Physics - Basics of Optics for Allied students

Optics
Ms Dhivya R
Assistant Professor
Department of Physics
Sri Ramakrishna College of Arts and Science
Coimbatore - 641 006
Tamil Nadu, India
1

Overview
1. Light
2. Properties of Light
3. Reflection of light
4. Laws of Reflection
5. Refraction of light
6. Laws of Refraction
2

Light
What is a light?
3

Light
1. A Radiation (EM Radiation)
2. Particles – Photons
3. Exhibits Duality (both particle and wave nature)
4. Objects – Two Classification
• Luminous
• Non Luminous
5. Source
• Natural or
• Artificial
4

Properties of Light
1. Light Travels Extremely fast - ?
• C = 3 X 108 m/sec
5

Properties of Light
2. Light Travels in a Straight Line
• Since Light travels in Straight line Shadows are made
• Light Radiates in all directions from a luminous object
6

Properties of Light
3. Light Can travel as a wave
• Individual photons travels as waves
7

Reflection of Light
Reflection is the change in direction of a wavefront at an
interface between two different media so that the
wavefront returns into the medium from which it
originated.
8

Laws of Reflection
Angle of Incidence = Angle of Reflection
Incident ray, the reflected ray, and the normal to the surface
of the mirror all lie in the same plane.
9

Refraction of Light
In physics, refraction is the change in direction of a wave
passing from one medium to another or from a gradual
change in the medium.
https://www.youtube.com/watch?v=sBb5WUw2_2I
Refraction of light is the most commonly observed
phenomenon, but other waves such as sound waves and
water waves also experience refraction.
10

Laws of Refraction
Sine i = Sine r Known as ???
Incident ray, the reflected ray, and the normal to the surface
of the mirror all lie in the same plane.
11

Optics
Ms Dhivya R
Assistant Professor
Tamil Nadu, India
12

Recall
1. Light
2. Properties of Light
3. Reflection of light
4. Laws of Reflection
5. Refraction of light
6. Laws of Refraction
13

Overview
1. Refractive Index
2. Optical Path
3. Dispersion
4. Velocity of light
5. Visible Range
14

Refractive Index
Refraction +
Index
15

Refractive Index
Refractive Index
(n)
= c/v
16

Refractive Index
Definition:
The ratio of the velocity of
light in vacuum(c) to its
velocity in a specified
medium(v) i.e., n = c/v
17

Refractive Index
https://www.youtube.com/watch?v=ZQcK9un0JH0
18

Optical Path
The path that a light ray follows as it passes through an
optical medium or system is often called the optical path.
v = d/t
t=d/v
n=c/v
v=c/n
t=dn/c
19

Dispersion
Dispersion is the state of getting dispersed or spread
The separation of white light into colours or of any radiation
according to wavelength.
Dispersion is the phenomenon in which the phase velocity of
a wave depends on its frequency. Media having this
common property may be termed dispersive media.
Sometimes the term chromatic dispersion is used for
specificity
20

Dispersion
https://www.youtube.com/watch?v=ASEdGwpyn58&list=PLG
2_S6yzON5cJTG6_AlOErW-oR_E-uxsk&index=5
21

Velocity of Light
Velocity of Light ‘C’ – Speed of light in vacuum
m/s
C = 3 X 108 m/s
22


c

Electromagnetic Spectrum
23

Visible Range
24

Optics
Ms Dhivya R
Assistant Professor
Tamil Nadu, India
25

Recall
1. Refractive Index
2. Optical Path
3. Dispersion
4. Velocity of light
5. Visible Range
26

Overview
1. Photons
2. Dual Nature
3. Fermat’s Principal of Least time
4. Lenses
5. Thin and Thick Lenses
6. Behaviour of Thick Lens as its thickness Changes
27

