Transcript Optical properties of materials

ENG2000 Chapter 10
Optical Properties of Materials
ENG2000: R.I. Hornsey
Optic: 1
Overview
• The study of the optical properties of materials is
a huge field and we will only be able to touch on
some of the most basic parts
• So we will consider the essential properties such
as absorption/reflection/transmission and
refraction
• Then we will look at other phenomena like
luminescence and fluorescence
• Finally we will mention applications, in particular
optical fibres and lasers
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Nature of light
• Light is an electromagnetic wave:
 with a velocity given by c = 1/(00) = 3 x 108 m/s
• In view of this, it is not surprising that the electric
field component of the wave should interact with
electrons electrostatically
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http://www.astronomynotes.com/light/emanim.gif
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• Many of the electronic properties of materials,
information on the bonding, material composition
etc. was discovered using spectroscopy, the
study of absorbed or emitted radiation
 evidence for energy levels in atoms
 evidence for energy bands and band-gaps
 photoelectric effect
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General description of absorption
• Because of conservation of energy, we can say
that I0 = IT + IA + IR
 Io is the intensity (W/m2) of incident light and subscripts refer
to transmitted, absorbed or reflected
• Alternatively T + A + R = 1 where T, A, and R are
fractions of the amount of incident light
 T = IT/I0, etc.
• So materials are broadly classed as
 transparent:relatively little absorption
and reflection
 translucent:light scattered within
the material (see right)
 opaque:relatively little transmission
http://www.tekano.pwp.blueyonder.co.uk/tekano/translucent.jpg
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• If the material is not perfectly transparent, the
intensity decreases exponentially with distance
• Consider a small thickness of material, x
• The fall of intensity in x is I so I = -a.x.I
 where a is the absorption coefficient (dimensions are m-1)
• In the limit of x  0, we get
dI
 a I
dx
• The solution of which is I = I0 exp(–ax)
• Taking “ln” of both sides, we have:
 I 
ax   ln 
I 0 
 which is known as Lambert’s Law (he also has a unit of light
intensity named for him)
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• Thus, if we can plot -ln(I) against x, we should
find a from the gradient
• Depending on the material and the wavelength,
light can be absorbed by
 nuclei – all materials
 electrons – metals and small band-gap materials
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ATOMIC ABSORPTION
• How the solid absorbs the radiation depends on
what it is!
• Solids which bond ionically, show high
absorption because ions of opposite charge
move in opposite directions
 in the same electric field
 hence we get effectively twice the interaction between the
light and the atoms
• Generally, we would expect absorption mainly in
the infrared
 because these frequencies match the thermal vibrations of
the atoms
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• If we think of our atom-on-springs model, there is
a single resonance peak:
absorption
f
f0
• But things are more complex when the atoms are
connected – phonons
 recall transverse and longitudinal optical phonons
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Electronic absorption
• Absorption or emission due to excitation or
relaxation of the electrons in the atoms
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http://www.nhn.ou.edu/~kieran/reuhome/vizqm/figs/hydrogen.gif
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Molecular materials
• Materials such as organic (carbon containing)
solids or water consist of molecules which are
relatively weakly connected to other molecules
• Hence, the absorption spectrum is dominated by
absorptions due to the molecules themselves
• e.g. water molecule:
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http://www.sbu.ac.uk/water/images/molecul5.jpg
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• The spectrum of liquid water
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http://www.sbu.ac.uk/water/images/watopt.jpg
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• Since the bonds have different “spring
constants”, the frequencies of the modes are
different
 when the incident illumination is of a wavelength that excites
one of these modes, the illumination is preferentially
absorbed
• This technique allows us to measure
concentrations of different gas species in, for
example, the atmosphere
 by fitting spectra of known gases to the measured
atmospheric spectra, we can figure out the quantities of each
of the gases
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Optical properties of metals
• Recall that the energy diagram of a metal looks
like:
empty
levels
T = 0K
EF
full
levels
 EF is the energy below which, at 0K, all electron states are
full and above which they are empty
 this is the Fermi Energy
• For T > 0, EF is the energy at which half of the
available energy states are occupied
• Semiconductors also have a Fermi level
 for an intrinsic material EF is in the middle of the bandgap
 nearer Ec for n-type; nearer Ev for p-type
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• This structure for metals means that almost any
frequency of light can be absorbed
• Since there is a very high concentration of
electrons, practically all the light is absorbed
within about 0.1µm of the surface
• Metal films thinner than this will transmit light
 e.g. gold coatings on space suit helmets
• Penetration depths (I/I0 = 1/e) for some materials
are:




water: 32 cm
glass: 29 cm
graphite: 0.6 µm
gold: 0.15µm
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• So what happens to the excited atoms in the
surface layers of metal atoms?
