Tip:
Highlight text to annotate it
X
Let us continue our discussion on transmission photoelasticity. And for you to understand
photoelasticity, you need to develop concepts related to crystal optics. And in this, one
of the very important concepts that we saw in the last class was, when I have a crystal
and when I have a light incident on it, I can look at the incident light with respect
to the optic axis. In the first case, the incident light is along the optic axis; in
the second case, the incident light is at an angle to the optic axis; in the third case,
the incident light is perpendicular to the optic axis.
And what I mentioned in the last class, was the third case is particularly attractive
to photoelasticity. The second case really brings out, how does one look at two images
in a crystal; so the second case helps in understanding what is birefringence. On the
other hand, the third case is what is useful from photoelasticity point of view, and the
first case is very similar to what happens in an isotropic medium; and in the third case,
both the ordinary and extraordinary rays travel in the same direction, but because of different
in refractive indices, they travel with different velocities. So, now what I find is for one
incident beam, I have two refracted beams; their planes of polarization are mutually
perpendicular; they also acquire a retardation within the crystal.
And in order to give you an idea, it is indeed so, we have also rotated a crystal and we
saw that one dot becomes two dot, which indicates that the incident light in relation to the
optic axis has a role to play. So, now the stage is set for how to analyze this mathematically.
And even before developing the concept, we have labeled this as Light Ellipse. So, you
can say that whatever we are go to do, finally we end up with equation for an ellipse. And
what you have is, for one incident light I have two refracted beams and they travel with
different velocities, and they could be easily represented by a x cos omega t plus alpha
1 and a y cos omega t plus alpha 2. So, what I have is, I essentially have two simple harmonic
motions, one in the x direction, one in the y direction, they have different amplitudes
a x and a y. And in general, you could also think of a phase, alpha 1 and alpha 2.
See, what you will find is, in photoelasticity literature, more than the absolute phase it
is the relative retardation that is very important. So, keeping this idea in mind, we would also
go back and recast the equation, that is what we will do later. So, what we will look at
is, we will look at relative phase difference between these two vibrations, label that as
delta, and delta is nothing but alpha 2 minus alpha 1. So, it is a relative phase difference
that is very important. So, what I have is, for one incident light
I have two refracted beams and they are simple harmonic, planes of vibration are mutually
perpendicular, and when I want to find out what is the resultant, the magnitude of the
resultant light vector is given by simple vector addition. Suppose, I want to find out
what is E at a particular instant of time, I have to simply take the amplitude of this,
I have to simply take this square root of it, so I have this as E x squared plus E y
squared, I can find out the amplitude. And this I do because they are mutually perpendicular.
It is not like, when I go to the pond, drop the two pebbles, both the waves in the same
plane. Here, the waves are mutually perpendicular, they travel with different phase. They acquire
a phase retardation when it comes out the crystal, when it comes out of the crystal,
you see the interaction of this, and what would be the nature of this interaction, the
polarization behavior changes. So, that is what we are going to look at.
Now, my interest is, what would be the trace of this light that comes out of the crystal
plate. So for me to do that, I have to eliminate time. So, what I want is, I want to get that
trace of that tip of the resulting electric vector on a plane perpendicular to the axis
of propagation, this is my interest, and this can be obtained by eliminating time. And I
have already mentioned that for you to carry on with photoelasticity, you need to brush
up your trigonometric identities, we will use several of them, even for this development,
we will use the trigonometric identity and simplify the set of expressions. I will give
you the clue, you have the expression for E y and that has a phase alpha 2. And I said
in photoelasticity we are interested only in relative phase difference. So, write that
in terms of delta and alpha 1, and you can simplify it. Take two minutes of your time
and do it. I have E y as this, and I would like you to
simplify this expression, as simple as that. So, what is the trigonometric identity I can
use? Cos a plus b. So, I can have this as cos omega t plus alpha 1, omega t plus alpha
1 I can take it as a, and delta as b. So, cos a plus b you will get it as cos a cos
b minus sine a sine b. So, when I do that, I will get this expression. So, what I have
is, I have a y cos omega t plus alpha 1 into cos delta minus sine omega t plus alpha 1
into sine delta. And this, I could replace in terms of E x as well as this also I could
replace it in terms of capital E x. Now, I will have an expression only consisting of
E y, a y, E x, a x and expression involving delta. You could simplify it, can you write
in this fashion? It is straight forward, you could do it easily, and when I do that I get
the expression like this. So, I have this as E x by a x cos delta minus square root
of 1 minus E x by a x whole squared into sine delta.
