The
slits are very narrow so the diffraction causes the light to propagate as
if coming from a point source.
To make the geometry simpler we will consider only parallel light rays
setting off from the slits at an angle θ. They’ll come together at infinity
(distant point) and interfere. Hence if we look at the light through a
telescope at angle θ to the grating a bright fringe will be observed.
If the path difference, PD, between neighbours is nλ then they will
interfere constructively, if (n + ½ ) λ then the interference will be
destructive.
d sin θ = n λ
d sin θ = (n + ½ ) λ
bright fringe
dark fringe
If white light is viewed through a diffraction grating,
each wavelength undergoes constructive interference
at different angles. This results in a spectrum.
The individual wavelengths can be calculated from
the angle using the formula
d sin θ = n λ
greater λ greater angle
The addition of further slits at the same slit separation has
the following effects;
• bright fringes maintain the same separation.
• bright fringes become much sharper.
• the overall amount of light being let through is increased,
so the pattern increases in intensity.
In practice, a diffraction grating is stated by its manufacturer to have “X lines per m, or cm, or mm”
For example: 600 lines per mm. Then slit separation is:
d = (1/600) mm = 1.67 x 10-6 m
15
Problems:
1 Calculate the frequency of light emitted when an electron changes from an energy of 10 eV to 6 eV
2 An atom has electrons that can exist in 4 different energy levels, 10eV, 9eV, 7eV and 2eV.
Calculate:
(a) the highest frequency radiation that can be produced
(b) the lowest frequency radiation.
3 What energy change would be required to produce EM radiation with a frequency of 1x10 18 Hz?
4. What is the wavelength of green light with a frequency of 6x10 14 Hz?
Solutions:
1. ΔE = hf ΔE = 4 eV = (4)(1.6x10-19) J = 6.4 x10-19 J
h = 6.63x 10-34 Js
f = ΔE/h = 0.97x1015 Hz
-19
-19
-34
2. highest ΔE = 8 eV = (8)(1.6x10 ) J = 12.8 x10 J h = 6.63x 10 Js
f = ΔE/h = 1.93x1015 Hz
-19
-19
-34
lowest
ΔE = 1 eV = (1)(1.6x10 ) J = 1.6 x10 J
h = 6.63x 10 Js
f = ΔE/h = 0.24x1015 Hz
-34
18
-16
-16
-19
3. ΔE = hf = (6.63x 10 )( 1x10 ) = 6.63x10 J = 6.63x10 /1.6x10 eV = 4.1x103 eV
4. c = λf λ = c/f = 3x108/6x1014
λ = 500 nm
Problems:
Use the spectrum to find out what type of radiation the following wavelengths would be and calculate their
frequency:
4. 430nm
5. 3.75m
6. 10 μm
7. 1nm
Problems:
8. If a light bulb emits 50 W of light what will its intensity be at a distance of 10 m?
9 If intensity of the radiation from the Sun reaching the Earth’s atmosphere is 1400 W/m 2 and the
Sun is 146 x 109 m from the Earth, calculate the power of the Sun.