Applied Optics

Professor Akhilesh Kumar Mishra

Department of Physics
Indian Institute of Technology, Roorkee
Lecture 01
Course Overview
Hello everyone, welcome to this course. I am Akhilesh Kumar Mishra, Assistant Professor in the
Department of Physics at IIT Roorkee. The title of this course is Applied Optics. Optics play a
very significant role in our life.

(Refer Slide Time: 00:44)

Even if you search the word optics in Google then you will see several results. Now, when I
searched, I found a few pictures which I am sharing with you. You see that there are pictures of
lenses and then the prisms are there, you can see you are launching a ray from left hand side and
then on the right hand side of the prism, you see different colors and the incoming ray is white
light and the prism is splitting this white light in its constituent colors.

The second picture is also of prism. Now, there are so many lenses you can see in this figure and
then there comes eye, the diagram of our eyes and because we know we see things through our
eyes and therefore, this is the major sensory organ which we have and we see the world through
our eyes. And then therefore, light has a very deep relationship with our eyes, it gives us the
perception of darkness, brightness, the colors of the light. Now, in this figure, you also see that
different colors are appearing here, here in lenses.
(Refer Slide Time: 02:20)

Now, whenever we say the word optics the things which comes in our mind is color, the first thing
which appear in our mind is colors. Therefore, we can relate optics to colors, which we see in our
daily life. Here we see colors in rainbow, we see color in soap bubbles, we see color in our daily
life. Now, apart from colors, if we move deeper, if we go in follow some academic route and then
from, if we go in our junior classes, then in science course, we all are introduced to reflection and
refractions, this is our first interaction with the formal interaction with the optics here.

And apart from reflection and refraction, the optics also comes in play when we talk about lenses,
or specs, the glasses which we wear this also has to do with the optics. Now, what are lenses?
Lenses are glass substance and which has particular shape.
(Refer Slide Time: 03:23)
Now, you see here I have brought a lens which is called convex lens and this convex lens is made
up of glass and which has curved surface. Both surfaces, the left and right surfaces, they both are
curved like this. The surfaces are bulging out. Therefore, it gives a different type of image. Had it
been a plain glass plate, you would have seen me as it is. You would have not seen any modification
in my image. But if you see through this convex lens, then you can see that my eyes look a bit
bigger. I hope that you must be seeing my eyes through this convex lens.

(Refer Slide Time: 04:16)

Similarly, instead of having this convex surfaces, if we make a lens which have this type of surface
which is concave surface, then the lens is called concave lens. In this case, the surfaces are pressed
in the middle and this is a concave lens. Now if you look in my eyes through this lens, then my
eyes will look a bit smaller, although it depends upon the position of the object with respect to the
lens or the position of the observer with respect to the lens which defines the original shape and
size of the image.

But if I put it here, then you can see that my eyes through this lens which is convex lens, it looks
bigger while with this lens it looks smaller, this one is called concave lens and this one is called
convex lens and these lenses are used in our specs.
(Refer Slide Time: 05:21)

Now, apart from these lenses, you have also seen the picture of a prism and this is prism. Now,
you see that it is a three-dimensional triangle, you draw a triangle on a paper and then stretch it
out then it will form a prism. And you see that this surface of the prism is not transparent and this
is called base of the prism. We put prism like this, and then if you launch a white light on this
interface, then from this face, we will see different colors of light coming out of, now here you
launch white light and here you will see range of colors coming out of this face.

(Refer Slide Time: 06:15)

Now, you must have seen Mirage also in deserts, we see Mirages, it is also an optical phenomena
and therefore, wherever we see it, we can relate it with optics. Now, in our junior classes, we also
study blueness or redness of a sky, this is also explained through optics. These are the phenomena
which we observe in our daily life and then understand optics, we can understand optics through
these phenomena.

Colored soap bubbles, we have already talked about, there is a phenomena called interference,
which we will devote few lectures on and due to this interference this thin films look color and
bubble is made up of thin film and it give different colors, you see different colors floating on the
surface of the bubble. This is due to the interference.

Now, a parameter which plays a major role in all this phenomena is called refractive index. We
will talk about refractive index also in greater detail in this course, but this is through this word or
through this phenomena we can perceive what optics is. Now, we will go much deeper with the
progress after course and try to understand different phenomena in a greater detail. Now, I have
shown you the pictures of this convex lens and concave lens.