 they relax again, emitting a photon
• The energy lost by the descending electron is the
same as the one originally incident
• So the metal reflects the light very well – about
95% for most metals
 metals are both opaque and reflective
 the remaining energy is usually lost as heat
• In terms of electrostatics, the field of the radiation
causes the free electrons to move and a moving
charge emits electromagnetic radiation
 hence the wave is re-emitted = reflected
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• The metal appears “silvery” since it acts as a
perfect mirror
• OK then, why are gold and copper not silvery?
 because the band structure of a real metal is not always as
simple as we have assumed
 there can be some empty levels below EF and the energy reemitted from these absorptions is not in the visible spectrum
• Metals are more transparent to very high energy
radiation (x- & - rays) when the inertia of the
electrons themselves is the limiting factor
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• Reflection spectra for gold and aluminum are:
aluminum
spectrum is
relatively flat
gold reflects lots of
red wavelengths
blue
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red
http://www.thermo.com/eThermo/CMA/Images/Various/109Image_12275.gif
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Electronic absorption in non-metals
• Dielectrics and semiconductors behave
essentially the same way, the only difference
being in the size of the bandgap
• We know that photons with energies greater than
Eg will be absorbed by giving their energy to
electron-hole pairs
EC
EG
EV
hole
 which may or may not re-emit light when they relax
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• Hence, the absorption coefficients of various
semiconductors look like:
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• Semiconductors can appear “metallic” if visible
photons are all reflected (like Ge) but those with
smaller Eg, such as CdS look coloured
 yellow for CdS which absorbs 540nm and above
• The above picture is good for pure materials but
impurities can add extra absorption features
EC
hf1
phonon
hf2
EV
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• Impurity levels divide up the bandgap to allow
transitions with energies less than Eg
• Recombination can be either radiative (photon) or
non-radiative (phonon) depending on the
transition probabilities
• Practical p-n diodes usually contain a small
amount of impurity to help recombination
because Si has a relatively low recombination
“efficiency”
 for the same reason that Si is inefficient at generating light
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Refraction in non-metals
•
•
One of the most important optical properties of
non-metallic materials is refraction
This refers to the bending of a light beam as it
passes from one material into another

•
We define the index of refraction to be
n = c/v

•
e.g. from air to glass
where c is the speed of light in a vacuum and v is the speed
of light in the material (which is in general wavelengthdependent)
A familiar example is the prism where the
different amounts of bending separates out the
wavelengths
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• Refraction is also vital for other applications,
such as:
 optical fibres – keeps the light in
 semiconductor laser – keeps the light in the amplifying cavity
of the laser
• Given that
v
1

and c 
1
 0 0
 where µ and µ0 (= µrµ0) are the permeability of the material
and free space, respectively (a magnetic property)
 and  and 0 (= r0) are the permittivity of the material and
free space, respectively (an electrostatic property)
• We find that n = √(µrr) (≈ √r for many materials)
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• Since light is an electromagnetic wave, the
connection with both the dielectric permittivity ()
and the magnetic permeability (µ) is not
surprising
• The index of refraction is therefore a
consequence of electrical polarization, especially
electronic polarization
–
+
• Hence, the radiation loses energy to the electrons
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• Since E = hv/, and  doesn’t change, the velocity
must be smaller in the material than in free space
 since we lose E to the atoms, v must also decrease
• Electronic polarization tends to be easier for
larger atoms so n is higher in those materials
 e.g. glass: n ~ 1.5
 lead crystal: n ~ 2.1 (which makes glasses and chandeliers
more sparkly!)
• n can be anisotropic for crystals which have noncubic lattices
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Reflection in non-metals
• Reflection occurs at the interface between two
materials and is therefore related to index of
refraction
• Reflectivity, R = IR/I0, where the I’s are intensities
• Assuming the light is normally incident to the
interface:
n2  n1 2
R  

n2  n1 
n1
n2
 where n1 and n2 are the indices for the two materials
• Optical lenses are frequently coated with
antireflection layers such as MgF2 which work by
reducing the overall reflectivity
 some lenses have multiple coatings for different wavelengths
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Spectra
• So we have seen that reflection and absorption
are dependent on wavelength
 and transmission is what’s left over!