And what I could do is, I could segregate the terms, and finally write what is the expression
that would give you the trace of the tip of the resulting electric vector. So, what I
have done is, I have just taken this expression, replaced alpha 2 in terms of delta plus alpha
1, used trigonometric identity and got this expression, then replaced this terms involving
time by E x by a x, and now I have the final expression, and this could be further simplified.
Can you do that simplification? Do that simplification, because if we do the simplification right
in the class, when you revise the notes, whatever you have learnt becomes very simple, it is
a very simple exercise and let us see what we get.
So, I am want to get an expression like this. What I have is E x squared by a x squared
plus E y squared by a y squared minus 2 E x E y divided by a x a y cos delta equal to
sine squared delta. And this is the generic expression of an ellipse. Suppose, delta becomes
pi by 2, what happens to this expression, you have this becomes 1 and this terms goes
to 0 and this is your famous equation of ellipse. You have x squared by a squared plus y squared
by b squared equal to 1, that you all know, that is the equation of an ellipse. And what
you have here is, this is an equation of an ellipse at some arbitrary angle. And that
is what you have here, I have this as the light ellipse, and this light ellipse, the
major and minor axis are shown here, and this is orientated at an angle beta, and this is
governed by a generic expression like this. And I have the amplitudes marked, and you
can also find out the expression for a as well as b, in terms of these quantities. That
is not our focus, so we will not really determine that, but would definitely find out what is
the expression for beta. And we will directly take that result from what is available in
the literature, we will not derive it, and what I have here is the azimuth beta of the
ellipse with the horizontal is obtained as, given as, tan 2 beta, and that is given in
terms of the amplitudes 2 a x a y divided by a x squared minus a y squared into cos
delta. And this is a very important learning, what
you have is, when I have two simple harmonic motion, which travel perpendicularly, and
they have a phase difference when it is comes out, and they interact, and you essentially
get an ellipse. And what you have is, you have two expressions, one expression gives
the equation of the ellipse, the other expression gives you the orientation of the ellipse,
and this is called the azimuth. And if I calculate a and b, if I have b by a, I also get the
ellipticity. In fact, if you go to optics literature, there is a quite a good measurement
approach is available, where they call it as ellipsometry. They find out the ellipticity,
they find out the azimuth they also find out the handedness of ellipse. So, what you find
here is, if I add two simple harmonic motions which are mutually perpendicular with the
phase difference, if I add them, in general I get the interaction as trace of an ellipse,
this is very important photoelasticity.
We would also see this little further. And what my interest is, when I changed delta,
what happens. For various values of delta, what way you will get the state of polarization.
We have already seen when delta equal to 0, what happens. When I have delta equal to 0,
I have two vibrations and they will give you a plane polarized light, where is the ellipse
comes, ellipse is not come there, delta equal to pi by 2, then you had equation of a simple
ellipse, whose axis coincide with the x and y direction.
And what we are looking here is, we want find out in the range 0 to pi by 2, when delta
lies, it is not 0 or not pi by 2, it is within this range how do you have is, you have an
ellipse like this. I want you to make a sketch, you will have sketch for all of these cases,
and also note down that this is rotating in a clock wise direction.
So, if delta is between 0 to pi by 2, their resulting trace of the light would be an ellipse
orientated with this orientation, and it will have handedness indicated in this fashion.