(Refer Slide Time: 08:07)

In your junior classes, you must have seen that when we draw a convex lens, this is called convex
lens then this is the axis of the lens we draw and then when we launch a parallel beam of light from
the left hand side then what does this lens do is that it focuses all these rays on a certain point.
You can see that it is converging all these rays which falls on this lens and this the distance of this
point from the lens is called focal length and this point is called focal point of the lens. When you
launch a parallel beam of light or when you launch parallel rays on a lens then it converges them
to a point.

Here what you are seeing is that there is a convex lens or a converging lens which is converging
the rays to a focal point, similarly if you draw a concave lens and then launch a parallel beam of
light then what will happen is that this lens will diverse these rays and you can say if this is the
axis of the lens, then it will diverge in such a way that these rays after refraction, it seems that they
are coming from a point.

You will see that these rays are diversed rays, but if you extend them back then they meet here at
point F on the axis this is again called focal point and this distance is called focal length. Therefore,
the first lens which is convex lens is called converging lens and this concave lens is also called
diverging lens. Now, how to explain why does this lens converges or diverges?

Now, to understand this what people do is that they split lens in smaller prisms, the dashed lines
they are splitting the lens into smaller prisms. Now, suppose a ray is launched in this direction.
Now, this is a prism what will it do? It will bend the light towards its base because we know that
a prism, what does it do is that, when we launch light then it refract and this dashed line is
perpendicular to the point of incidence.

Now, this after refraction the ray within the prism falls on the second interface here we draw a
perpendicular and then again exercise Snell's law and then this is how the refracted ray look like
and this ray which is coming out of the prism, it is bend towards the base of the prism and similar
things happen here in the lens in this first, in this first prism the ray falls and then it get bent.

Similarly, the second ray it falls under second prism and it also get bent and this is how all the ray
get focused on same point and this is why this convex lens is also called converging lens. In case
of convex lens, in case of concave lens, the prisms are inverted their base is on top and the vertex
is downward and therefore, the bending is up in upward direction and therefore, the rays get
diverged.
Now, these explanations they fall in the category of ray optics, why? Because we only talk about
rays. And how do we represent a ray? We draw a line with an arrow, the direction of arrow tells
about the propagation direction and this line is called a ray, while defining a ray, we neglect the
finiteness of wavelength. Here, we have assumed that wavelength is almost equal to 0.

And this can be assumed in cases where all the optical instruments are very large as compared to
wavelength and we know the lenses like these, they are very big as compared to the optical
wavelength, optical wavelength varies from 400 to around 750 nanometer and as compared to
those wavelengths, these lenses, the dimension of these lenses are very huge.

Therefore, we can safely neglect the finiteness of wavelength. We can assume that wavelength is
almost equal to 0 and there we can define ray, there we can explain things through the concept of
rays. And the phenomenon of optics which can be defined through ray diagram through ray tracing
it falls in the category of ray optics. But there are certain phenomena which cannot be defined or
which cannot be explained through ray optics.

And therefore, people researched more and they came up with wave theory or wave optics. What
is wave optics? Now, in wave optics, what people do is that instead of drawing this straight line,
they consider waves for representing this light and these waves they oscillate with certain
frequency and they propagate in certain direction. Now, how to explain this convergence and
divergence in convex and concave lens using wave theory, here is the explanation let us again
draw this convex lens and this is the lens axis.

Now, instead of drawing rays, we will draw wave front or phase front. Wavefronts are locus of
points which oscillate in same phase. Now, suppose you have a point source and from this point
source the wave is coming out in all the directions. There what we will see is that since the point
source is having spherical symmetry therefore, it will emit spherical wavefront, why? Because on
the sphere the all points are oscillating in the same phase and therefore, it will form a spherical
wavefront.

Similarly line source, it will emit a cylindrical wavefront. Extended source extended plane source
will extend a plane wavefront. I repeat, wavefront is locus of points which oscillate in same phase.
Now, suppose we launch a plane wave on a convex lens. Usually plane waves are drawn, usually
plane waves are represented by these planes and they propagate in this direction.
Now, here since our paper is in two-dimension, therefore, let us represent these planes with a
straight line, if you take a cross section of a plane you will get a straight line and let us assume that
this is plane wavefront which is falling on the convex lens. Now, these wavefronts will come and
the center portion of this wavefront will see the lens surface first because there is a curvature on
the lens surface, the central portion is bulging out.

Therefore, the plane wavefront which is approaching towards the lens it will see the central portion
of the lens first, and then it will the central portion of the wavefront will start traveling within the
lens medium. While the extremities, the extremities of the wavefront will see the medium of the
lens a bit later. In addition, the central portion of the lens is thicker as compared to the extremities.

