Good morning. Let me, first recapitulate some
of the important things which we have learnt
in the past few classes.
So, we first considered a situation where
we have an electric dipole which is essentially,
2 metal wires 2 of their 2 of which aligned
like this. And connected to a voltage source
and we saw that if you feed a sinusoidal voltage
the charged particles inside these 2 metal
wires in this oscillate up and down, you have
an oscillating electric dipole. And if you
look at the radiation pattern at a large distance,
you get a sinusoidal plane wave.
So, if you are located along the x axis at
a large distance from the dipole remember,
the dipole is aligned along the y direction.
Then, the electric field at this point is
going to be parallel to the direction of the
dipole. So, the electric filed is also going
to oscillate up and down the dipole oscillates
up and down the electric field is also going
to oscillate up and down over here with the
phase difference with the oscillation the
dipole.
The phase difference occurs because, of the
propagation time. So, the electric field is
going to oscillate up and down. And the oscillating
electric field pattern is going to propagate
forward along the x direction. So, at any
given instant of time you have a sinusoidal
electric field and the whole pattern propagates
forward along the positive x direction.
Remember, the there is also going to be a
magnetic field and the magnetic field is perpendicular
to both the direction of propagation of this
wave and the electric field. The magnetic
field also oscillates at the same phase as
the electric field. So, the this is what we
refer to as an electromagnetic wave, the electromagnetic
wave has an electric field and magnetic field
both mutually perpendicular oscillating in
phase. And both are perpendicular to the direction
in which the wave propagates.
So, if you go to some other direction for
example: the 1 over here again you are going
to have the electric the wave propagating
outward from the dipole. The electric field
is going to be along the direction of the
dipole projected normal to the line of sites.
So, it is going to be in this direction and
the magnetic field is perpendicular to both
of these. So, this is the pattern which you
get, the electromagnetic field pattern which
you get when, you have a single dipole oscillating.
And then, we moved over to a situation in
the last class where we have 2 crossed dipoles.
So, we have now got 2 dipoles instead of 1
aligned along the y axis and another along
the z axis. And we were discussing the electric
field pattern at a point along the x direction
which is perpendicular to both of these dipoles.
So, we were discussing the electric field
at a point over here a large distance away
along the x direction. Now, the electric field
here is going to be in the plane perpendicular
to the line of site. So, it is going to be
in the plane perpendicular to the x axis and
in the situation, where I feed the same voltage.
So, if I feed in the voltage which has the
same phase, but different amplitudes into
these 2 crossed dipoles. Then, both of them
are going to oscillate with the same phase.
So, the oscillations are both the electric
filed along the y direction and the z direction
can be represented as the same cos omega t
plus kx kz minus kz in this case. And you
have these factors Ey into j plus Ez into
k outside this should be Ey into z plus Ez
into k Ey into j and Ez into k outside.
So, if you change the magnitudes of Ey and
Ez the direction in which the electric field
oscillates is going to change. The direction
quantify through this angle theta with respect
to the y axis is the direction that is quantified
through theta is given through tan inverse
of Ez by Ey. So, if you change the ratio of
the voltages the direction in which the electric
field oscillates changes.
In all situations when, the electric field
when the voltage fed into the these dipoles
oscillates in same phase. The electric field
is going to oscillate up and down in a line
over here this the radiation is said to be
linearly polarized and the angle the magnitude
of the vector electric field vector and the
angle at which it oscillates both of them
are given over here.
We then, consider another situation. So, the
next situation which we considered the voltage
applied to the 2 cross dipoles had a phase
difference of phi by 2. So, we considered
a situation where the electric field where
the voltage applied to the dipole along the
z direction had an extra phase of phi by 2.
The magnitude of the voltages were the same.
So, let me repeat you have this voltage of
the same magnitude applied to both the dipoles,
but there is a phase difference of phi by
2 and there is a an extra phase of phi by
2 to in this z direction.
So, again the resultant electric field is
a super position of the 2 electric fields
produced by the 2 dipoles. But there is extra
phase of phi by 2 along the z direction, this
extra phase. So, if I put in this extra phase
into the cosine omega t minus kz this will
become minus sin omega t minus kz. And can
see, that the electric field is going to go
around in a circle because, the cos and the
sin terms are 1 of them peaks the other 1
is going to have a value 0 and then, as this
peaks up this is going to go down.
So, if you look at a fixed position fixed
value of z you will see that the electric
filed goes around in a circle. And in the
situation, where you have given an extra phase
along the z direction the electric field is
going to go around this way along the direction
which I show over here. Which is shown over
here and I had told you in the last class
that this is referred to as being left circularly
left circular polarized.