Photons
1. The photon is a type of elementary
particle
2. Photons are mass-less, and they always
move at the speed of light in vacuum,
299792458 m/s
3. The photon is sometimes referred to as
a "quantum" of electromagnetic energy
4. Photons are units (packets of energy) of
an electromagnetic wave.
28

h
E 

Dual Nature
1. Wave Nature & Particle Nature
2. https://www.youtube.com/watch?v=Q_h4IoPJ
XZw
3. https://www.youtube.com/watch?v=_riIY-
v2Ym8
Further Reading
https://www.youtube.com/watch?time_continue=1
&v=I9Ab8BLW3kA&feature=emb_logo
https://www.youtube.com/watch?v=e5_V78SWGF0
https://www.youtube.com/watch?v=FlIrgE5T_g0
29

Fermat’s Principle of Least Time
Fermat's principle states that the path
taken by a ray between two given
points is the path that can be
traversed in the least time.
https://www.youtube.com/watch?v=bIt
ZbUxrgww
30

Lenses
Lenses
1. Types
• Concave
• Convex
• Plano concave
• Plano convex
• Concavo Convex
31

Terms Used
Focal Length: The focal length is the distance between the optical
centre and the focal point or focus of the lens
Radius of Curvature: The distance from the centre of curvature to
the circumference of the circle.
Focal Point: Focus is the point onto which collimated light parallel
to the axis is focused.
Centre of Curvature: A lens has two spherical surfaces, these two
spherical surfaces form a part of a sphere. The centre of
these spheres is known as the centre of curvature.
Aperture: The effective diameter of the circular outline of a
spherical lens is called the aperture of the lens
Optic Centre: The centre point of a lens is called the optical centre
of a lens. Optical centre is usually denoted by O.
Principal Axis: Principle axis is an imaginary line passing through
two centers of curvature is called the principal axis.
32

Terms Used
33

Terms Used
34

Thin Lens and Thick Lens
Thin Lens: A thin lens is a lens with a
thickness (distance along the optical axis
between the two surfaces of the lens)
that is negligible compared to the radii of
curvature of the lens surfaces.
Thick Lens: Lenses whose thickness is not
negligible are sometimes called
thick lenses.
35

Thick Lens Equation
R2 is positive the surface is concave, and
if R2 is negative the surface is convex
Lensmaker’s Equation
The lensmaker’s equation can be greatly
simplified if the lens thickness d is very
small compared to R1 and R2.
36
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Optics
Ms Dhivya R
Assistant Professor
Tamil Nadu, India
37

Unit 2 – Wave Optics
1. Electromagnetic Nature of Light
2. Wavefront and its properties
3. Huygen’s Principle
38

Electromagnetic Nature of Light
Waves
 Light Waves Exhibit ?
 Electromagnetic Waves with Transverse
Vibration
39

Wavefront
 A wave front is defined as a surface over which the phase
of the wave is constant. In a particular wave front, at a
given moment of time, all particles of the medium are
undergoing the same motion.
 There are 3 types of wavefronts:-
 Spherical wavefront(spherical in shape)
 Plane wavefront(linear in shape)
 Cylindrical wavefront(cylinder in shape)
40

Properties of Wave Front
 Wave front is defined as locus of all points having same
phase at a given instant of time.
 The shape of wavefront depends on the shape of the
source of disturbance.
 A wavefront is always normal to the light rays.
 A wavefront does not propagate in the backward
direction.
41

Spherical Wave Front
 When the source of light is a point source the wavefront
formed will be spherical wavefront.
 Point source means the source of light is so small that it is
considered as point. It can be considered as
dimensionless.
 For example: - Ripples in water are in the form of
concentric circles which are spherical wavefronts.
42

Plane Wave Front
 When the small part of a spherical or cylindrical wavefront
originates from a distant source like infinity then the
wavefront which is obtained is known as plane wavefront.
 For example: -Rays coming from infinity like Sun.
43

