Greetings to you.
We are starting our next session i.e Interaction
of a matter with electromagnetic radiation.
We had also discussed about the reflection
of radiation.
I had shown you this slide where the reflection
laws are presented.
Earlier I had explained to you the equation
governing the reflection.
When radiation crosses an interface between
media having different refractive index.
Reflection always occurs for a beam entering
an interface at right angles.
We normally give it as a ratio of reflected
intensity Ir of the reflected radiation I0
is the intensity of the incident radiation.
The ratio is given by (n2-n1)2/n2+n1 whole
square.
Where, n1 and n2 are the refractive indexes
of the two media.
This is the figure I had shown you yesterday
also.
You can imagine that the light ray is coming
at slanted angle which is not exactly perpendicular
to the media.
I have shown you media is a glass here and
it comes from the air a passes through the
glass and exits at the other end.
But you can see that it bends a little bit
depending upon the refractive index of the
sample.
Whenever we design a spectrophotometer or
spectrometer we have to take care of all these
aberrations and then fix the optical bench,
so that the radiation from the source reaches
the detector properly.
This is refraction phenomena.
The refraction phenomena 
can be defined as, when the radiation passes
at an angle through the interface between
two media having different densities, owing
to the changes in the velocity of the radiation
in the two media abrupt change in its direction
occurs.
This is called refraction.
The extent of refraction is given by Snell’s
law that is sinθ1/sinθ2 is equal to n2/n1
that is also reflected in the velocities of
the two beams in the two media.
So we have here sinθ1/sinθ2 is equal to
n2/n1 that is also equal to V2/V1.
Where, θ1 and θ2 are the angles of incidence
and refraction, n2 and n1 are the refractive
indices, V2 and V1 are the velocities of the
light in the first and second media respectively.
Refractive indices of materials would be different,
because by nature every material is different.
So, refractive index of air is different and
some gases are different, glasses are different,
quartz are different, water is different like
that there are several materials which are
having different refractive indexes.
But normally the measurement is done with
air as one medium and other has the test medium.
So, the refractive indexes of different materials
as compared with air are available in the
databases.
Whenever we want to design a prism or something,
we have to see what are the refractive indices
of the media, whether it is glass or quartz
etc.
In vacuum change in velocity is 0 and n1 is
unity.
So, instead of n1/n2 we can write n2 vacuum
is equal to sinθ1 vacuum/sinθ2.
Such calculations are possible whenever we
want to design optical table for the infrared
radiation to pass through the different parts
of the instrument.
Then we should know a little bit about scattering
of radiation.
Here momentary absorption of radiant energy
by the atoms, ions and molecules are followed
by re-emission of the radiation in all directions.
It is known as scattering.
Suppose I have a small particle, radiation
will scatter it.
It is a very well known phenomena experienced
by all.
For example in the room where you are sitting,
if there is a light source it just does not
travel in straight line and leave the remaining
parts dark.
Is it not?
So, the remaining parts are also illuminated
because the incident radiation falls on the
particulates, air etc.,then gets reflected
in different directions not necessarily in
the direction of propagation that is known
as scattering.
What makes the scattering phenomena universal?
Because it is observed whenever there are
atoms, ions, particulates, molecules.
These things are always there in the air.
When e.m. radiations fall on the particles
re-emission of the radiation occurs in all
directions.
Particles having comparable dimension to that
of the incident 
radiation 
present in the media removes most of the re-emitted
radiation by destructive interference except
those travelling in the original direction.
A very small fraction of the radiation is
transmitted at all angles from the original
path and its intensity increases with the
particle size.
If the particles are very small the scattering
will be minimum.
That is the bottom line.
Scattering by molecular aggregates having
still smaller dimensions than the incident
radiation is called as Rayleigh scattering.
There are three different kinds.
That are Particulates having almost same size,
particulates bigger in size and particulates
having smaller size than the amplitude of
the electromagnetic radiation.
The amplitude is measured in distance, so
the particle size also can be measured in
distance.
We are talking about the interaction in equivalent
size particles, smaller particles and bigger
particles.
Scattering by molecules are aggregates having
smaller dimension is called as Rayleigh scattering.
Larger molecules scatter radiations in different
quantities that too in different directions
this is called as Mie scattering.
When the scattered radiation is also quantized
to some extent those occurring in the vibrational
level or rotational energy levels etc.