So, this kind of an electromagnetic wave where
the electric field at any fixed position goes
around in a circle is said to be circularly
polarized. And it could go around in 2 different
ways depending on the phase which I have given.
If I had given an extra phase of phi by 2
along the z direction it goes around this
way which we referred to as left circularly
polarized.
And if it goes in the opposite direction which
would occur if I have to give a phase log
of phi by 2 along the z direction the electric
field would go around in a circular in exactly
the opposite direction. We referred to this
as the right circular polarized light. So,
light can be the radiation the electromagnetic
radiation can be circularly polarized. So,
we have seen two situations.
One where the electromagnetic wave is linearly
polarized the electric field oscillates up
and down in a straight line. And then, we
have circularly polarized where it is goes
around in a circle. Now, let us consider a
more general situation and that the more general
situation is as follows. We still have, a
phase difference of phi by 2 between these
2 dipoles. The voltage applied to these 2
crossed dipoles still has a phase difference
of phi by 2.
But now, the amplitude of these 2 voltages
is different. What will be the electric field
pattern at a fixed point large distance away
along the x axis? Where this fixed point over
here a large distance away along the x axis
what will the electric field look like. So,
this is a small generalization of the circularly
polarized electromagnetic wave which we have
been discussing. Again, the electric field
here is the super position of this electric
field at this electric field, but now they
both have different amplitudes and there is
a phase difference of phi by 2.
So, it is quite straight forward to realize
that the electric field now instead of going
around in a circle, it is going to go around
in an ellipse. The elliptical motion of the
electric field could either be clock wise
that is left circular. If it is goes around
clockwise and it could be anticlockwise and
if you retain the same convention as for the
circularly polarized light you can call this
1 where it is goes around anticlockwise at
right circular.
So, this is polarized the right circular,
this is left circular, left elliptical right
elliptical. So, you have a elliptical polarized
light. The major axis and minor axis of the
ellipse they are aligned with the y z directions
in this case. Now, you could think of a even
more general situation is that I have voltages
being applied to these dipoles. Whose magnitudes
are arbitrary, not only are the magnitude
of the voltage is arbitrary, but also the
phase difference between these 2 voltages
is also arbitrary.
So, I have tw2 different voltages and two
with arbitrary phase difference could any
30 degree 40 degree any angle whatever. So,
I have two difference voltages being applied
to these dipoles and the phase difference
between these two voltages could be arbitrary.
In this situation, the electric filed goes
again goes around in an ellipse, but the major
axis and the minor axis of the ellipse are
no longer aligned with the y and z directions
this is the most general situation. So, the
most general polarized state of electromagnetic
wave is where I have the electric field going
around in an ellipse. And the ellipse is not
aligned with the y or z axis which I have
chosen.
So, let me recapitulate again we have considered
a situation where we have 2 crossed dipoles.
And we have looked at the electromagnetic
wave a large distance away, along a direction
perpendicular to both the dipoles. And we
saw that, if the voltages fed into these 2
dipoles which are crossed has the same phase.
You are going to get linearly, polarized electromagnetic
waves. The electric field at any fixed point
will be seen to oscillate up and down in a
line.
We next considered a situation, where we had
a phase difference of phi by 2 in the voltages
being fed to the 2 cross dipoles. If you have
a phase difference of phi by 2 in the 2 voltages
being fed to the 2 dipoles which are perpendicular
to each other. Then, at a large distance away
along the direction perpendicular to both
of these dipoles you will get a circularly
polarized electromagnetic wave. If the amplitude
of the 2 voltages are the same.
If the amplitude of the 2 voltages being fed
to the 2 dipoles are different, you will get
elliptically polarized electromagnetic waves.
The major axis and minor axis of the ellipse
will be aligned, with the y and z direction
which are the direction in which the dipoles
are also aligned. Now, we then moved on to
a more general situation where the magnitude
of the voltages is being fed to the 2 dipoles
are different also. The phase difference between
these 2 voltages could be arbitrary.
In this situation, you will get elliptically
polarized electromagnetic waves and the major
axis and the minor axis of the ellipse will
not be aligned will not be aligned with the
directions of the dipole. The major axis and
the minor axis will be in some arbitrary direction
which 1 can calculate and the major axis and
the minor axis will not be aligned with the
directions in which the dipoles are aligned
which are the y and z axis here.
So, the elliptically polarized electromagnetic
wave is the most general situation the most
general polarized polarization state of an
electromagnetic wave is where we have elliptically
where it is elliptically polarized and the
major axis and the minor axis of the ellipse
are arbitrary. This is the most general polarization
state of an electromagnetic wave.