And this is why the central portion of the wavefront will see more lens material as compared to
the wings or edges of the wavefront and we know that the lens is kept in air and lens is made up
of glass which has a refractive index which is larger than that of the air. You know that refractive
index n is defined by c by v, where c is the speed of light in vacuum while v is the speed of light
in the medium.

Now, you know that n for the glass is larger than that of air, therefore, the velocity of the wavefront
within the lens would be smaller. Since central part of the wavefront is staying for longer duration
within the lens, therefore, it would be delayed as compared to the extremity of the wavefront. And
therefore, this the central part this part it would be delayed and this part will be ahead in time.

Central part is staying longer in the lens because lens, the thickness of the lens is larger while at
the tip of the lenses, the thickness of the lens is smaller and therefore, the part of the wavefront
which is going through the tip of the or the thinner portion of the lens. It will stay for a shorter
duration within the lens medium.

And therefore, although it would be delayed, but the relative delay between the central portion of
the wavefront and the edge of the wavefront, the upper and lower portion of the wavefront the
relative delay would be different. The central portion would be delayed more and therefore, at the
output the wavefront will look like this, something like this.

You see here that there is a difference here, this difference is because of the thickness of the lens,
the varying thickness of the lens instead I should say. And at the center the lens is thicker, therefore,
the central portion got delayed more, at the extremities the lens is a bit thinner therefore, the delay
is less at the extremity of the wavefront at the top and bottom portion of the wavefront are less
delayed as compared to the central portion.

And this is why we see this type of curvature at the output in the wavefront. Due to this curvature
the wavefront propagates and get focused here and this is the same distance as was observed in the
ray theory description here in the left most figure and this point is called your focal point. Now,
this explanation falls in the domain of wave theory.

(Refer Slide Time: 21:57)

Now, coming to the content of this course the content is divided in two parts. The first part is
geometrical optics and the second is wave optics. And now I hope that you understand why this
differentiation is because in geometrical optics, we apply ray theory and in wave optics, we apply
wave theory which is well explained in the previous slide.

The part, I again repeat, of optics which can easily be explained using ray theory, it falls in the
category of geometrical optics, while the part of the optics, which can be explained through wave
theory, it falls in the category of wave optics. Therefore, the optics can majorly be defined in these
two parts geometrical optics and the wave optics. And the course is also divided in these two
categories all the content of the course.
Therefore, the first part of the course falls in the category of geometrical optics while the second
part in wave optics. But apart from these two categories, there exists a third one, which is called
quantum optics. In quantum optics we quantize the light. To understand the differences, let us
suppose that we have a candle.

Now, if you want to understand the emission of light in this through this candle then there are
several ways the first way or the first method is this ray, geometrical optics and in geometrical
optics if you want to understand the emission of light from the candle then just draw these rays
then in geometrical optics the emission of light from the candle can be understood through these
ray picture.

There is a candle and the candle is emitting light rays and this such a description falls again in the
category of geometrical optics. And while in the wave optics we know that a wave is nothing but
a disturbance and if we hold a rope and start waving our hand up and down, then it will create a
sinusoidal like pattern and this is the typical representation for a wave. A sinusoidal pattern is a
typical representation of a wave but generally any disturbance can be defined like a wave.

And if you want to understand the same phenomena of light emission in the wave optics then again
let us draw this candle and then here we say that the waves are emitting it is a rough description
although, still okay. The emission here is explained through this wave picture which is nothing but
a wavy line.

But what about quantum optics as I said in quantum optics we discretize the light, it means the
light wave is no more continuous you cannot draw a continuous line be it a straight or wavy.
Therefore, in this description we can draw this broken line, it represents it symbolizes quantization
or discreteness. But the course Applied Optics it covers only geometrical optics and wave optics,
we will not discuss quantum optics in this course.
(Refer Slide Time: 26:19)

Now, with this let us go to the course content as I said before the course is divided in two parts
geometrical optics and wave optics and in total there are 12 modules. This is a 12 weeks long
course and therefore, there are 12 modules. In geometrical optics, we have 2 module while in wave
optics, we have 10 modules.

In the first module, I will introduce you to the geometrical optics and the ray theory, then Fermat’s
principle will be introduced and using this Fermat’s principle we will try to understand the
phenomena of refraction, reflection, total internal reflection we will derive Snell's law using
Fermat’s principal and using this principle we will try to understand refraction from single and
double interfaces.