The transitions in the molecules as a consequence
of polarization process is called as Raman
scattering.
The Raman scattering in terms of quantitation
which won the Nobel Prize for Professor Raman
in 1931.
Raman’s scattering is also a very typical
of several materials.
Now a days there is a separate branch of science
for the identification, differentiation of
particles and chemicals etc. by Raman’s
scattering.
We are not going to study Raman’s spectra
right now in this course.
But it is good to know that the radiation
scattering is a phenomena occurring everywhere.
It occurs inside the instrument.
This scattering is of no use in general because
the scattered light does not reach the detectors
100%.
So in the instrument we want the scattering
to be minimum.
The optical path should be very precise and
there should not be many particles in between
the source and the detector that is air particles
and other things.
We also want it should be minimum.
Usually most of the instruments do have about
1 to 5% of scattering whatever you do.
However dark system you make still you cannot
make an instrument without joints.
There will be some parts to be joint together
etc.
If you observe any machine you will see that
it is composed of several components and which
are joined together by either screws or press
fit etc.
So, they cannot altogether stop these scattering
of the radiation and no instrument is an exception
to this rule.
So, it is not possible humanly to eliminate
scattering totally but it is possible to minimize.
We can paint the inside of a spectrophotometer
black, so that it absorbs all other radiations
etc.
But the best one can achieve is about 1% of
scattering, less than that makes the instrument
very costly.
It may not be worth it.
But more than that there is some problem with
respect to the sensitivity.
That is the minimum quantity that can be detected
or determined in presence of high scattering.
That is the little bit of a problem anyway.
Having known so much about of the scattering
we are going to talk about polarization of
radiation.
We have seen the effect of polarization in
our day to day life.
Whenever you see two pictures imposed on one
another especially in TVs and movie halls.
If you are looking at the screen you will
can see that one picture is imposed on another
quite often.
That is all effect of polarization.
Ordinary radiation usually consists of electromagnetic
waves in which vibrations are equally distributed
among a huge number of planes centered along
the path of the beam.
Here what I am trying to tell you is the phenomenon
of polarization and ordinary radiation.
It consists of bundle of electromagnetic waves
in which vibrations are there in all sides
of the propagation.
There are huge number of planes centered along
the path of the beam.
In general one is electromagnetic wave, another
is electric field, magnetic field etc.
Even in those fields there will be slight
variations and bundle of electromagnetic field
around the propagation path of the radiation.
So, viewed end on how does it look like?
It looks like an infinite set of electric
vectors fluctuating from 0 to a maximum amplitude.
This is how it looks.
Here I have an incident beam unpolarized on
the left side.
So, you can see here there are number of planes.
But all those amplitudes are not only perpendicular
to the plane of propagation but they are also
oriented in different planes.
This is what we normally see in unpolarized
light (watch the video for better understanding).
There are number of planes that are present
along electric field and magnetic field also
oriented in different directions in the space
along the propagation field.
The vector in any one plane, say xy can be
resolved into two mutually perpendicular components,
we have already seen that.
Removal of one of the resolved planes of vibration
produces the plane polarized beam.
That means, in general when the propagation
is going on like this I have the electric
field as well as magnetic field suppose I
remove the electric field then what I have
here is, what comes out, I put a barrier to
stop the electric field to come and then only
the magnetic field will be there, oriented
parallel to the propagation of incident beam.
Similarly, if I remove the magnetic field
there will be only vertical propagation.
That means the radiation that comes out after
the interference will be more disciplined.
Radio waves emanating from an antenna and
micro waves produced by a Klystron tube are
usually plane polarized.
If you wish to know more about it you can
take a look at how the antenna, radio waves
and other things are emanating from a radio
station etc.
The information is available in the YouTube
or Google etc.
Polarized ultra violet and visible radiation
normally produced by passing e.m beam through
a media that selectively absorbs, reflects
or refracts that vibrates in only one plane.
Here I have a barrier to stop all these Haphazard
planes than the vertical barrier I have introduced
so I am getting only one horizontal beam.
So, this is vertically polarized light beam.
Depends upon your perception vertically or
horizontally how you look at it.
(watch the video for better understanding)
Now I want to talk to you about dispersion.
Dispersion is little bit of a complex phenomena.