You should also bear in mind that the electric
field oscillates perpendicular to the direction
in which the wave is propagating and the magnetic
field is perpendicular to both the electric
field and the direction in which the wave
is propagating. So, the magnetic field is
perpendicular to the both of these. So, in
this case the wave is propagating along the
x direction. So, the magnetic field is perpendicular
to the x direction it is also in the y z plane.
So, if and if the electromagnetic wave goes
around in an ellipse then, the magnetic field
also goes around in an ellipse, but the magnetic
field is always perpendicular to the direction
of the electric field. So, if the electric
field goes around in an ellipse with the minor,
major and minor axis. The magnetic field will
also go around in an ellipse. And the major
and minor axis of the magnetic field ellipse
will be perpendicular to the major and minor
axis of the electric field ellipse.
These two are always perpendicular. So, the
and they are in phase. So, the major axis
of 1 will be perpendicular to the major axis
of the other. And both of them will be in
the y z plane. So, this is the general structure
of the electromagnetic waves. Now, let me
ask you a question. Suppose, we consider a
bulb the radiation coming from a bulb. For
example: you could, it could be the lamps
which are illuminating this room or it could
be the light coming out from a torch light.
Whatever, whichever situation you consider
if I ask you the question what the polarization
state of the electromagnetic radiation which
is produced by the sources.
Is it elliptically polarized or is it linear
polarized or is it circularly polarized. What
kind of polarization does the light that comes
out from 1 of the sources which we usually,
encountered. Let us say, the sun or possibly
the bulb in this room or any of these sources,
what kind of polarization state does it have.
Now, the point here is that the radiation
produced by any of these natural sources of
light is usually, unpolarized. So, let me
briefly explain to you what we mean by the
radiation being unpolarized.
So, if the radiation is propagating along
the x direction, the fact that the electric
field should be in the y z plane that is the
electric field is perpendicular to the direction
of the propagation of the wave is true irrespective
of what kind of electromagnetic wave. I have
whatever, be the source in vacuum if I have
an electromagnetic wave in vacuum, the electric
field is always is going to be perpendicular
to the direction of propagation.
The electric and magnetic fields are always
going to be perpendicular to the direction
of propagation of the wave. So, even for the
electric, electromagnetic wave coming out
from a bulb or torch, from the sun the electric
field is always perpendicular to the direction
of propagation.
But the electric field does not have a well
defined polarization. So, it does not the
electric field if you follow its evolution
as a function of time it does not trace out
any well defined trajectory. It randomly changes
direction and the magnitude also goes around
goes on changing. So, the electric filed from
such natural sources, the direction of the
electric field and its magnitude both of them
actually change randomly. So, it keeps on
jumping around in some kind of a random fashion.
So, you cannot associate any of these states
of polarization which we have discussed we
cannot associate any of them with this kind
of a behavior of the electric field. So, the
natural light which we have produced by source
like a bulb etcetera. The electric field acts
to the direction of the electric field and
its magnitude also goes around changing randomly
and you have what is called unpolarized light.
So, this radiation is not does not have any
well defined polarized as you can refer to
it as un polarized an electromagnetic wave
the electric field keeps on jumping around
randomly. And this has to do with the fact
that when, you have the radiation from the
bulb the radiation from inside the bulb if
you look at it at the microscopic level also
originates from a large number of oscillating
dipoles.
But there are a large number of the fact that
there are a large number of dipoles tells
us that these and these dipoles did not be
aligned with each other. So, you have a large
number of dipoles inside all of which are
randomly oriented as a consequence the radiation
which comes out. If it were a single dipole
or if there were many dipoles all aligned
together oscillating you would have a well
defined polarization for the radiation that
comes out.
But you have all these dipoles which are randomly
aligned inside the bulb, inside the filament
of the bulb the filament which from which
the radiation originates. For example: you
have a large number of dipoles oscillating,
but these dipoles have no well defined direction
they are randomly oriented. So, the light
which comes out the polarization, the electric
field and the light which comes out keeps
on jumping around randomly with time.
So, this is what we mean by unpolarized light
there are devices are called polarizer’s.
Which if you send this light through a polarizer,
it will only allow a particular polarization
to pass through. So, if there is a there are
device called polarizer’s if you send it
through that it will allow, only particular
polarization to pass through and the resultant
electric field will oscillate only up and
down in a line.
Then, you can do all kinds of manipulations
with it we shall discuss it later on this
course. But in this part these course, we
just discuss what we mean by light being polarized
and what are the possible states of the polarization
of light and how these are related with the
electromagnetic wave nature of light. And
we have discussed it in the more general setting
of electromagnetic waves.
