Optics is the branch of physics that studies light, including its properties, production and propagation. There are three main branches: geometrical optics deals with laws of reflection and refraction, physical optics studies the nature of light, and quantum optics applies quantum theory to light. Optical instruments like microscopes use lenses, mirrors and prisms to observe objects. Optical fibers use total internal reflection to transmit light signals for communication. They have advantages over copper cables by being lighter, more flexible and having greater information carrying capacity.

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Module # 37
Optics, Optical Fiber & Total Internal Reflection
Optics
It is that branch of physics which is concerned with the study of
light, its production, propagation, measurement and properties. It
is divided into the following three types:
(1) Geometrical Optics
(2) Physical Optics
(3) Quantum Optics
Geometrical Optics
It is the branch of optics dealing with the laws of reflection, laws of
refraction, and their applications in optical instruments.
Physical Optics
It is the branch of optics dealing with nature of light.
Quantum Optics
It is the branch of optics which deals with the quantum theory of
light and of its relations to atoms and their electronic structure.

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Optical Instruments
Optical instruments are the devices used for observing finer
details of very tiny or distant objects or the objects which are out
of view of the observer. These are the combinations of lenses,
mirrors and prisms to see the desired objects that cannot be seen
with naked eye. For example, microscopes and refracting
telescopes are made by using the lenses of different focal
lengths. In reflecting telescopes, lenses and mirrors are used,
while, in periscope and binocular, prisms and lenses are used.
Optical Fiber
An instructing application of total internal reflection is in the
exciting field of fiber optics. Light can be trapped by total internal
reflection to travel along a curved path. A single very thin plastic
or glass fiber of about the thickness of a human hair (1/I00mm)
behaves the same way. The curvature of the light guide is very
small. This allows total internal reflection to take place
everywhere inside the fiber. In this way, light is made to bend. If
several thousands of these fibers are taped together, a flexible
light pipe is obtained that can be used by doctors and engineers
to light up some inaccessible spot for inspection or to photograph
the inside of a person.

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In an optical fiber, the light can travel with little loss because the
light is totally reflected whenever it strikes the core cladding
interface.
In developed countries, optical fibers are used to carry telephone
signals and other modern communication systems using laser
beams. A single strand of light carrying fiber can carry several
thousand telephone calls at the same time without interfering with
each other. Optical fibers are very light in weight, more flexible
and much cheaper than copper cables. A bundle of 30 fibers are
often used to form a cable. The information carrying capacity of
light is thousand times greater than that of electricity or radio
waves.
Clad
Fig: Internal reflections in an optical fiber
(OCR = Optical Character Recognition)

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Prism
A prism is a transparent refracting body which is bounded by
three rectangular and two triangular surfaces, as shown below
Fig: Prism
Angle of Prism
The angle between the two refracting rectangular surfaces
opposite to the base is called the angle of prism.
Periscope
It is an instrument used to see the object which is above the level
of eye or situated at place from where it cannot be seen directly.
A ray on passing through a totally reflecting prism undergoes a
change in direction of 90°. This property is used in periscopes as
reflectors. In a periscope, two totally reflecting prisms are used.
Light entering and leaving each prism undergoes total internal
reflection, but, no refraction because the angle of incidence is
zero. Light rays strike the hypotenuse side at an angle of 45°
which is greater than 42°, the critical angle of glass, and undergo
total internal reflection.

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Construction
It consists of a long tube fitted with two totally reflecting prisms.
Working
The rays of light from the object are reflected twice at angle 90°
and are received by the eye and the object is seen.
Uses
Periscope is used in tanks and submarines. The images of the
objects on the surface of water are seen through submarine with
the help of periscope. The soldier sitting in the tank sees the
image of the objects outside the tank.
Real Image
A real image is formed by the actual intersection of rays. Thus, an
image which can be obtained on a screen and is always inverted
is called a real image.
OR
The image formed is real when rays of light after reflection
actually pass through it and it can be obtained on the screen. This
image is always inverted. For real image q (distance of image
from the pole of the mirror) is always positive.

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Virtual or Imaginary Images
A virtual image is one formed by the apparent intersection of rays
when their directions have been produced backwards. Thus, an
image which cannot be projected on a screen and is always erect
is called a virtual image.
OR
If the image is formed behind the mirror and is always erect, then,
it is called a virtual image.
If a lighted candle is placed on one side of a concave lens and a
screen on the other side and the lens is slowly moved to obtain an
image on the screen, we will get no image on the screen. We will
observe that although a small erect image of the lighted candle
can be seen through the lens, it cannot be obtained on the
screen. Such an image is called a virtual image.
For virtual image q (distance of image from the pole of the mirror)
is always negative.
Magnification or Linear Magnification
The ratio of image size to the object size is known as
magnification. It is denoted by M. For an object of size ho, placed
at a distance p greater than focal length f, a real image of size hi
is formed at a distance q from the pole.