Dispersion curves usually show two regions,
one is normal dispersion in which there is
gradual increase (I have discuss this earlier
also a little bit).
Another one is anomalous dispersion, it occurs
coinciding with natural harmonic frequency
of some part of a molecule.
That means the dispersion curve will not be
changing uniformly there will be abrupt changes.
That’s what anomalous dispersion occurs.
In spectroscopy we want dispersion curves
to be sort of ordered and disciplined.
We want uniform change in the dispersion instead
of abrupt changes.
Dispersion curves are important for optical
components such as lenses or even mirrors.
Most suitable components for the manufacture
of lenses are those in which refractive index
should be very high and constant also throughout
the media.
This results in reduced chromatic aberrations.
In the fabrication of prisms, refractive index
should be as large as possible 
and also frequency dependent.
This is the figure of dispersion for quartz
and you can see that here I have plotted frequency
here 1013, 1014 and 1015 this is the refractive
index.
But what is coming out of these is all normal
dispersion.
Anomalous dispersion is here.
Its keeps on gradually increasing.
Then it keeps on gradually decreasing.
Here the slope is different.
These things should not be there as far as
possible.
This is known as anomalous dispersion because
if the material is of uniform dispersion it
should be just like this or it should keep
on increasing depending on the thickness.(watch
the video for better understanding).
Another phenomena that you should know about
the interaction is diffraction.
Diffraction refers to the bending of the parallel
beam of electromagnetic radiation as it passes
through a sharp barrier or a narrow opening.
Its a consequence of interference which can
be demonstrated in the laboratory.
It can be destructive, it can be constructive
interference also.
What is important is when a parallel beam
of radiation is allowed to pass through a
small pin hole, two closely spaced pin holes
on the screen allow them to pass through.
Suppose I place a screen on the back side
of the pin hole, what do I see?
I see dark and bright stripes.
If the radiation is monochromatic i.e having
a single wavelength, all the radiation should
have a single wavelength that is known as
monochromatic radiation.
Monochromatic radiation if I use a series
of dark and light images appear perpendicular
to the plane of radiation.
I will show you the figure here like this,
this is a pin hole here.
This is a screen.
Radiation is coming out like this.
The white lines you see on the left side of
this figure is the media and the radiation
comes out like this.
But what you see on the screen after this
pin hole is bright patch, small dark patch,
small bright patch etc.
They are all differing in intensity.
This is known as pin hole diffraction(watch
the video).
Now if I have 2 pin holes like this.
One is B, another is C, O is the midpoint.
What I see here is a number of crisscrossed
interaction of the wave beam.
And here I have on the left side the parallel
beam.
This is the parallel beam and diffraction
by single slit will be like this dark patch
white patch dark patch white patch, but if
I do it with the 2’s pin holes, I get to
see a series of interactions and if I catch
it on the photographic plate you can X, D,
E and then Y.
This is something like a photographic plate.
This is the phenomenon of diffraction.
Now we can show that this phenomenon of diffraction
there will be the distance between bright
and dark patches can be calculated depending
upon the incident radiation as well as the
distance between the 2 pin holes.
So I will not going to details of this but
you can see these things also.
You will see this phenomenon explained very
nicely.(watch the video)
Now I can show you that in the previous figure
the distance between the two fringes can be
show that CF is equal to BC*sinθ for two
beams to be in phase, we need to have this.
Reinforcement occurs at 2λ, 3λ etc.
Hence nλ = BC*sinθ where n is the integer
called the order of interference.
So, I can except number of interference fringes.
n=0, 1, 2, 3, 4 etc., so depending upon the
number of pin holes and other things I get
different constructive and destructive patterns.
When the phase difference is remain entirely
constant which time the system is said to
be coherent.
Then only a regular diffraction pattern can
be obtained.
So, what about the spacing then?
The spacing of the bands depends upon the
distance distance between the slits that is
denoted by d.
This following relation holds to determine
the spacing between the two bands that is,
nλ is equal to d sinθ, n is the order lambda
is the wavelength.
These the distance between the two spacing
and θ is the angle of incidence.
If two different wavelengths, for example
one red light and one blue light are used
the two colors will be separated on the screen.
That is the beauty.
You can see both blue and red patches on the
screen, but if I use a white light, a number
of small rainbow colors containing all the
colors will appear.
So by placing a moving slit across the screen
I can have any color or wavelength selected.