Now, so having discussed so, this brings us
to kind of a conclusion of our discussion
of electromagnetic of the properties of electric
magnetic waves. So, we have seen that electromagnetic
waves are essentially electric field and oscillating
electric field pattern and an oscillating
magnetic field pattern both of these oscillate
in the direction perpendicular to the direction
in which the wave is propagating.
Now, let us now discuss the possible frequency,
the frequencies with which you have such electromagnetic
waves. So, you have actually got electromagnetic
waves of all possible frequencies. And different
part so when, you have magnetic waves of a
particular frequency we have a different name
associated with that.
So, this brings us to a discussion of the
electromagnetic spectrum. So, let us start
with radio before starting our discussion
of radio waves we should realize that, in
nature and also in manmade situations. We
have electromagnetic waves of we could have
a electromagnetic waves with large variety
of frequencies, large variety of frequencies
also means a large variety of wavelengths.
The frequency and wavelength as we have already
discussed are related lambda into mu is equal
to C where C is the speed of light 3 into
10 to the power 8 meters per second. And the
question is that in our discussion till now,
this mu or lambda which are equivalent have
not been specified. We in the discussion until
now, mu and lambda have not been specified
and they the discussion was valid irrespective
of the value of the frequency or the wave
length. So, the discussion was valid for all
for electromagnetic waves of all frequencies
or all wave lengths. It was not specific to
a particular, to a frequency or to a particular
wave length.
Now, in nature or in manmade situations you
could have electromagnetic waves of a large
variety of frequencies. The frequency can
span a large variety a large range. And the
phenomena related to different frequency ranges,
different frequency bands, different ranges
of frequencies in this entire range are different.
There is also a different name given to the
electromagnetic wave then, it is of a in a
particular range of frequencies or range of
wavelength.
The phenomena associated with different values
of the frequency or the wave length are different.
So, the names are different the phenomena
associated are also different and this is
what we are going to discuss here. So, let
us start with the low frequency, the lowest
possible frequencies for the electromagnetic
waves the low frequency part. So, the electromagnetic
waves of the lowest possible frequencies that
is frequencies less than 1 gigahertz.
So, if I have electromagnetic radiation waves
of frequencies less than 1 gigahertz these
are referred to as radio waves. So, radio
waves we have encountered them I am sure all
of you must have heard the radio sometime
or the other and the AM radio transmission
about which we shall study in some more little
bit more later on as we go long.
The AM amplitude modulation the radio transmission
is usually, in 100s of kilo hertz to 1 megahertz
. So, may be 800 900 kilohertz to 1 megahertz.
So, if I have a 3 let me let us, also estimate
the wave length corresponding to this. So,
the amplitude modulation transmission usually,
occurs at around 800 900 kilohertz to 1 megahertz.
So, let us estimate the corresponding wave
length.
So, 1 megahertz means lambda is 3 into 10
to the power 8 divided by 10 to the power
6 which gives us 300 meters. So, the radio
waves are typically of the order of 100s of
meters may be a kilo meter also kilo meter
to 100s of meters. And radio waves have got
application as we all know in communications.
So, the radio transmission is an important
means of communication and these work at frequencies
typically less than 1 gigahertz.
FM transmission is at 100s of megahertz roughly,
100s megahertz in order of 100s of megahertz.
So, does the TV also works at frequencies
of around 100s of megahertz in the radio part
of the spectrum.
The next part of the spectrum from 1 gigahertz
to 3 into 10 to the power 11 hertz. So, this
is referred to as microwave. Now, a point
which you should remember is that, I am giving
you names for different frequency bands. So,
I am what I am doing is, I am telling you
that this frequency range to this frequency
range is called something. So, here I am telling
you that 1 gigahertz to 3 into 10 to the power
11 hertz is referred to as microwave.
Now, you should remember that these frequency
the values of the frequency limits are not
very rigorous they are always quite fussy.
And somebody may also refer to for example,
as 1 4 gigahertz as radio wave. And it would,
you would, it should not be absolutely incorrect
because, these boundaries are not all that
rigorous are in strict they are quite fussy.
So, somebody could refer to something which
is on the boundary as something 1 4 gigahertz
also as radio waves. So, these are just some
typical numbers you should bear this in mind.
So, we refer to 1 gigahertz to 3 into 10 to
the power 11 hertz as microwave. The corresponding
wave length is 30 centimeters to 1 millimeter.
