# Optical Properties

Today, we are going to talk about the optical
properties of materials. So far we have covered all the mechanical properties of materials.
However, there are many cases where the optical property becomes important along with the
mechanical property. Let us say we are designing an oven for a very high temperature and we
want to carry out some experiments that means what is happening inside the oven for example,
the polymer is changing its glass transition temperature and you want to visualize that
how it is happening. Now, in all such cases you actually need to
send light from outside, which should go penetrate this particular oven casing and it has to
go inside and get reflected back from which you get the information. So in this case that
part of the oven which is has to be transparent with respect to light has to also be oven
like that means high temperature proof, so it is a special mechanical material where
both temperature and optical property will be important. Again there are other materials other cases
where it is optical property which is to be matched with magnetic property or optical
property which is to be matched with of the dynamic properties, etc. So thus property
becomes important in many of the applications. So what we are going to first while initiating
the discussion today and later on we will take it further, we are going to first talk
about the basic concepts related to the optical property, so we are going to talk about the
basic concepts, then the optical properties of metal first let us discuss, then the optical
properties of nonmetals and then some applications of the optical phenomena, so these are the
4 things that we are going to tackle. Now the first important thing is that, when
we are talking about the optical property, we are talking about the electromagnetic spectrum.
In that electromagnetic spectrum of the wavelength, we have shorter wavelengths at one extreme
which is like the gamma rays and longer wavelength at the other extreme which are like the radio
waves, so as the wavelength increases the lambda, we are starting from the gamma rays,
which goes somewhere up to 10 raise to the power minus 4 nanometer or so, one nanometer
is 10 to the power – 9 meter, so you can imagine that how small that wavelength is.
Then there is x-ray there and then from x-ray, when the wavelength further increases then
we come somewhere in between we have the ultraviolet radiations and then we have the entire visible
part of the visible light. In that visible light, where exactly our eyes are also very
sensitive it starts from 400 nanometer of wavelength and it ends at 700 nanometer of
wavelength. So at the very low wavelength and high energy end, we start with Violet,
then there is indigo, then there is blue, green, yellow, orange, red, red is around
700 nm, so that is what is the spectrum of the optical part which we generally call as
the visible light. Then once that wavelength further increase
we come to the infrared radiation types and that goes somewhere up to millimeter level.
If the wavelength is even more, then we come to microwave and if it increases further in
the from the meter level to kilometer level, then we come to the radio waves. Interesting
thing is that this picture we have discussed from shorter wavelengths to longer wavelengths,
but in terms of energy it is just the reverse. What it means is that those which are having
their shorter wavelengths like the gamma rays, you can see that they have the highest energy
in terms of electron force. And then gradually as you the wavelength increases,
the energy actually reduces and the radio waves would have the lowest amount of energy.
For example, if you consider it in the visible spectrum itself, red has energy of about 1.62
electron volts, orange 2.08, yellow 2.15 electron volt, green 2.52 electron volt, blue 2.73
electron volt, it is increasing gradually and violet is 3.17 electron volt. Another
interesting thing you might have noted that this energy is really not, it is distinct
there is no doubt in it, but it is not very evenly spaced that is very interesting that
you can see here however, the colors are very-very distinct. Now, we are talking about the electromagnetic
radiation. Now in the electromagnetic radiation from the functional point of view it is actually
a combination of two time varying waves one of the electric field wave and another is
a time varying magnetic field. So if you denote one in this manner as it is here as the time
varying electric field suppose, then the other one is the time varying magnetic field, so
it is just transverse to the two. So these 2 waves, that is why he say that for electromagnetic
wave these two fields, the electric field and magnetic field they are just always coexistent
with each other. And the speed of the electromagnetic radiation
at vacuum for both of them is close to 3 into 10 to the power 8 meter per second. The velocity
at any particular medium in fact is inversely proportional to the square root of Epsilon
0 and Mu 0, where Epsilon 0 is the electric field permittivity of vacuum and Mu 0 is the
magnetic permittivity of vacuum, so this is interesting. What it means is that if suppose
you consider a particular medium in which you have high electric permittivity, but low
magnetic permittivity but it is the product that would matter and that would be the velocity
of the electromagnetic wave in that particular medium.