And suppose I got delta equal to pi by 2, which we have already looked at it, we will
see pictorially. So, when delta equal to pi by 2, the major and minor axis of the ellipse
coincide with the reference direction x and y. This is a very important result, this is
very useful result in photoelasticity. The vibration along the major and minor axis having
a phase difference of pi by 2, that is very important information you have. So, if the
vibration is, we having a phase difference of pi by 2, then those axis form the axis
of the ellipse.
And what happens when I have the range goes to pi by 2 to pi. The orientation changes
and you have the handedness still remains, the handedness is still clockwise. And when
you complete this picture, you will have a nice picture, nice set of pictures that you
will have. If I go to the range pi to 3 pi by 2, you will find the handedness also changes.
So, that is what I have, the handedness changes, orientation remains same, but the handedness
changes. So what you find here is, for different values
of delta, you see different forms of elliptically polarized light. So, you can look at it the
other way, when I look at the light ellipse, it is possible for me to find out, what would
be the value of delta that would have caused this, our interest is the reverse. But in
order to understand the cos of delta, we look at for various values of delta, how does the
light characteristic changes, that is what we are look at.
And when I have delta equal to 3 pi by 2, pi by 2 and 3 pi by 2 share a commonality,
you will have the axis coincide with the reference axis. But the handedness changes, when it
was pi by 2, the handedness was clockwise, and when it is 3 pi by 2, the handedness is
anticlockwise. And what you need to appreciate here is, in conventional photoelasticity,
people never bothered about the handedness, it was not really affecting the results. The
moment digital photoelasticity came, where they used CCD cameras as electronic eye and
they wanted to automate the procedure in order to minimize the error sources, change of handedness
helped in minimizing the error due to quarter wave plate. So, though in conventional photoelasticity
handedness does not play a significant role, it does play an important role when you come
to the domain of digital photoelasticity. So, it is better to know, the handedness has
it’s importance.
And when I go to the range 3 pi by 2 to 2 pi, I have the ellipse orientated in this
fashion, and this is anticlockwise. So, you have three cases where you have anticlockwise,
we have three cases where you have clockwise. And when delta equal to 0 or delta equal to
pi or delta equal to 2 pi, you will have plane polarized light coming out as plane polarized
light, except the case which is slightly different is when you have delta equal to pi. When delta
equal to pi, it will be rotated by some angle. But the state of polarization will remain
still plane, but it will get rotated by some angle.
And now, we come to another important aspect, what happens to this expression when a x equal
to a y. So, it becomes undefined. When tan 2 beta becomes infinity, 1 by 0 you have,
so it becomes undefined. And when the amplitudes are equal, you have essentially a circularly
polarized light. Because there is no specific axis, you have only circularly polarized light
that comes out of the model. And this is a very important state of polarization we want,
because I said that you have a plane polarized scope, you have a circular polarized scope.
In a plane polarized scope, you impinge a plane polarized light, in a circular polarized
scope, you impinge a circularly polarized light. So, I need to generate a circularly
polarized light and make it hit on the model and this gives a via media. So, I have a crystal
plate in between, a plane polarized light can be converted into a circularly polarized
light.
And what you have here, when delta equal to pi by 2, the handedness is clockwise, when
delta equal to 3 pi by 2, the handedness is anticlockwise. So, handedness tells you what
is the value of delta. So, in ellipsometry, they measure the ellipticity, they measure
the azimuth, they also measure the handedness. So by knowing this, you can fix delta. Our
idea is to find out delta by optical measurement. I said, light is a sensor and light gets modified
within the model because of the sources applied, and you get exit light, which is in general
elliptically polarized. If I analyze what is a light coming out, I can fix what is the
delta, that is what you have learnt it now. We will also look at it in a slightly elaborate
way, when you look at what is retardation plate. As far as this discussion goes, what
you find is, when I have two simple harmonic motions, which are mutually perpendicular,
which have a phase difference for different values of phase difference, I get different
states of polarization as the exist light. So, this gives you a hope to use light as
a sensor. Because essentially, I will find out what happens to the exit light, with the
exit light I will go back to find out what was the delta that has caused. Now, we will
relate delta to sigma 1 minus sigma 2 later, that is how we will merge physics and stress
analysis. But before we get into that, we need to know little more about what happens,
suppose I take a crystal plate, that we will see now.