Now, microwave and radio the higher part of
the radio frequency and microwave. Have got
very important applications in communication
So, the earth’s atmosphere is transparent
from 1 centimeter to 30 meters, 1 centimeter
to 30 meters just let us, just go back. So,
1 centimeter is in the microwave and 30 meters.
So, this microwave the largest wave length
in microwave is 30 centimeters. So, 30 meters
would be in the radio.
So, the radio the high frequency radio and
the microwave both of these are the atmosphere
is transparent to both of these. So, you can
use it for space communications. So, if you
wish to communicate with the satellite in
outer space which is beyond the atmosphere
you could use this that wave length range
1 centimeter to 30 meters for such communication.
Radio the radio waves larger than 30 meters
are reflected by the ionosphere which is there
in the upper atmosphere of the earth they
are reflected back. And this reflection prevents
it from being used for communication with
space for space communication, but it has
important applications if you want use this
reflected wave for communicating on earth.
Let me, explain this point a little bit over
here.
The surface of the earth we know is spherical.
So, if you wish to communicate from here to
here you cannot send a radio wave straight
away. Because, it would then have go through
the earth. You could built a antenna which
would increase the range, where you could
communicate, but still you could not be you
would not be, able to communicate to a region
over here with an antenna of this size you
would have to build a even higher antenna.
Now, this can be overcome if you use radio
waves which get reflected from the ionosphere.
So, this is the ionosphere 
which reflects radio waves which are much
larger than 13 centimeters. So, 30 meters
sorry. So, if you are working in the range
where the wave length is more than 30 meters
the atmosphere it not transparent. So, the
radio wave will get reflected and if the radio
wave gets reflected then, you can actually
send signal here by reflecting it of the ionosphere.
So, this is also useful in communication.
So, before you had satellites this was you
could have communicated with the point over
here, from here using the reflection from
the ionosphere. But now with satellites you
could actually send the signal to a satellite
and then, the satellite could send it back.
So, if you wish to communicate using satellites,
you should work in this range the larger wavelengths
are reflected back by the ionosphere.
Now, this range where the atmosphere is transparent
to microwave and radio waves it also useful
for radio astronomy. You cannot see objects
beyond the atmosphere at wave lengths much
larger than this and it is difficult to see
it at wave lengths much smaller than this
also. So, this is very suitable for radio
astronomy.
.
Now, let me just divert a little and tell
you a little bit about something which is
very interesting in radio astronomy. In particular
we know, it is well known now that hydrogen
is the most abundant known element in the
universe. So, if you ask the question what
is it that is most abundant then, it is hydrogen
in the universe. And if hydrogen is neutral.
So, by neutral hydrogen we have a spectroscopic
notation for neutral hydrogen let me, first
introduce that.
In the spectroscopic notation neutral hydrogen
is denoted by H1. So, if you have neutral
hydrogen atom it is referred to as H1. Now,
as we know hydrogen, neutral hydrogen has
a proton and an electron. So, if you have
hydrogen in the ground state, you have a proton
and an electron. And the electron is going
around in an orbit around the proton. Now,
we all know that the proton and the electron
both of them have spins.
So, consider a hydrogen atom in the ground
state. So, this picture here shows you a hydrogen
atom in the ground state. You have the proton
and the electron and here the spins of the
two particles the spin of the proton and the
spin of the electron are both aligned. Now,
you could also have a hydrogen atom in the
ground state where, the spin of the proton
and the electron are aligned in opposite directions.
Now, it turns out that the situation where
the 2 spins are in opposite directions has
a slightly lower energy then, the situation
that the 2 spins are aligned. So, the hydrogen
atom could do a transition from this energy
state to this energy state. Such a transition
is called a hyperfine transition and there
will be a small energy difference between
these 2 states.
So, if I have a hydrogen atom in the ground
state and if it goes state from here to here
there will be a small energy difference this
energy difference will come out in the form
of electromagnetic waves. And the electromagnetic
waves that are emitted when, the hydrogen
atom goes from here to here comes out at 1420
megahertz a 1 42 gigahertz. Which is somewhere
in the border of radio and microwave.
The wave length corresponding to this is 21
centimeters. So, neutral hydrogen in the ground
state emits radiation at 21 centimeters to
this hyperfine transition. Now, as I told
you that hydrogen is the most ubiquitous element
it is there all over the universe. So, you
can use this to image different parts of the
universe.
So, here I will show you an image made using
the 21 centimeter radiations it is its image
of a distant galaxy. A galaxy is a collection
of stars it also has gas. So, this shows you
2 galaxies, the black things which you see
here is where the stars in the galaxies are.