• Thus the three components for a green glass are:
ENG2000: R.I. Hornsey
Callister Fig. 21.8
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Colours
• Small differences in composition can lead to
large differences in appearance
• For example, high-purity single-crystal Al2O3 is
colourless
 sapphire
• If we add only 0.5 - 2.0% of Cr2O3 we find that the
material looks red
 ruby
• The Cr substitutes for the Al and introduces
impurity levels in the bandgap of the sapphire
• These levels give strong absorptions at:
 400nm (green) and 600nm (blue)
 leaving only red to be transmitted
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• The spectra for ruby and sapphire look like:
• A similar technique is used to colour glasses or
pottery glaze by adding impurities into the molten
state:
 Cu2+: blue-green, Cr3+: green
 Co2+: blue-violet, Mn2+: yellow
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http://www.valleydesign.com/images/sapp.jpg
http://home.achilles.net/~jtalbot/glossary/photopumping.gif
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Translucency
• Even after the light has entered the material, it
might yet be reflected out again due to scattering
inside the material
• Even the transmitted light can lose information by
being scattered internally
 so a beam of light will spread out or an image will become
blurred
• In extreme cases, the material could become
opaque due to excessive internal scattering
• Scattering can come from obvious causes:
 grain boundaries in poly-crystalline materials
 fine pores in ceramics
 different phases of materials
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• In highly pure materials, scattering still occurs
and an important contribution comes from
Rayleigh scattering
• This is due to small, random differences in
refractive index from place to place
• In amorphous materials such as glass this is
typically due to density or compositional
differences in the random structure
• In crystals, lattice defects, thermal motion of
atoms etc. also give rise to Rayleigh scattering
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• Rayleigh scattering also causes the sky to be
blue. The reason for this is the wavelengthdependence of Rayleigh scattering
 scattering goes as -4
 so since red ~ 2blue blue light is scattered ~16 times more
than red light
• This mechanism is of great technological
importance because it governs losses in optical
fibres for communication
• But before we get onto fibres, we will mention a
couple more basic effects
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Dispersion
• Dispersion is a general name given to things
which vary with wavelength
• For example, the wavelength-dependence of the
index of refraction is termed the dispersion of the
index
• Another important case arises because the speed
of the wave depends on its wavelength
• If a pulse of white light is transmitted through a
material, different wavelengths arrive at the other
end at different times
 this is also called dispersion
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Luminescence
• Luminescence is the general term which
describes the re-emission of previously absorbed
radiative energy
• Common types are photo- , electro-, and cathodoluminescence, depending on whether the original
incident radiation was
 light of a different wavelength – e.g. fluorescent light
 electric field – e.g. LED
 electrons – e.g. electron gun in a cathode ray tube (CRT)
• There is also chemo-luminescence due to
chemical reactions which make the glowing rings
seen at fairgrounds!
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• Luminescence is further divided into
phosphorescence and fluorescence
• Fluorescence and phosphorescence are
distinguished by the electron transitions
requiring no change or a change of spin,
respectively
 hence fluorescence is a faster process because no change
of spin is required, around 10-5 – 10-6s
 phosphorescence takes about 10-4 – 101s
• Thus the energy diagram might be like:
E2
flip
phosp.
fluor.
E3
incident
E1
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flip
phosp.
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• If the energy levels are actually a range of
energies, then:
phonon emission
~10-12s per hop
fluorescence, ~10-5s
• So the light emitted by fluorescence is of longer
wavelength than the incident light
 since the energy is smaller
 and phosphorescent light is typically longer wavelength than
fluorescent light
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• In fluorescent lights, the plasma generates UV
light, and a fluorescent coating on the walls of the
tube converts this to visible light
 these lights have a visible flicker because (60Hz)-1 > 10-5s
• Rather confusingly, materials that do this are
generally called phosphors
• To obtain a white light, a mixture of phosphors
must be used, each fluorescing at a different
wavelength
• TV tubes usually use materials doped with
different elements to give the colours:
 ZnS doped with Cu+ gives green
 ZnS:Ag gives blue
 YVO4:Eu gives red
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Optical fibres
• Fibre-optic technology has revolutionised
telecommunications owing to the speed of data
transmission:
 equivalent to >3 hrs of TV per second
 24,000 simultaneous phone calls
 0.1kg of fibre carries same information as
30,000kg of copper cable
• Owing to attenuation in the cable, transmission is
usually digital and the system requires several
sections:
optical
optical
encoder
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conversion
to optical
repeater
detection
decoder
http://www.ngflscotland.gov.uk/connected/connected5/images/fibreoptic.jpg
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• Obviously, the loss in the cable is important
because is determines the maximum
uninterrupted length of the fibre
• We know that losses depend on the wavelength
of the light and the purity of the material
 recall the penetration depth for glass was ~30cm
• In 1970, 1km of fibre attenuated 850nm light by a
factor of 100
• By 1979, 1km of fibre attenuated 1.2µm light by a
factor of only 1.2
 this light is infrared
• Now, over 10km of optical fibre silica glass, the
loss is the same as 25mm of ordinary window
glass!