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Magnification is given by:
M = hi / ho = q / p
Magnifying Power or Angular Magnification
The apparent size of an object depends upon the angle
subtended by it at the eye. This angle is called the visual angle.
The greater is the visual angle; the large is the apparent size of
the object.
The smaller the distance of the object from the eye, the greater
will be the visual angle and consequently it will appear large.
Therefore, if we wish to see the fine (or minute) details of a small
object, then, we have to bring it as close to the eye as possible,
thus, increasing the visual angle and getting a large and real
image on the retina of the eye. But, there is a limit on how close
an object can be brought before an eye for obtaining a distinct
image. We know that if the object is placed at a distance of about
25cm from the eye, which is called the least distance of distinct
vision of a normal human eye, then, the image formed will be
clear and distinct. If the object is brought more close than 25 cm,
then, the image formed at retina will not be clear and will be
blurred. The ratio of the angle subtended (or formed) at the eye
by an object when it is viewed through a lens (or an eye-piece) to

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the angle formed by the object on an unaided (naked) eye, is
called the magnifying power or angular magnification thus,
Angle formed at the eye when viewed through an eye-piece
Magnifying Power = -------------------------------------------------------------------------------------
Angle formed at the naked (or unaided) eye
i
= -------
o
Rectilinear Propagation of Light (Path of Light)
When light coming from a source falls on an opaque object, a
shadow is formed behind it. This means that light travels in a
straight line.
Angle of Deviation
The angle through which the incident ray is refracted or deviated
is called angle of deviation.
On entering the prism, the ray of light bends towards the base of
the prism. This refracted ray, on coming out of the prism, again
bends towards the base of the prism, thus, an angle is formed
between the incident ray and emergent ray. This angle is known
as angle of deviation.

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Angle of Minimum Deviation
In case of refraction of light through a prism, the angle of
deviation changes with angle of incidence. When the angle of
incidence is increased from small to large enough value, the
angle of deviation first decreases, reaching a minimum value, and
then starts increasing. It may be verified experimentally that the
angle of deviation is least when the incident ray and the emergent
ray make equal angles with the normal i.e., when the refracted ray
is parallel with the base of the prism.
The minimum value of angle of deviation is called angle of
minimum deviation and is denoted by Dm. The refractive index n
of the material of prism can be determined as
Sin A + Dm
----------
2
n = -----------------------------------
Sin A/2
Where, A is the angle of prism.
Critical Angle
When light enters a rarer medium from a denser medium, the
angle of incidence for which the angle of refraction is 90° is called
critical angle. It is represented by C.

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Relation between Critical Angle and Refractive Index
If critical angle of a medium is 'c' then its refractive index is given
by
1
Refractive index (n) = ----------
Sin c
Mirage
It is an optical illusion which is normally seen in the deserts. The
image of distant trees is seen inverted. It appears that this image
is formed in a pool or lake of water.
It is so because in deserts, during day time, the sand becomes
hot due to sunlight. Thus, the air on the sand surface becomes
rarer as compared to the layers of air above it. As we go up, the
layers of air go on becoming denser. Hence, the different layers of
air are formed which have different densities. The rays of light
coming from the top of a tree are refracted many times during
passing through these layers of different densities. The angle of
incidence goes on increasing as the rays pass from layer to layer.
As a result, the angle of incidence becomes greater than the
critical angle. The rays then suffer total internal reflection and are
directed upward. When these rays enter the eye of a traveler, an
inverted image of the tree is seen and hot sand appears like a
lake of water.

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Regular Reflection of Light
When parallel rays of light strike a smooth and shining surface,
like a plane mirror, most of them are reflected in a particular
direction as shown in fig: below. Such a reflection is called regular
reflection or specular reflection of light. This phenomenon is used
in image formation by mirrors.
Because of this regular reflection, we can converge or diverge
light rays according to our need using spherical reflecting
surfaces.
Incident Rays Reflected Rays
Fig: Regular Reflection
Total Internal Reflection
When the value of angle of incidence becomes greater than the
critical angle, the ray of light no longer suffers refraction, but,
whole of it is reflected back in the same medium. Such type of
reflection is known as total internal reflection. Consider a beam of
light which travels from water (denser medium) to air (rarer
medium). It is observed that as the angle of incidence increases,
the angle of refraction also increases, till for a certain value of

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angle of incidence, the corresponding angle of refraction becomes
90° and the refracted ray runs along the surface separating two
media. The angle of incidence for which angle of refraction
becomes 90° is called critical angle. When the value of angle of
incidence becomes greater than the critical angle, there is no
refraction and the whole ray is internally reflected back in the
denser medium. Such reflection is called total internal reflection.
(iv) (v)
Fig: Total Internal Reflection
Here, the critical angle for light traveling from water to air is 48.8°.
It may thus be concluded that for all light rays with incident angle
greater than 48.8°, there is no refracted light, and, the light is
totally reflected back into the water.

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Conditions for Total Internal Reflection
There are two conditions necessary for total internal reflection.
(1) The ray of light should travel from denser to a rarer medium.
(2) The angle of incidence should be greater than the critical
angle.
Examples of Total Internal Reflection
Totally Reflecting Prism
A totally reflecting prism has one of its angles equal to 90° and
each of remaining two angles equal to 45°. Critical angle for glass
is 42°. If a ray of light falls normally on one of its faces, it moves
straight and meets the hypotenuse at 45°. It suffers total internal
reflection. The reflected ray strikes the other face perpendicularly
and comes out of the prism without any further change in
direction.
Binoculars and Projectors
Totally reflecting prisms are used in a combination with a series of
lenses in binoculars and projectors to change the inverted image
into an erect one.

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Rainbow
It is an arc of beautiful colors that appears across the sky during
or after rain fall.
Formation of Rainbow
After the rain, innumerable droplets of water remain suspended
high up in the air. When sunlight falls on these droplets, it gets
split up into spectral colors, as each drop acts like a prism. Each
ray of light entering the drop suffers refraction, dispersion and
total internal reflection.
The eye sees an arc with red color on the top and the violet
below. Sometimes, the light is further reflected before emerging
and this gives rise to a secondary rainbow seen above the first
rainbow.
Red color
Fig: Formation of Rainbow