We live in a galaxy like this.
So, there is a this is the galaxy the black
thing or the stars in the galaxy. And the
white contours white contours show you, how
the mutual hydrogen is distributed. The white
contours were measured using the 21 centimeter
radiation that comes out from the neutral
hydrogen.
How are such measurements done? So, let me
show you something of particular interest
to me and to us in general this is because,
India now as the world’s largest low frequency
radio telescope called the joint meter wave
radio telescope the GMRT. This is located
in a place called Narayangaon near Pune. So,
in a place called Narayangaon near Pune we
have this radio telescope which is the world’s
largest low frequency radio telescope at present.
There are 30 antennas, each 45 meters in diameter.
This picture shows you 1 of the antennas in
the GMRT. The diameter of this antenna is
45 meters. And there are 30 such antennas,
the 30 antennas are distributed in a Y shape
like this the length of each of these arms
in the Y is around 16 kilometers. So, you
have this low frequency antennas, the antennas
each antenna is a dish it reflects, it focuses
the radiation incident on it from far away
sources it focuses it to the point over here.
And at this point you have a dipole you have
actually 2 crossed dipoles, which can measure
the detect the electromagnetic wave which
is focused on to it. So, this is roughly how
this whole thing works. And this joint meter
wave radio telescope works in a range of frequencies
shown over here. The 1420 megahertz these
values are in megahertz.
The 1420 megahertz band can be used to make
images of the 21 centimeter radiation that
comes from neutral hydrogen this shows you
another image made using the giant meter wave
radio telescope. This is an image of a galaxy
called DDO 210 black thing over here is where
the stars in the galaxy are. And the contours
are determined from radio measurements of
the 21 centimeter emission from neutral hydrogen’s.
So, the contours show you how the hydrogen
in these galaxies are distributed. This picture
is from a paper by Begum and Chengalur who
used the giant meter radio wave telescope
to observe this particular galaxy. And such
studies can be used to infer very interesting
things about these galaxies we shall not go
into it in over here.
Let me, now move on to another very interesting
thing which is there in the microwave band.
And this very interesting radiation is referred
to as the cosmic microwave background radiation.
So, let me first tell you briefly the history
of this radiation in the 60s when, microwave
radiation radio. And microwave communication
was being developed 2 scientists there were
essentially, communication engineers at the
Bell laboratories were investigating what
are the possible sources of noise in radio
communication.
And what they did was, they took a radio receiver
and they were studying possible sources of
noise in that radio receiver. So, you take
the radio receiver and point it in different
directions and see what is the noise which
comes from different directions. And they
found that, there was a noise which those
noise contribution which seemed to be there
present there in all directions in the sky
irrespective of where you point your radio
receiver there was a noise contribution.
Which seemed to be coming uniformly, from
all directions in the sky. And this was something
quite mysterious, but interestingly quite
unaware of this. And much earlier actually,
a Russian scientist called George Gamow had
predicted that our universe that the whole
of space should be filled with an electromagnetic
wave with the radiation. And at the time which,
at which this noise in this radio receiver
was detected by 2 communication engineers
at the Bell labs Penzias and Wilson at the
time.
When, they detected this there was a group
of scientists at Princeton University who
were trying to detect this radiation which
was predicted to fill the whole universe.
And when, they heard that Penzias and Wilson
had discovered this kind of a noise which
seems to be coming from all direction in the
sky they realize, that Penzias and Wilson
had discovered a radiation which fills the
whole universe.
So, this radiation is something which fills
the whole universe and it was the discovery
of this radiation that is that it provides
very significant evidence for the big bang
theory of the universe. So, it is a consequence
of the big bang theory of the universe that
the universe should be filled with the radiation
like this which permeates the whole universe.
And it is this radiation which was which is
being detected by this radio receiver. Which
if you point in any arbitrary direction you
get same the amount of radiation. This radiation
which was the Penzias and Wilson received
the Nobel Prize for this discovery. Now, this
radiation was also predicted to be a black
body radiation. And this prediction was verified
roughly, a little more than 10 years ago.
The people who made the person who was the
leader of the team which verified the black
body nature of this radiation received the
Nobel prize in physics this year in 2006,
that is last year in 2006. So, let me tell
you a little bit now about what was the discovery.
What is it that was actually, but measured.
So, this curve over here shows you the spectrum
of the radiation that was measured this for
which the Nobel Prize was given last year.
So, now let me digress a little what you mean
by a black body radiation.
So, I am sure of all of you would have heard
of black body radiation earlier. The question
is what do we mean by black body radiation?
Or rather what do we mean by a black body?