I will just take a crystal plate and you have to observe it very carefully, we will do this
two-three times. So, what I have here is, you keep your note book horizontal and draw
this sketch, and we will see part by part and then explain, and what we are going to
discuss is retardation plates and wave plates. So, what I have here is, I have a crystal
plate, it is not loaded, it is a natural crystal and I have this in a form of a plate. And
what I have is, I have a light source and I have put a polarizer. Now, you must be familiar
and we will just see what happens. So, what you have here is, I have a natural source
of light, after the polarizer I have a plane polarized light impinges on the model.
So, what you have is, I have a plane polarized light, because I want to use light as a sensor,
so I should know the input light characteristic. Input light is simply a plane polarized light.
And when it hits the model, when it hits the crystal plate, it is not the model, model
also behave likes a crystal when it is loaded, and here we are looking at in general what
happens to the crystal plate. And what do you anticipate? You anticipate for one incident
light there will be two refracted beams, because that is what the whole of the crystal optics
tells you. For one incident beam, I will have two refracted beams, and these two refracted
beams are plane polarized, and their planes of polarization mutually perpendicular. Let
us see this, that is what is shown in the animation, you carefully watch.
So, what I, what happens is the light vector on entering the plate splits into two components
along the fast and slow axis. So, you have to understand, I am bring in two new terminologies,
fast and slow axis. The reason for this labeling would become clear, when we look at what happens.
So, what we saw is, I have a natural source of light which become plane polarized, hits
the model and then on the front surfaces it splits into two components. Let us see the
two components. Is the idea clear? I send a vibration, a cos omega t, this will become
two rays within the model, within the crystal plate. And you have a, depending on the orientation,
you have one of this amplitude is longer, another amplitude is smaller, so amplitude
is plate. And this is nothing but they are, the planes
of vibration is in this direction, planes of vibration is in this direction and they
are perpendicular. So, for one beam within the model, I will have two rays. And what
you have here is, if you watch it very carefully, whatever is the thickness is expanded as two
planes, I have one plane coinciding with the fast axis, another plane coinciding with the
slow axis. And let us see what happens. So, what happens is, you know that when light
enters the crystal, it splits into two rays, and because it is perpendicular to the optic
axis, they travel in the same direction. But the plane of vibration is mutually perpendicular,
you have one plane like this, you have another plane like this, and you have a wave travels
like this. And what has happened? This wave has travelled past the other wave, that is
what is shown in the sketch. So, this has traversed the thickness of the plate faster
than the other wave. So, I call this axis has fast axis. And this wave has taken little
more time and it has acquired a retardation delta within the plate. I will repeat the
animation, then you will understand. So, what you find here is, I have a natural source,
I put a polarizer definitely, and I know what kind of light that impinges on the crystal
plate, and this splits into two rays when it enters the model. Depending on the angle
theta, you will have the amplitude as a cos omega t cos theta a cos theta into a cos omega
t, that is the expression for the light vector, and you will have this as a sine theta cos
omega t, and within the model which is shown in an expanded fashion, I have this like this.
Make a neat sketch of this. And what do you anticipate? I have two simple harmonic motion,
which are mutually perpendicular, which has acquired a phase difference. When they come
out of the crystal plate, how will it appear. We have just now seen mathematical expression.
It will appear like an ellipse, that is why we develop the mathematics. If I have two
simple harmonic motion which are mutually perpendicular, if they have a phase difference,
depending on the difference in phase, you will see lights different states of polarization.