In vacuum, Epsilon 0 is 8.854 into 10 to the power – 12 farad per meter and magnetic permittivity
is 1.257 to 10 to the power – 6 Henry per meter . So in one case the unit is farad per
meter for the electric field and for the magnetic field it is Henry per meter, we have to keep
these points in our mind. And how do we calculate the energy? Well, that is E equals to h Mu,
where h is the Planck’s constant right, which is known to you and Mu is the frequency.
That means as I already told you that for example, the frequency of each of these cases
of these light wavelengths is known to you, violet, blue, green or these things we know
the wavelength, you also can then find out the frequency and as the frequency, you can
actually find out what is the energy content corresponding to this. In fact, the wavelength
and the frequency as you can see simply related by this relationship that Mu equals to C over
Lambda. In other words, if I know Lambda and I know
the velocity in a medium then I know what is going to be the frequency, so I should
be able to find out that what is the energy for a particular wavelength, wavelength we
usually measure in meter and velocity in meter per second. So these are the very basic fundamental
things that we have to keep in our mind corresponding to the electromagnetic waves. Next is that light as an electromagnetic wave,
when it falls on a solid what happens to it? Well, the incident light when it falls on
a solid, it can either be reflected or it can be absorbed scattered and/or transmitted.
So we can write that I 0 incident light is going to have at least 3 parts I T, I A and
I R. That means this is my incident light I 0, some part of the light may get reflected
that is I R, some part of the lightning may get absorbed inside, it may not absorb for
a very long time you will see that sometimes it absorbs and then retains it. And some part
of it may get actually transmit, so that is what is our I T part. Absorbed is I A and
reflected is I R, whereas the incident is I 0.
Now, we always say that there are these 3 types of materials, one is the transparent
material, so when we are talking about transparency, it means that most of the light is actually
transmitted through the system like a single crystal. Sometimes we say that it is translucent,
well translucent means some part of the light is actually absorbed and some part of the
light is getting transmitted that is like the polycrystalline dense.
And sometimes we say that it is opaque and when we say that it is opaque, what it means
is that this does not occur, so the light is absorbed and maybe partly reflected back
like polycrystalline porous materials. So, thus different materials can have this type
of different optical property based on whether it allow the light through pass through it,
it absorbs the light or it reflects the light. Let us first discuss on the metals that is
the optical properties of the metals. Now, all frequencies of visible light are
absorbed by metals because it has continuously available empty electron states, which permit
the electron transition. I already told you that metal has always as if a cloud of electrons,
it has never like a lack of any electron. So, if you take a metallic piece and shine
light on it so the photons are going to get absorbed by the electrons at the low-energy
state of which it has an infinite supply let us say. So and then, as the gate they are
absorbing the energy, some of them jumps towards the higher energy state.
So there is a Fermi energy level and there are some filled states and there are some
empty states in the metal, so as the photons get absorbed they go from field state, they
frequencies within the visible range excites electrons into unoccupied energy states like
these states above the Fermi energy level, so the incident radiation is absorbed and
hence, metals are opaque because it is not allowing any light to pass through it because
it uses the entire light to excite its own source of electrons and that is why it is
opaque. Now, the Fermi energy is the maximum energy
occupied by an electron at 0 degree Kelvin that is the way it is actually defined. The
change in the energy of the electron delta E is equal to the energy of the photon because
this is the energy that it is absorbing, so the change in delta E is actually the amount
of energy that is coming to the photon. What happens if it does not stay in that position?