This is the principle used in gratings.
Because, in any spectroscopic technique what
I need is an electromagnetic radiation of
a specific wavelength.
For example I have a lamp that gives all kinds
of wavelengths corresponding to infrared radiation
or spectroscopic radiation.
But when I need to have only one wavelength,
stopping all other wavelengths reaching the
sample.
So, how do I select from a given source, the
correct wavelength which needs to be pass
through the sample?
That is done by gratings.
If I put my detector here it will detect only
the radiation coming in this range.
For example it will show radiation coming
through this that means I can choose different
wavelengths from a diffraction grating to
cover the entire range of the electromagnetic
spectrum corresponding to infra red spectroscopy.
For example here I have shown you a prism
and here white light comes and then all other
colors get separated.
Because of the refractive index I put a screen
here and if I put a hole here I will get red.
If I put it here I will get orange, if I do
it there I will get yellow, I put a hole here
I will get blue color.
Like that I can choose any color that comes
out of the prism.
Exactly same thing happens when I am using
grating (watch the video).
In grating what happens is, the wavelengths
are more precise than the prisms.
We will see about gratings how they are made
etc in some other contexts later.
But essentially gratings and prisms do the
same job.
They separate the different wavelengths of
the incident radiation.
By placing a prism I separate and then I put
a mechanical hole in front of the separated
radiation and pick up the exact wavelength
whatever I need or I can make the slit move
from one end to the other end.
And then scan the whole lot.
I have a choice of using a prism or a grating
in a given instrument.
then how does the prism work?
Prism also works on the same principle.
I have a prism here in this slide you can
see this it disperses the incident radiation
depending on its refractive index and its
variation with wavelength.
That is the principle function of the prism.
A prism can be used to disperse ultraviolet
rays, visible rays, infra red several other
things also.
To disperse these things I can use a prism
or grating.
Which material I should take?
Glass prism or quartz prism or polished aluminium
prisms etc.
Many prism materials have different characteristics.
So the material of construction depends upon
the wavelength region which we want to select.
Here I am showing you two types of arrangement
one is a prism with 600 angle.
This is a sort of isosceles triangle all the
3 angles are 600.
A prism is made like this and inside white
radiation comes here then it separates into
different wavelengths, the extent of separation
depends upon the material as well as its refractive
index.
I cut this prism into 2 parts.
So here I have cut and take an only one part.
But I am going to put a mirror here.
That is what I have shown on the right side,
this is known as 300 prism.
I have a half prism in my hand.
In this half prism the one part is rectangular
remaining part is just like what it was earlier
in this arrangement.
Any radiation that comes in goes to the mirror
surface.
It cannot pass through.
It is reflected back and comes out on the
same side.
So you can see the difference between these
half prism and full prism.
That is if I use an ordinary prism with 600
apex angle.
If I use only 300 apex angle, and mirror it
on the other side the radiation will come
here, go here travels the same path that means
the distance travelled will be exactly same
as this.
If I mirror the one side, so this is no there
are 2 different types of arrangements (watch
the video)
One is I can take two 300 prisms if I take
one more and fuse it here, I get 600 apex
angle.
So, a prism can be constructed by fusing two
30 degree prisms is called as 
Cornu type And 300 prism 
is Littrow type.
In Cornu mounting the disperse radiation is
collected across the prism and in Littrow
mounting it is collected on the same side.
So this is only the difference between the
two.
Actual instrument in Littrow mounting refraction
takes place twice on the same side with less
material coupled with the saving of space.
In most of the analytical equipments or infrared
spectrometers 
we would like to be of Littrow mounting.
Earlier in Russian models etc., instruments
used to be huge because they were using bigger
prisms and every instrument was taller and
bigger than a human size.
But now-a day’s thanks to technology all
these things have become table top, bench
top and portable.
That is the beauty of instrument.
This is another way of looking at the apical
angle and this is the Litrrow mounting.
We can see that the radiation comes in and
hits here and comes back and it gives you
different wavelengths.
This is a grating here.
You can see that, the prism looks like a boat
now.
It is essentially a collection of small small
prisms.
You can see in the figure small small ridges.
There are five ridges.
That means I have made 5 prisms here with
the same size.
This is the cross section of a diffraction
grating showing the angles of a single grew
which are microscopic on an actual grating.
We will continue discussion in the next class.