Cylindrical Wave Front
 When the source of disturbance is
a slit (i.e. line source) then the
wavefront is cylindrical because all
the points are equidistant from the
source and they lie on the surface
of the cylinder.
 For example: - In the figure we can
see when rays of light fall on a lens
after coming out of lens, they will
converge at a point.
 The waves are bending and
converging at a point so the shape
of the wavefront is in the form of
cylinder.
 Many concentric circles are formed
and the wavefront is in the form of
cylinder.
44

Huygens's Principle
“Every point on a wavefront is in itself the source of
spherical wavelets which spread out in the
forward direction at the speed of light. The
sum of these spherical wavelets forms the
wavefront”.
45

Huygens's Principle
Advantages and Disadvantages of Huygens Principle
Advantages:
 Huygens concept proved the reflection and refraction of light.
 The concepts like diffraction of light, as well as interference of light,
were proved by Huygens.
Disadvantage:
 Concepts like emission of light, absorption of light and polarization of
light were not explained by Huygens principle.
 Huygens principle failed to explain the photoelectric effect.
 A serious drawback is that the theory proposes an all-pervading
medium required to propagate light called luminiferous ether. This
was proved to be false in the 20th century.
46

Optics
Ms Dhivya R
Assistant Professor
Tamil Nadu, India
47

Unit 2 - Interference
1. Light Waves
2. Superposition of waves
3. Interference
4. Coherence
5. Techniques of obtaining interference - Division of
amplitude & Division of wavefront
48

Light Waves
Light Waves – Electromagnetic Waves
Light waves are different from mechanical waves, however,
because they can travel through a vacuum. Light
waves are just one type of electromagnetic wave. Other
electromagnetic waves include the microwaves in your
oven, radio waves, and X-rays.
49

Light Waves
Two Types of vibrations
 Longitudinal Vibration
 Transverse Vibration
50

Light Waves
Longitudinal Vibration
51

Light Waves
Transverse Vibration
52

Light Waves
 Light Waves Exhibit ?
 Electromagnetic Waves with Transverse
Vibration
53

Superposition of Waves
Superposition – Placing One Above the other i.e., Overlap
Principle of Superposition:
The superposition principle states that when two or more
waves overlap in space, the resultant disturbance is
equal to the algebraic sum of the individual
disturbances.
54

Superposition of Waves
55

Interference
Constructive & Destructive Interference
56

Coherence
Two or more wave maintain a constant
phase difference over a long distance and
time, then they are said to be coherent
https://www.youtube.com/watch?v=0aE02B
APlRk
Further Reference:
https://www.youtube.com/watch?time_con
tinue=28&v=RUc1I90w6lE&feature=emb_
logo
57

Coherence time
It is the average time during which the wave remains
sinusoidal and phase of the wave packet can be
predicted reliably
The coherence time is the time over which a propagating
wave (especially a laser or maser beam) may be
considered coherent, meaning that its phase is, on
average, predictable.
In long-distance transmission systems, the coherence time
may be reduced by propagation factors such
as dispersion, scattering, and diffraction.
58

Coherence Length
It is the length of the wave packet over which it may be
assumes to be sinusoidal and has predictable phase
Coherence length is the propagation distance over which
a coherent wave (e.g. an electromagnetic wave)
maintains a specified degree of coherence.
Wave interference is strong when the paths taken by all of
the interfering waves differ by less than the coherence
length.
A wave with a longer coherence length is closer to a perfect
sinusoidal wave.
59

Conditions for Interference
I. The Waves from the two sources must be of same frequence
II. The two light waves must be coherent
III. The path difference between the two overlapping waves must
be less than the coherence length of the waves.
IV. If two sets of waves are plane polarized, their planes of
polarisation must be the same
V. The two coherent sources must lie closer to each other in
order to discern the fringe pattern
VI. The distance of the screen from the two sources must be
large.
VII. The vector sum of the overlapping electric vectors should be
zero in the dark regions
60