After it gets the energy, then it reemits reemission of a photon of light takes place
by the direct transition of an electron from a high to a low-energy state. So it first
gets excited, go to the higher energy state and then it reemits the photon, it does not
hold that energy with it. Metals are opaque to low-frequency radiation
for example, radio waves to about some middle of UV rays, but they are transparent to high
frequency radiations. So high frequency radiation that these source of photon they do not absorb
that, so actually high-frequency waves can actually get passed through it. But if it
is of a lower frequency, then this situation always happens that it absorbs it, the photon
goes to the high energy state and then the photon emits this energy at a time scale.
In fact, later on we will tell you what happens when it emits this energy back. So here the same thing we are telling that
incident photon energy let us say H Mu, H is the Planck’s constant and Mu is the frequency
of the incident light. And from the field state, the Fermi energy level, the Delta E
energy is given the H Mu is coming as the source of the Delta E, and then it is jumping
from here to the high energy state. Unfilled electrons states are adjacent to the field
states, so it just does that and near surface electrons absorb the visible light in the
case of the metals. Now, most of this absorbed radiation is actually
reemitted from the surface in the form of visible light of the same wavelength which
appears as the reflected light. So, when we see that some light is reflected, is not the
same light which actually is incident on the system that is what we have to understand.
That light falls on the metallic surface and then that light gets absorbed by the electron,
the energy that is absorbed by this electron that it absorbs and it goes to the high energy
state I told you, but it cannot be sustained at a high energy state why because minimization
of energy or maximization of entropies, they are in the nature of every system.
So as soon as it goes to the excited state, it again tries to jump back to the low-energy
state in order to minimize the energy. And as a result, this photon is going to emit
the energy which is approximately of the same frequency as the incident energy that is coming
and then it is coming back as a reflected energy. Now, it is this reflected energy that
I have actually watching, but this reflected energy is coming from the electrons of the
metal that is the important thing, the source is inside the material we have to keep it
in our mind. The reflectivity of metal can be actually
measured in terms of the ratio of the incident energy and the is the reflected energy, so
the I R over I O ratio, which is generally between 0.9 to 0.95. A little bit of energy
gets absorbed into the system, but generally it is of very high reflectivity 90 to 95percent.
In fact, before glass was discovered by people, actually mirror shiny mirror was used as mirrors.
So you can easily imagine that people use to use for example shining copper surfaces,
etc. as their mirrors. Of course there is a problem there that copper
for example, will get oxidized pretty fast, so that is how the glass is much better because
it does not get oxidized so fast. But it is because of this high reflectivity, you can
easily imagine that you can see your image very nicely on the metallic surface because
the light wave which will get reflected from your body and then go to this metallic surface
will actually almost 90percent to 95percent will come out and hence we will be able to
see this and you will be able to see the image. Now we will talk about the nonmetals. So with regard to nonmetals, 4 optical phenomena
are important; reflection, absorption, refraction and transmission, so let us look into them
and buy one. First of all we will talk about the reflection
of a system. So when light photons are transmitted through a material, they actually cause polarization
of the electrons and in turn, the speed of the light is reduced and the beam of light
changes its direction , so from the vacuum for example the light is coming to any such
nonmetallic system, suppose it is coming into glass , so the moment it is coming inside
the system, there is a polarization and the speed of light will get change and as a result,
the speed of light will get change, will not be able to progress in the same direction
but it is going to get change. Now refractive index n is nothing but the
ratio of speed of light in a vacuum to the speed of light in a medium. So any medium
is going to slow down if the light comes from vacuum and to a medium. Let us say sunlight
is coming from space to the atmosphere of earth, it is going to get refraction because
it is going to get slowed down in the medium. Now for any medium what will be the speed