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• For such high-purity materials, Rayleigh
scattering is the dominant loss mechanism:
water
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• The Rayleigh scattering results from minute local
density variations which are present in the liquid
glass due to Brownian motion and become frozen
into the solid
• The really clever part about optical fibres is that
the light is guided around bends in the fibre
• This is achieved by total internal reflection at the
boundary of the fibre
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• Thus, the cross section of the fibre is designed as
follows
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http://www.datacottage.com/nch/images/fibreconstruct.gif
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• The light is transmitted in the core and total
internal reflection is made possible by the
difference in the index of refraction between the
cladding and the core
• A simple approach is the “step-index” design:
n
• The main problem with this design is that
different light rays follow slightly different
trajectories
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• So different light rays from an input pulse will
take slightly different paths and will therefore
reach the output at different times
• Hence the input pulse is found to broaden during
transmission:
signal
signal
t
in
t
out
• This limits the data rate of digital communication
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• Such broadening is largely eliminated by using a
“graded-index” design:
n
• This is achieved by doping the silica with B2O3 or
GeO2 parabolically as shown above
• Now, waves which travel in the outer regions, do
so in a lower refractive index material
 and their velocity is higher (v = c/n)
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• Therefore, they travel both further and faster
 as a result, they arrive at the output at almost the same time
as the waves with shorter trajectories
• Anything that might cause scattering in the core
must be minimised
 Cu, Fe, V are all reduced to parts per billion
 H2O and OH concentrations also need to be very low
• Variations in the diameter of the fibre also cause
scattering
 this variation is now <1µm over a length of 1km
• To avoid dispersion of different wavelengths,
lasers are used as the light sources
 many data channels are possible using wavelength division
multiplexing (WDM)
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• A convenient fact is that compound
semiconductor lasers can emit IR light close to
the 1.55µm wavelength where the fibre absorbs
least
• Referring back to the system diagram, it would be
advantageous to integrate the encoder and
transmitter
 so the circuits and the light emitter can be integrated
• This is why there is so much interest in getting
light out of porous silicon or Si compounds
 where thin strands of material exhibit quantum-mechanical
effects which adjust the Si band structure to facilitate efficient
light emission
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http://ghuth.com/Porous%20silicon.jpg
http://porous.silicon.online.fr/images/poreux.jpg
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Lasers
• LASER stands for Light
Amplification by the Stimulated
Emission of Radiation
• The key word here is “stimulated”
• All of the light emission we have mentioned so far
is spontaneous
 it happened just due to randomly occurring “natural” effects
• Stimulated emission refers to electron transitions
that are “encouraged” by the presence of other
photons
• Einstein showed that an incident photon with E ≥
Eg was equally likely to cause stimulated
emission of light as to be absorbed
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http://www.007sdomain.com/gf_laser.jpg
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equally likely
as
• The emitted light has the same energy and phase
as the incident light (= coherent)
• Under normal circumstances, there are few
excited electrons and many in the ground-state,
 so we get predominantly absorption
• If we could arrange for more excited than nonexcited electrons, then we would get mostly
stimulated emission
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• Since we get more photons out than we put in,
this is optical amplification
 hence lAser
 this system was first used to amplify microwaves for
communications (maser)
• Such a condition is called a population inversion
• This stimulated emission is what gives the laser
its coherent output
 which is what makes it useful for holography, for example
• Clearly, random spontaneous emission “wastes”
electron transitions by giving incoherent output
 so we minimise them by using transitions for which the
spontaneous emissions are of low probability
 so-called metastable states
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• The energy levels of a laser material therefore
look like:
• Ruby is a common laser material, which we saw
was Al2O3 (sapphire) with Cr3+ impurities
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http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter4a_files/image022.gif
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• So all we need to make a laser is to achieve
 (i) a population inversion
 (ii) enough photons to stimulate emission
• The first is achieved by filling the metastable
states with electrons generated by light from a
xenon flash lamp
• The second condition is achieved by confining
the photons to travel back and forth along the rod
of ruby using mirrored ends
 next slide
• The ruby laser has an output at 694.3 nm
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http://www.repairfaq.org/sam/laserop.gif
• In order to keep the coherent emission, we must
ensure that the light which completes the round
trip between the mirrors returns in phase with
itself
• Hence the distance between the mirrors should
obey 2L = N
 where N is an integer,  is the laser wavelength and L is the
cavity length
• Semiconductor lasers work in just the same way
except that they achieve the population inversion
electrically
 by using a carefully designed band structure
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• Some laser characteristics are given in the
following table:
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Callister
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Summary
• We have looked at how the electronic structure of
atoms and their bonding leads to varying optical
behaviours in materials
• In particular, properties such as absorption and
emission are closely related to the electrons
• Applications of this knowledge include
 anti-reflective coatings for lenses
 fibre-optic communications
 lasers
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Closing remarks
• this first half of ENG2000 is an introduction to a
subject area that is very subtle, and the course
covers a huge range of subjects
• As you gain more experience, the pieces of the
jigsaw will fit better and better
• So, if all the connections etc are not crystal clear
right now, have patience!
• For me, the success of the course is how often
you say “oh yes, we saw that in ENG2000” !
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THE END
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