The word black body refers to something, which
absorbs whatever radiation is incident on
it, but it just it does not just keep on absorbing
radiation and does nothing else. No, it absorbs
whatever is whatever radiation is incident
on it and it emits radiation of all wavelengths
or of all frequencies with equal efficiency.
So, this. So, these 2 properties are what
define a black body. Let me, take up an example
of a black body. So, suppose we have a cavity
this is a black body cavity, we have a cavity
possibly made up of some metal kind of some
kind of metal. And the outer wall the cavity
let me join it like this it has a finite thickness
also. So, this is my cavity it has some kind
of a thickness and this cavity is brought
is maintained at a temperature T. So, this
T is the temperature of the cavity in Kelvin.
So, I bring this cavity, metal cavity to a
temperature T and there is a small hole over
here. So, that some radiation can go through
and come out. So, we have kept this cavity
at the temperature T. Now, what will happen
the question is what will happen if some radiation
comes inside, what happens to the radiation
which is there inside this cavity. Now, the
walls of this cavity emit radiation and radiation
emitted from here will reach here and get
absorbed. And this wall will again, reemit
radiation of all wave lengths equally efficiently.
So, any radiation which comes inside which
happens to come inside will again get absorbed
over here and get reemitted equally efficiently
in all wave lengths. So, if you keep this
cavity at a temperature T for sufficiently
long, the radiation which is there inside
the cavity will get emitted absorbed, emitted
absorbed many times until finally, the radiation
inside this cavity will be in thermal equilibrium
with the walls of the cavity with the inner
wall of the cavity.
This radiation which is there inside over
here some part of it will leak out which,
you can measure that is why we have the hole
over here. So, this radiation which is there
inside this cavity which we assume is in equilibrium
with the walls of the cavity through repetitive
absorption and reemission. So, it will get
absorbed reemitted many times till finally,
on the average the radiation inside does not
change.
So, the radiation inside this cavity in equilibrium
with the cavity at a temperature T is what
is called black body radiation. So, this is
what is referred to as black body radiation.
And since, this radiation is in thermal equilibrium
with this cavity at a temperature T. The spectrum
of this radiation it is found is characterized
is uniquely, characterized by the value of
the temperature and nothing else.
So, the spectrum of the black body radiation
is completely characterized by the temperature
of the black body with which it is in equilibrium.
So, the crucial point is that when, radiation
is in equilibrium with matter which can emit
and reabsorb the radiation equally at all
wave lengths. When, this radiation comes to
equilibrium with matter it has the black body
spectrum.
The spectrum is completely defined just by
the temperature of the black body of the matter.
So, the radiation also has the same temperature
because, it is in equilibrium with the matter
and the spectrum of the radiation is completely
specified by the value of the temperature.
So, how do you quantify the spectrum.
The quantity which, the we use to quantify
the spectrum is as follows. I have shown it
over here. You take a unit volume element
inside and ask the question what is the energy
in the a small frequency range in this volume.
So, this is what I show over here. The question
being asked is how much is the for this small
volume which I showed you over there. What
is the energy for frequency interval in the
frequency interval d nu?
So, if I look at a frequency nu frequency
range between the 2 frequencies nu and nu
plus d nu. How much energy is there per unit
volume? That is what so, d nu is the energy
per unit volume in the frequency range d nu.
And d nu can be written as u nu this spectral
energy density into d nu. And this…So, when
I talk of the spectrum of the black body radiation
I am essentially referring to u nu.
So, it is being found that u nu has this form
given over here. This is called the black
body spectrum or the Planck function. So,
this the spectrum of the black body radiation
has a form which depends only upon the temperature.
There are other constants over here which
are there are other numbers over here which
are constants. So, you have the Planck constant
h and the Boltzmann constant K. And the only
parameter which depends on the nature of the
which decides the spectrum is the temperature.
So, if you wish to calculate the spectrum
the value the energy density at any particular
frequency you have to put in the value of
the nu here And for a particular value of
the temperature this has a unique spectrum.
So, this shows you the spectrum of the black
body here it is plotted as the function of
the wavelength. So, you have the energy in
the wavelength interval d lambda and it is
plotted as a function of the wavelength.
So, the point to note there are a few points
very important points to note over here. These
black body spectrum the spectrum is decided
only by the value of the temperature and nothing
else that is the first point. The second point
is: that these black body spectrum curves
do not intersect if I change the temperature,
I will get a different curve which does not
intersect with the previous curve that is
the second point.