of light? Well, for any electromagnetic system I already told you that it is actually one
over square root of Epsilon Mu, whereEpsilon is the permittivity and Mu is the permeability
of the medium. So if I want to calculate n as C over V, then
it is simply square root of E Mu over square root of E 0 Mu 0. In other words, it is square
root of Epsilon r Mu, where Epsilon r is nothing but Epsilon over Epsilon 0 and Mu r is nothing
but Mu over Mu 0. That means relative permittivity and relative permeability will come into the
picture. Now also we know that the Snell’s law you must have studied earlier and that
says that if my incident angle is theta I and refracted angle is theta r, then n 1sine
theta I equals n 2 sine theta r. This is an important relationship, which we will later
on we will see that for optical fiber we are going to use this principle. Now, the refractive index of some of the very
common materials let us say silica glass ceramics, it has refractive index of 1.458, so quite
a low refractive index. Then we have borosilicate glass 1.47, 1.51 like that Al2O3 is 1.76,
so that is the kind of refractive index that you are finding in the ceramics. In the polymers
it is even lower like 1.35 for Polytetrafluoroethylene PTFE we call it, then polyethyl methacrylate
1.49, polypropylene 1.49. In fact some of them are somewhat similar
to the glass that is why some of the polymers today are used as glasses, polyethylene 1.51,
and polystyrene 1.60. So it is possible today to have optically transparent systems made
from polymers as well as from ceramics. That is good because ceramics are brittle you know,
but polymers are not. Now let us come to the reflection, reflectivity
is defined as the fraction of light that is reflected at an interface, so it is the ratio
of I R over I 0, this we have also discussed when we have discussed about the metals. So
if the light is normal or perpendicular to the interface, then the R can be actually
derived to be something like n 2 – n 1 square and in to plus n 1, so n 2 – n 1 by n 2 plus
n 1 whole square where n1 and n2 are the refractive indices of the two mediums.
Higher is the refractive index of the solid, the greater is the reflectivity of the medium.
So in comparison to between the two materials, if the refractive index is higher, then we
can say that R is actually going to be more for this particular material. Now in metals,
the reflectivity is typically I told you of the order of 0.90 to 0.95, whereas it is just
the reverse for the glass, it is about 0.05. So what it means is that the value of the
refractive index is very-very high in the metals and as a result, you get a very high
reflectivity in metals, whereas for glasses it is just the reverse. High reflectivity
of metals is also one of the reasons that they are opaque; anyway we have explained
the fundamentals to you. Now let us come to the absorption part of it. When a light beam is impinged on a material
surface, portion of the incident beam that is not reflected by the material is either
absorbed or transmitted through the material. The amount of light which is absorbed by a
material actually can be calculated using Beer’s law. So here IT is the transmitted
light intensity and I0 is the incident light intensity. Suppose if the absorption coefficient
Beta and the sample thickness L, then you can say that the transmitted light intensity
is I 0 e to the – Beta L. So the intensity of IT will actually with
respect to the thickness as well as with respect to the absorption coefficient, it will follow
an exponentially way of actually falling down. So with respect to length or with respect
to if I consider the absorption coefficient Beta either of them it exponentially falls
down, so that is about the light which is absorbed in the system that is the IT part
of it. Now materials that have large beta values, they are considered to be highly absorptive
because they are taking most of the transmitted most of the light energy into the system. There are several absorption mechanisms, one
is known as the Rayleigh scattering, where the photon interacts with the electrons and
it is deflected without any change in its energy, so that is called the Rayleigh scattering,
without any change in energy is very-very important, so photons simply interact with
electron and gets deflected. For example, the sunlight gets deflected and the blue color
you see all over the sky, so it is like a Rayleigh scattering. There is also Tyndall
effect, where scattering occurs from particles which are much larger than the wavelength
of light, and colloidal suspension for that matter shows this Tyndall effect.
Compton catering where the interacting photon knocks out an electron losing some of its
energy during the process. So not like Rayleigh scattering, in the Compton scattering the
photon during the impact loses some of its energy and then the scattering takes place.