We will take curve interfaces and on this curve interfaces we will launch rays and we will try to
understand its refraction. Now, in module two, we will talk about matrix method in paraxial optics.
Then, we will derive the lens formula for thick and thin lenses we will also derive the expression
for the focal length for both thick and thin lenses.

And thereafter, principle planes would be introduced wherein we will talk about unit planes and
nodal planes and at last we will study system of thin lenses wherein we will put instead of one we
will analyze two lenses when they are placed together with a certain separation between them. And
in this topic, we will also derive a focal length for this combination of the lens system.
After this we will move to the wave optics part, wherein first of all we will be introduced to the
concept of wavefront then we will talk about Huygens principle and its application which would
be followed by superposition principle and introduction to the polarization. And in polarization we
will talk about linearly polarized light, circularly polarized light and elliptically polarized light. In
module four interference would be introduced, wherein we will talk about the famous historical
Young's double slit experiment.

And in Young's double slit experiment, we will also learn the role of polarized light, what role
polarization plays, how would it affect the fringes or fringe formation, fringe visibility, this all
would be discussed in module four. Apart from this, we will also learn interference with the white
light. We will see that if in Young's double slit experiment, what will happen if we cover one of
the slits with thin transparent film.

And then, we will also talk about Fresnel’s biprism experiment. In module five, we will continue
with interference but here we will talk about interference by division of amplitude here because in
module four whatever interference was studied it falls in the category of division of wavefront here
we will talk about division of amplitude wherein we will talk about thin parallel films, wedge
shaped films, Newton's ring and famous Michelson interferometer and its application.

(Refer Slide Time: 30:25)

We will continue with interference in module six as well, and in module six, we will see
interference with multiple beam that will be followed by Fabry-Perot interferometer and etalon
and then the concept of coherence would be introduced which is a very important part. With
module six, we will finish the interference and module seven will start diffraction. In module
seven, you will be introduced to diffraction and we know that diffraction is of two kinds the first
is called Fraunhofer diffraction second is called Fresnel diffraction.

In module seven, we would be focused with Fraunhofer diffraction, wherein we will talk about
single double and multiple slit diffraction pattern. In module eight, we will talk diffraction at a
rectangular and circular aperture, then diffraction grating which would be followed by grating
spectrum and resolving power. And at the end, we will be introduced with Fresnel diffraction.

In module nine, you will continue with a Fresnel diffraction and here we will learn Fresnel half,
learn about Fresnel half period zones, vibration curve, diffraction through circular obstacle, then
the concept of zone plates would be introduced, then diffraction through rectangular aperture
would be talked about, then diffraction of a plane wave by long narrow slit and transmission to the
Fraunhofer region, then diffraction at the straight edge, diffraction by a narrow obstacle and at last
Babinet’s principle.

In module 10, we will be introduced with Brewster’s law, Malus law, phenomenon of double
refraction, normal and oblique incidence and production of polarized light. In this module, you can
see that, that this phenomena of double refraction is something which is very new, which you must
have not heard up till your intermediate classes. And in module 11, quarter and half wave plates
will be introduced.

And then using these wave plates, we will learn how to analyze a polarized light if a light is given
to us, then how to know what is the state of polarization of this light, this would be covered in
module 11. Then we will talk about optical activity and then a theoretical foundation would be
introduced for wave propagation in anisotropic media. The mediums can be categorized in two
categories, one is called isotropic media and another is called anisotropic media.

In anisotropic medium, optical properties are direction dependent, while in isotropic medium
optical properties are direction independent. In the last module, we will talk about the applications
of what we studied till module 11. The first application is antireflecting coating that would be
followed by holography.
Then we will be introduced with the basic concepts and ray optics consideration of optical fibers.
And at last you all would be introduced to lasers. This is the whole syllabus, 12 week long syllabus
of this course on Applied Optics.

(Refer Slide Time: 34:24)

As a reference book, I would be majorly following optics by E. Hecht and A. R. Ganesan and
optics by A. K. Ghatak, off and on, I would also be resorting on fundamentals of optics by F. A.
Jenkins and H. E. White. I hope that this course would introduce you to the basic concepts of
optics, it will not only give you the exposure to the ray optics, which is geometrical optics, but it
will also go deep into the wave optics.

And then there in the wave optics, you will learn about the very important phenomena of
interference, diffraction, then you will be introduced with polarization, birefringence, optical
activity, and there so many applications. And these applications are important not only to the
scientists, but also for the engineers.

In addition to these a very new concept of holography will also be introduced to you in this course
and at last we will also cover lasers. With this introduction, I end my today's lecture, hope to see
you in the next class, thank you for joining me.