Techniques for Obtaining
Interference
Wave front Splitting: Interference due to division of Wave
front.
A wavefront splitting interferometer divides a light wavefront
emerging from a point or a narrow slit (i.e. spatially
coherent light) and, after allowing the two parts of the
wavefront to travel through different paths, allows them
to recombine.
61

Techniques for Obtaining
Interference
Amplitude Splitting: Interference due to division of
Amplitude.
An amplitude splitting interferometer uses a partial reflector
to divide the amplitude of the incident wave into
separate beams which are separated and recombined.
62

Summary
https://www.youtube.com/watch?v=CAe3lkYNKt8
This Link has the summary of all that is learnt in today’s
session
63

Optics
Ms Dhivya R
Assistant Professor
Tamil Nadu, India
64

U3 – Diffraction - Overview
• Huygens – Fresnel Theory
• Fresnel’s Assumptions
65

Diffraction
• Diffraction refers to various phenomena that occur when a
wave encounters an obstacle or a slit. It is defined as the
bending of waves around the corners of an obstacle or
through an aperture into the region of geometrical
shadow of the obstacle/aperture.
66

Diffraction
67

Huygen’s Fresnel Theory
Each progressive wave produces a secondary wave, the
envelope of which is secondary wavefront
68

Fresnel’s Assumptions
Augustine Jean Fresnel in 1885, combines Huygen’s wavelets
with the principle of interference and explained Bending
of light.
69

Fresnel’s Assumptions
1. A Wave front can be divided into a large number of strips
called Zones (Fresnel’s Zones)
2. The effect at any particular point will depend on the
distance of the zone from the point
3. Effect will also depend on the obliquity of the point with
reference to the zone
70

Optics
Ms Dhivya R
Assistant Professor
Tamil Nadu, India
71

Recall
• Fraunhoffer diffraction
• Diffraction in single slit
72

Overview
• Diffraction in double slit
• Multiple slit and Diffraction grating
• Fresnel diffraction pattern of a straight edge
73

Fraunhoffer diffraction
• Diffraction at double slit
74

• Diffraction phenomenon due to two things
• Interference due to secondary waves from the corresponding
points at the two slits
• Diffraction due to the secondary waves from the two slits
individually
• Diffraction angle is denoted as Ѳ (angle between direction of
direct ray and the direction of secondary waves)
75

76

77
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78
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Plane diffraction grating
• Large number of narrow slits side by side
• Slits separated by opaque spaces
• Light transmitted through slit and blocked by opaque
regions
• So they are called Plane Transmission Grating
79

80

81

82
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• Number of Principal maxima = Number of wavelengths
• Angle of different wavelengths are different
• if there are two wavelengths
83
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84
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Summary
85

Optics
Ms Dhivya R
Assistant Professor
Tamil Nadu, India
86

U4 – Polarisation - Overview
• Polarised and un polarised light
• Natural light
• Types of polarisation
• Production of plane polarised light
• Brewster’s Law and its application
• Polarised and analyser
• Production and detection of linearly polarised light
• Malus’ Law
• Calcite crystal
• Huygens's Explanation of Double refraction
• Application of polarised light
87

Overview
• Polarised and un polarised light
• Natural light
• Types of polarisation
• Production of plane polarised light
• Brewster’s Law and its application
• Polarised and analyser
88

Polarization – Polarized and
unpolarized Light
• The action of restricting the vibrations of a transverse
wave, especially light, wholly or partially to one direction.
• The action of causing something to acquire polarity.
89

unpolarized Light
90

unpolarized Light
91

unpolarized Light
92

Types of Polarization
Depending on how the electric field is oriented, we classify
polarized light into three types of polarizations:
•Linear polarization
•Circular polarization
•Elliptical polarization
• Apart from these light may also be partially polarised
93

Linear polarization
Linear polarization:
The electric field of light is confined to a single plane
along the direction of propagation.
Picture
94