And let us see that. So, I will have a light ellipse coming out of the model. I use model
and crystal plate interchangeably, please pardon me. And model behaves like a crystal
plate when stressed, in a crystal plate it is naturally having birefringence, that is
only difference. So, what I have here is, when I have a normal light source, I have
a polarizer, I put a crystal plate, in general I will have a light ellipse. And how this
light ellipse has come about? I know that within the crystal plate I have two rays traveling,
one plane of vibration is in this plane, another in the plane perpendicular to it, they acquire
a phase difference delta. And we just now has seen, if I have two simple harmonic motions
with the phase difference which are mutually perpendicular, I get essentially an ellipse.
If you understand this, the whole of photoelasticity is mastered. And what we will do is, we will
see the animation again, I will stop at intermediate stages, and you can verify your drawing as
well as improve your understanding.
So, what this shows is, I have a source of light, I have a plane polarizer, after the
plane polarizer, I have a plane polarized light, hits the crystal plate. As soon as
it touches the front surface, it splits into two components. Because within the crystal
you will have two refracted beams, you are not going to have only one refracted ray.
And these two refracted rays will have different amplitude, which are shown, which is depicted
by the angle theta. So, when you look at a crystal, crystal will
always have a fast axis and slow axis, which are mutually perpendicular. And you may have
to perform an experiment to find out these axis, their labels F and S are again arbitrary,
appearing we do not know whether it is a fast axis or a slow axis. You can label it as fast
axis and carry on, but once you do this, you must match your optical arrangement to the
actual physical polarized scope. And again in conventional photoelasticity, whether it
is a fast or slow axis did not play a significant role. The moment you come to the digital photoelasticity,
whether at the point of interest, the axis could be label the fast or slow had an effect
in digital photoelasticity. And that is very important, you had ambiguity and these ambiguous
zones need to be corrected. So, it is better know, it is an arbitrary label. And how to
do it? You have to do an extra step, you have to do some kind of calibration to establish
this, without calibration you cannot do it. And with this, you can really go back and
see which way you can relate this to stress analysis. Even without looking at what others
have done it, with the information you have gathered, you can really find out, we have
also looked at photoelasticity gives a sigma 1 minus sigma 2, and then it gives you orientation
of theta, you have answers for that in this slide. One answer is, when I look at fast
and slow , they could be thinking of coincide with the sigma 1 and sigma 2 direction, and
this is what your theta. So, if you find out the theta, you get the principles of direction.
And we are talking about delta, that is acquired within the crystal plate, and this delta,
whatever the delta you have acquire is nothing but sigma 1 minus sigma 2. In a crystal plate,
the fast and slow axis are same at every point in the whole crystal plate. In an actual model,
the fast and slow axis change from point to point depending on the state of stress, as
simple as that. And you have a very nice animation here, this animation gives you what happens
pictorially within the model, and what you see when the light comes out. And when the
light comes out, you have this as an elliptically polarized beam of light.
And now what I am going to do is, I am not going to stop in between, I am going to redo
this animation, you just watch. Whatever the concept that I have developed, you will understand.
So, is the idea clear? I have a natural light source, you have plane polarized beam of light,
when it hits the front surface, it splits into two components, within the thickness
of the crystal plate it acquires a retardation. Why it acquires a retardation? Because it
has different refractive indices and we have looked at the refractive index as ratio of
velocities, that is why we said, we always want to look at as ratio of velocities, because
we want to feel that one wave will travel faster than the another, I have ordinary and
extraordinary rays that travel with different velocities.