And then the Photoelectric effect, when photon energy is consumed to release an electron
from atomic nucleus, this is the famous effect for which Einstein got his Nobel Prize, so
there are such various mechanisms of absorption of light Rayleigh scattering, Tyndall effect,
Compton scattering and Photoelectric effect. Now, about the transmission of light IT is
very similar to the reflection. Here there is a law which is very similar to Beer’s
law, it is IT is now I 0 into 1 – R whole square times e to the power – beta L, so that
is what is the IT. So if I 0 is the intensity of the incident wave, then part of it gets
reflected I R, which is I 0 times R and part of it gets transmitted, which is I 0 times
1 – R whole square times E to the power – Beta L, so this is what is when the light is transmitted
from the system. Now, I told you that materials absorb energy
but I told you that when it absorbs the energy, then electrons go to a higher energy state
but it cannot sustain the higher energy state because it has to come down for the minimization
of energy, so it will actually emit the energy back and it will come down to lower energy
state. If this emission of radiation occurs and this entire phenomena what we will be
calling as luminescence, but if this occurs within 10 raise to the power – 8 seconds after
excitation, then the luminescence is called fluorescence, and if it takes longer than
10 to the power – 8 seconds, then it is called phosphorescence.
Ordinarily, pure materials not display this phenomena, but some special materials called
phosphors have this capacity for example, Yttrium, ZnS, cadmium sulphide and a very
complex one which contains barium, magnesium, aluminium and oxygen, etc. There are examples
of many applications of this effect like fluorescent lamps, CRTs, plasma video display, white LEDs,
in all of them in some way or the other exploits this fluorescence and phosphorescence of a
phenomena of an optical property of a material. The second interesting case is called photoconductivity
which is actually important for materials like semiconductors. If you bombard the semiconductors
by photons, then what happens is that the energy in this case, which is equal to the
energy in that can create the electron-hole pairs that means it is greater than the band
gap, they actually can use to generate a current and that is known as photoconductivity.
So it is different from the photoelectric effect because in the photoelectric effect
the photon is actually absorbed by the electron itself, whereas it is the electron-hole pair
which gets this energy the band gap energy and then that actually excites the flow of
this electron-hole pairs and that generates a current. So this current which is produced
through photoconductivity is directly related to the incident light intensity.
As a result, these light meters you see in cricket matches, etc. people use, they are
actually based on this photoconductivity of the incident light, so it is based on the
electron-hole pair for example, cadmium sulphide is one of the very common example in light
meters. And today’s solar cells, they are also based on mostly the photoconductivity,
so this is another very good application of the optical property. The third and the most
important one and towards the end of this course we will show you some of the applications
to LASERS is actually Light Amplification by Stimulated Emission of Radiation. So in this case for example, if we see this
particular case that you have a Ruby Crystal and then you have a flash lamp from which
you are providing energy to the system, you see in the case of luminescence the energy
is coming out but it is incoherent the phase relation continuously changes. Whereas, laser
emission is very much coherent, constant phase difference and the same frequency will be
emitted. So when you consider this Ruby, which is a
single crystal of AL2O3 doped with very little amount of chromium oxide or yttrium aluminium
garnets YAG we call them or neodymium, helium neodymium lasers, this type of materials when
you excite them, what happens is that you first get these atoms in the excited state,
the incident photon is coming and then some of the electrons are getting excited to the
high-energy state. But after that what happens is that they actually
start to excite more of these electrons in the system and then this happens, this gets
multiplied and then that actually becomes a source of the coherent light emission in
the system, so this kind of a system at the end generates a coherent beam and that coherent
beam can be used for many-many detection of physical properties of materials.
So we have seen here the various properties of we have discussed today, various optical
properties of metals and nonmetals on some of the very important optical phenomena. In
the next lecture you will study the optical fibers and its principles and types and various
applications of optical fiber thank you. Keywords- absorption, reflection, refraction,
transmission, energy band gap and applications such as Luminescence, photo-conductivity,
lasers

## 5 thoughts on “Optical Properties”

1. masooma ibrahim says:

Thanks for very clear lecture!

2. Numan Zafar says:

many many thanks for compact and easily understood lessons…