Circular polarization
Circular polarization:
The electric field of light consists of two linear
components that are perpendicular to each other, equal in
amplitude, but have a phase difference of π/2. The resulting
electric field rotates in a circle around the direction of
propagation and, depending on the rotation direction, is called
left- or right-hand circularly polarized light.
Picture
95

Elliptical polarization
Elliptical polarization:
The electric field of light describes an ellipse. This
results from the combination of two linear components with
differing amplitudes and/or a phase difference that is not π/2.
This is the most general description of polarized light, and
circular and linear polarized light can be viewed as special
cases of elliptically polarized light
Picture
96

Partial polarization
Partial polarization:
The electric field of light is neither confined to a
single plane nor unpolarised along the direction of
propagation are known partially polarised light.
97

Degree of polarization
Degree of polarization:
Percentage of polarization:
98
min
max
min
max
I
I
I
I
P



100
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min
max
min
max
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I
I
I
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P
of

Production of Plane Polarised
Light
Plane Polarised light may be produced from unpolarised light
by the following techniques
1. Reflection
2. Refraction
3. Scattering
4. Selective absorption (dichroism)
5. Double refraction
99

Polarization by reflection and
refraction
100

Brewster’s Law
101

Brewster’s Law
The tangent of the angle at which polarization is obtained by
reflection is numerically equal to the refractive index of the
medium.
This is known as Brewster’s Law
102
B

 tan


Applications of Brewster’s Law
1. To Determine the refractive indices of opaque materials
2. To calculate the polarizing angle, given with the refractive
index. (not applicable for metallic surcfaces)
3. In Laser Production
4. In transmitting a light through OFC without reflection
losses.
103

Brewster’s angle
104

Polarizer And Analyser
Polarizer:
Polarizers and analyzers are parts of optical instruments that
use plane polarized light.
A polarizer can filter light waves in order to generate
polarization of light.
In other words, a polarizer can generate plane polarized light
from light waves coming from a normal light source.
105

Polarizer And Analyser
Analyser:
The analyzer acts as a second polarizer. Polarizers and
analyzers are used in polarized light microscopy.
Although both polarizers and analyzers are used as light
filters, there are differences in their applications.
The main difference between polarizer and analyzer is
that polarizer produces plane polarized light whereas
analyzer can be used to check whether the light has been
polarized or not.
If an unpolarised light of intensity Io is passed through a
polariser, the intensity of the transmitted light becomes
Io/2
106

Production of Linearly Polarized
Light
107

Detection of Linearly Polarized
Light
108

Production and detection of
Polarized Light
https://www.youtube.com/watch?v=8YkfEft4p-w
109

Summary
110

 Fiber optics
 Basic principles
 Physical structure of optical fibre
 Propagation characteristics of optical fibre

 Guided media, which are those that provide
a conduit from one device to another, include
twisted-pair cable, coaxial cable, and fiber-
optic cable

 The most electronic communication was carried by copper
cables, whether twisted pairs, coaxial cables or copper
waveguides.
 Communication was accomplished by sending electrical
signals through the copper cables or waveguides.
 In recent years, a new medium has been introduced: Optical
fibers.
 In optical fiber communication, light signals replace electrical
signals.
 This branch of science is called fiber optics.

 The propagation of light can be analyzed in detail
using electromagnetic wave theory.
 Light falls in the general category of
electromagnetic waves, much like radio waves.
 The behaviour of light is sometimes easier to
explain by using ray tracings.
 The propagation of light in a fiber can be
described in terms of rays.

 When a light ray is incident on a reflecting
surface, the ray bounces back like a handball
when it hits a wall.
 A reflecting surface is one that is highly polished,
opaque and coated with special reflective
materials.
 The law of reflection states that the angle of
incidence is equal to the angle of reflection.
 The incident ray is the line AO, the reflected ray
is OB and ON is the normal to the reflecting
surface.
 The incident and reflected angles, 1 and 2,
respectively, are those between the rays and the
line perpendicular to the surface.