And when they come out, you have this as elliptically polarized beam of light. Suppose, I go and
adjust the thickness of the plate, and then ensure that I have delta equal to pi by 2,
it is one quarter of a wave, so I call that as a quarter wave plate. So, what happens
here, this beta will coincide with theta, whatever I have shown this as beta, it will
coincide with theta. The major and minor axis of the ellipse coincide with the fast and
slow axis of the retarder. So, what you get is, you get beta equal to
theta. You write only this statement, you do not have to redraw this complete figure,
what you learnt here is the major and minor axis of the ellipse coincide with the fast
and slow axis of the retarder. So, if I have a quarter wave plate, when I send the beam
of light, because the fast and slow axis themselves became the axes of the right ellipse that
comes out of it. In general, it is an ellipse, in particular cases, it can be plane polarized
or it could be circularly polarized, depending on how do I manipulate the amplitudes. How
do I manipulate the amplitude? I can orient this theta in such a way that I make it 0,
I make theta 0, the fast axis coincide with the plane of incident light. What happens?
Only a plane polarized light will pass through, on the other hand, when I have this angle
as 45 degrees, I will have this as amplitude same, when the amplitude is same, I will have
a circularly polarized light. In fact, if I have a polarizer and a quarter wave plate,
I can get light ellipse of any azimuth, any ellipticity. You have complete control. How
do I control the azimuth? I simply rotate the quarter wave plate axis, because that
determines, because the quarter wave plate slow and fast axis acts like major and minor
axis of the light ellipse, so that I can control. And if I control the relative orientation
between the quarter wave plate axis and the polarizer axis, I can control the ellipticity.
So, I can have light of all characteristic generated with combination of polarizer and
a quarter wave plate.
And what is fundamental here? Fundamental to our photoelasticity is I should get plane
polarized beam of light. And it is worthwhile to go back to the literature and find out
how we can look at it. There is a large body of literature available and as a very nice
development, starting from 1669. See, we do all this quickly, you have this double refraction
was found out in 1669, double refraction is the first concept. Then you have, in 1690
Huygens, a Dutch scientist, demonstrated polarization with the aid of two calcite crystals arranged
in series. Then what you have, then you have Malus in
1808, observed that light reflected at a certain angle from glass is polarized. And he defined
the plane of polarization of the reflected light as the plane of incidence, that is the
definition he has used. And it was Brewster who developed this Brewster’s law. So what
you find is, double refraction is crucial, that is how crystal behave. And even for this
understanding, it took almost hundred and fifty years, it is not so simple, we see that
very quickly now. So, you have to have a concept of double refraction, then they understood
what is polarization, then Malus found out that light reflected at a certain angle gets
polarized, and it was Brewster who formulated this as a law, it is in his honor that the
law is given. And we also know that Brewster found out temporary birefringerence, then
photoelasticity got developed. So, if you look at, we want a plane polarized
beam of light, and if you look at these names, they are the celebrated people in the field
of physics, and you have for each one of them, you have laws associated with them, and Huygens
principles is very famous wave optics.
And then what happened, then what all development that took place. You also had Arago in 1812,
he invented optical rotation, that you will understand when you look at half wave plate,
it behaves like a rotator, and he invented piles of plates polarizer, he invented a new
form of getting a polarized beam of light. And Biot in 1815, discovered Dichroism, this
is important from the point of view of the polarized sheet that we have. We have a polarized
sheet and I have simply said, in polarized sheet, if you put a polarized sheet, the natural
light becomes polarized. How it function as a polarizer? You have to understand, that
understanding is better. Because we are going to use polarized sheet in and out in photoelasticity
So, it operates on the principle of Dichroism. So, you have to understand what is Dichroism.
And once you talk of polarization optics, you cannot forget Nicol, you have the Nicol
prism, that is also another form of getting the polarized beam of light. I have already
mentioned that, you get very high quality polarized beam of light when you use the prism,
but the field of view is limited. And it was land who invented Dichroric sheet type polarizer
in 1938. Dichroism was observed in 1815, and it became available as a commercial product,
for us to use in photoelasticity only in 1938.