The third point is: that the energy density
increases continuous monotonically if I keep
on increasing the temperature, the curves
get higher and higher. And the peaks of the
curve also shift to a smaller wavelength as
I increase the temperature. And it has been
found, that the product of the peak wavelength
and the temperature of the black body, the
product is a constant this is called the Wein
displacement law.
So, it has been found that the product of
lambda m into the temperature of the black
body this is a constant. Lambda m refers to
the wavelength where the black body spectrum
peaks. And T refers to the temperature of
the black body. So, it has been found that
as you increase the temperatures the wavelength
where, the black body spectrum peaks keeps
on getting smaller and smaller.
So, the black body radiation is the radiation
that arises this has is the spectrum of the
radiation that arises. When, you have radiation
in thermal equilibrium with matter.
Now, what this curve shows is the spectrum
of the radiation that you get coming from
space. So, you have if you take a radio receiver
and point it in any arbitrary direction you
will find that there is some radiation coming
which is independent of the direction in which
you point your receiver it is coming from
all direction in space. So, if I am sitting
on the earth over here there is some radiation
coming from all directions in space.
This was discovered by Penzias and Wilson
and they did the measurements only in a particular
frequency. So, the spectrum was not very well
known. And if you make a measurement that
only 1 frequency if you assume it is a black
body if you make measurement at only 1 wavelength
of frequency. If you assume it is a black
body you can get the temperature straight
away because, the curves do not intersect.
So, the observation made by Penzias and Wilson
indicated that it had a temperature of around
3 Kelvin the black body nature was not very
well known then, but later on people did more
on more observations and finally, in the 1990s
NASA sent a satellite called COBE. Which measured
the spectrum of this radiation which comes
from space all comes from all directions in
the sky they measured the spectrum and the
spectrum was found to be a black body this
is what is shown over here.
So, the spectrum of this radiation which comes
from all direction in space, all directions
in this sky was found to be a black body with
the temperature of 2 73 Kelvin. And this black
body which was measured by COBE by the COBE
satellite is possibly the most precise black
body curve that has ever been measured. So,
what this finally, tells us is that there
is a black body radiation with a temperature
of 2 73 Kelvin coming from all directions
and we interpret this as the whole universe,
the whole of space the whole universe is filled
with the black body radiation at a temperature
of 2 73 Kelvin. So, it is as if the whole
universe is inside a black body cavity and
it is filled with a black body radiation of
2 73 at a temperature of 2 73 Kelvin.
This is 1 of the most important discoveries
which have been make and this clearly puts
the big bang theory of cosmology where the
universe is expanding the universe started
from a big bang and which this validates the
big bang theory of cosmology.
Now, let me move on to another application,
another very interesting thing which has to
do with microwaves. We have already discussed
molecules and the vibrations of molecules.
We discussed the vibration of benzene molecules
now, molecules in addition to vibrating can
also rotate. And molecules have the vibrations
and rotation of molecules are actually quantized.
So, corresponding to different vibrational
and rotational states you have different quantized
energy levels.
And if you have transitions between these
energy levels. So, if I have a molecule in
a excited vibrationaly excited energy level.
If it is goes back to the ground state there
will be some radiation which comes out and
these transitions correspond to radiation
in the microwave and in the infrared. Now,
water molecule we know, the water molecule
it has a hydrogen 2 hydrogen atoms and an
oxygen atoms it is polarized.
So, if i put in an external electric field
the dipole movement of the water molecule
will try to align with the external electric
field. And if the electric field oscillates,
the dipole moment will also start to oscillate
and it will set this will basically, set the
water molecule into rotation. So, if I have
an external electric field which is rotating,
which is oscillating the it is sets the water
molecule into rotation this is another kind
of excitation of a molecule it is a rotational
excitation. These rotational excitations are
quantized.
So, if I have a water molecule which is rotating
and if it comes down to the ground state it
will emit radiation and vice versa. So, there
is a rotational transition of water molecules
which occurs at 2 45 gigahertz. And this is
the transition that is used in microwave ovens.
So, in microwave ovens you have microwave
at 2 45 gigahertz which is incidental whatever
you want to heat.
The water molecules inside this thing that
you wish to heat will start rotating when,
it this radiation falls on it. And this rotational
energy gets converted into the random motions
of the molecules which is what we call heat.
So, this is how the microwave oven works and
this is a an important daily, day to day application
of this microwave these Another so, I should
tell you a interesting thing which follows
from this. So, this is why if you put in say
dry piece of paper or something like that
into a microwave oven the oven. The microwave
will not be heated, microwave can only heat
things which have water in them. So, I think
let us bring today’s lecture to a close
here. And we shall resume our discussion with
the from here in the next class.