 The law of reflection states that the angle of incidence is
equal to the angle of reflection. the incident ray is the line
AO, the reflected ray is OB and ON is the normal to the
reflecting surface.
 The incident and reflected angles, 1 and 2, respectively,
are those between the rays and the line perpendicular to the
surface
1 = 2
 A direct result of this law is the fact that if 1 is 90, 2 is 90
and the reflected ray is in line with the incident ray

 When a ray travels across a boundary between two
materials with different refractive indices n1 and n2,
both refraction and reflection takes place. The case
where n1 > n2; that is where the light travels from
high to low refractive index materials.
 The refracted ray is “broken” that is, the angle 2
is not equal to 1. The relation between 1 and 2
is given by Snell’s law of refraction.
2
2
1
1 sin
sin 
 n
n 
1
2
2
1
sin
sin
n
n



(or)

 A ray travelling from a high to a
low index material will move away
from the perpendicular.
 The angle of incidence is smaller
than the angle of the refracted ray.
 The reverse holds for rays
travelling from low to high index
material. The relation between the
incident and refracted angles can
be stated in terms of the
propagation velocities in the
media
 Here, the two materials involved
are transparent and allow light
propagation.
2
1
2
1
sin
sin
v
v



1
1
n
c
v 
2
2
n
c
v 
Where &

 When 2, the angle of refraction becomes
90, the refracted beam is not traveling
through the n2 material. Applying Snell’s
law of refraction,
 The angle of incidence 1 for which 2 =
90 is called the critical angle c:
1
2
1
sin
n
n



 If the ray is incident on the boundary
between n1 and n2 materials at the critical
angle, the refracted ray will travel along
the boundary, never entering the n2
material.
 There are no refracted rays for the case
where 1 c.
 This condition is known as total internal
reflection, which can occur only when light
travels from higher refractive index
material to lower refractive index material.

Contd.
 The light can be restricted to the material
with the higher index of refraction if the
incident angle is kept above the critical
angle.
 A sandwich of high index material placed
between two slabs of low index material will
allow a beam of light to propagate in the high
index material with relatively little loss.
 This concept is used in constructing fibers
for fiber optic communication.

 An optical fiber is a transparent rod, usually made of glass or
clear plastic through which light can propagate.
 The light signals travel through the rod from the transmitter
to the receiver and can be easily detected at the receiving
end of the rod, provided the losses in the fiber are not
excessive.
 The structure of the modern fiber consists of an optical rod
core coated with a cladding.
 The core and the cladding have different refractive indices
and hence different optical properties.

Countd.
 The refractive index of the core is always greater
than that of the cladding (i.e.) n1 > n2.
 The light travels within the core by the principle of
total internal reflection.
 An unclad fiber and a clad rod through which the
light travels.
 With the unclad rod, only a small potion of the light
energy is kept inside; most of the light leaks to the
surroundings.
 The clad fiber is a much more efficient light carrier.

Countd.
 The losses of the light as it travels through the
fiber are much smaller for the clad fiber than
for the unclad one.
 The thickness of the core of a typical glass
fiber is nearly 50 μm and that of cladding is
100 – 200 μm.
 The overall thickness of an optical fiber is
nearly 125 – 200 μm.
 Thus an optical fiber is small in size and light
weight unlike a metallic cable.

 Light weight
 Small in size & flexible
 Non-Conductive, Non-Radiative & non –
Inductive
 High bandwidth & Low Losses
 No Short Circuit
 Withstand temperature & Moisture
 No need to ground, no voltage problems

 The light rays, during the journey inside the
optical fiber through the core, cross the core axis.
Such light rays are known as meridinal rays.
 The passage of such rays in a step index fiber is
Similarly, the rays which never cross the axis of
the core are known as the skew rays.
 Skew rays describe angular ‘helices’ as they
progress along the fiber.

Countd.
 They follow helical path around the axis of
fiber.
 A typical passage of skew rays in a graded
index fiber is shown in the following Fig.
 The skew rays will not utilize the full area of
the core and they travel farther than
meridinal rays and undergo higher
attenuation.