So any physics, it takes a long time for it to become as a technology, there must be need
for it, people should know where to use it. They observed the physics, but this has to
be translated into technology. And we have also seen, it is only around 1930s, photoelasticity
become popular. So, when photoelasticity become popular, they also felt you need larger and
larger field of view. So, that prompted people to look for alternatives. And this is what
you have to understand, most useful polarizers, which came in sheet form in large sizes, are
thin, light weight, they cost less compared to prism type polarizers and can be easily
rotated. This advantage, because when I want to analysis light, I want to rotate the polarizer,
if I have crystal, I need to have some kind of holding arrangement and do, it becomes
difficult, and they all have the characteristic call Dichroism. And what is Dichroism? A dichroic
material is one which absorbs light polarized in one direction more strongly than light
polarized at right angles to that direction. That is why I am taking up now, we have look
at crystal optics, in crystal optics we found for one incident ray, you have two refracted
beams, and these two refracted beams travel with different velocities in a crystal at
appropriate orientation, we have seen. But in a dichroic material, one of these rays
is absorbed, so that helps you. And we have seen that, these are light with different
planes of polarization, they are mutually perpendicular, they are plane polarized. And
that is what is depicted in the figure, it is a complex figure, you see the horizontal
component as it travels within the crystal it gets absorbed, the vertical component go
undiminished, whether I incident a natural light or polarized beam of light within the
crystal, you will have only polarized beam of light.
And what you fine in a dichroic material is, one of the vibration is completely absorbed
within the thickness. So, it allows only one light to pass through. So, I have this plane
polarized, horizontal component is fully absorbed, vertical vibrations partially absorbed. So,
I get linearly polarized transmitted light. That is a useful information, I have a dichroic
material, that is a useful information. You make a neat sketch of this. And for your benefit
I can show the animation again. So, what I have here is, the horizontal components
gets absorbed, the animation is not shown simultaneously for vertical and horizontal,
it is only emphasized for the horizontal, the horizontal component gets absorbed over
the thickness of the sheet. So, what you have here is, the most useful
polarizers employ Dichroism. And what is the meaning of Dichroism? A dichroic material
is one which absorbs light polarized in one direction more strongly than light polarized
at right angles to that direction. So, that is what you see here. This horizontal component
is absorbed, vertical component is allowed to pass through.
And we will continue our discussion further in the next class. And what we have seen today
was, we have looked at, for a crystal you have for a single incident beam of light you
have two refracted beams, they travel in the same direction, when the incident light is
perpendicular to the optics axis of the crystal. And these two ways travel in this same direction
but with the different velocities. Two simple harmonic motions with different phases, when
they interact, they give that trace of light as an ellipse. And by changing the retardation
delta, you get different forms of light ellipse. So, by looking at light ellipse, you can go
back and find out what delta that has caused. That is the main focus of this lecture.
And we also looked at, that in a crystal plate, what really happens when I impinge a plane
polarized beam of light. We are seen one light travels faster in one plane, we labeled that
plane as fast axis, we also labeled another axis, which is perpendicular to this as slow
axis. And I mentioned that these two are arbitrary classifications and you how to do some kind
of calibration to fix, this is the fast and slow axis, and we also indirectly saw this
fast and slow axes could be related to sigma one and sigma two directions.
And we are already seen your famous expression tan to theta equal to 2 power x by divided
by sigma x minus sigma y is ambiguous. So, if you ought to resolve that ambiguity, you
need auxiliary information, like more circle, or go for a Eigen value Eigen vector type
of recasting the mathematics to fix the direction. A similar exercise you may also have to do,
when you do an experiment. And finally, what we saw was, in order to
use light as a sensor, it is not good sending a natural light, I must have the complete
control on incident light. And one of the simplest incident light in photoelasticity
is the plane polarized light, and we saw how we get a plane polarized beam of light. The
sheet polarizers are essentially dichroic in nature, we will continued discussion further,
we will spend few more minutes on this dichroic sheet polarizers, then we move on to other
aspects of photoelasticity, we will also develop the stress optic law in the next class. Thank
you.