 Acceptance Angle :
The fiber core will propagate the
incident light rays only when it is incident
at an angle greater than the critical angle
c.

c
a
Acceptance
angle
Acceptance Cone
B
A
Lost by
radiation
Core
Cladding

 A meridinal ray A is to be incident at an angle a in
the core – cladding interface of the fiber.
 The ray enters the fiber core at an angle a to the
fiber axis.
 The ray gets refracted at the air – core interface
at angle c and enters into the core – cladding
interface for transmission.
 Therefore, any ray which is incident at an angle
greater than a will be transmitted into the core –
cladding interface at an angle less than c and
hence will not undergo total internal reflection.

Contd.
 The ray B entered at an angle greater than a
and eventually lost propagation by radiation.
 It is clear that the incident rays which are incident
on fiber core within conical half angle c will be
refracted into fiber core, propagate into the core
by total internal reflection.
 This angle a is called as acceptance angle,
defined as the maximum value of the angle of
incidence at the entrance end of the fiber, at
which the angle of incidence at the core –
cladding surface is equal to the critical angle of
the core medium.

Acceptance cone :
 The imaginary light cone with twice the
acceptance angle as the vertex angle, is
known as the acceptance cone.
Numerical Aperture (NA) :
 Numerical aperture (NA) of the fiber is the
light collecting efficiency of the fiber and is a
measure of the amount of light rays can be
accepted by the fiber.

A ray of light is launched into the fiber at an angle 1 is
less than the acceptance angle a for the fiber as shown.

 This ray enters from a medium namely air of
refractive index n0 to the fiber with a core of refractive
index n1 which is slightly greater than that of the
cladding n2 . Assume that the light is undergoing total
internal reflection within the core.
 Applying Snell’s law of refraction at A,
1
0
1
2
1
sin
sin
n
n
n




2
1
1 sin
sin 
 n

In the triangle ABC,
2
2


 
 

 

2
2
or




 cos
2
sin
sin 1
1
1 n
n 








 2
1
2
sin
1
cos 
 

 2
1
2
1
1 sin
1
sin 
 
 n
From the above two equations,
When the total internal reflection takes place, θ = θc
and θ1 = θa . Therefore,
 2
1
2
1 sin
1
sin c
a n 
 


Also, at B, applying the Snell’s law of refraction, we get
1
2
1
2
sin
(or)
90
sin
sin
n
n
n
n
c
c

 

 2
1
2
2
2
1
2
1
2
1
2
1 1
sin n
n
n
n
n
a 




















From the above equation, we get
This is called the numerical aperture (N.A). The numerical aperture is
also defined as the sine of the half of the acceptance angle .
c
a n
A
N 
 sin
sin
. 1



In terms of refractive indices n1 and n2, where n1 is the core index and n2
the cladding index
2
1
2
2
2
1 )
(
. n
n
A
N 

The half acceptance angle a is given by
)
.
(
sin 1
A
N
a



2
1
2
2
2
1
1
)
(
sin n
n 
 
2
1
2
2
2
1
2n
n
n 

 2
1
2
2
)
.
(
n
A
N

2
1
1 )
2
(
N.A 

 n
From the above eqns, we get

Two layers of glass are placed on top of each other. The light is
travelling from n = 1.45 to n = 1.40. Find the range of angles ,
for which total internal reflection takes place.
n1 = 1.45 and n2 = 1.40.
We know that
Substituting the values of n1 and n2
= 74.9
Thus, for the critical case x = 90 – 74.9 = 15.1, and for all angles
x less than 15.1, total internal reflection takes place.

A fiber has the following characteristics: n1
= 1.35 (core index) and  =2%. Find the
N.A and the acceptance angle.
n1 = 1.35 ;  = 2% = 0.02
W.K.T
= 1.35  (2  0.02)1/2 = 0.27
a = sin – 1 (N.A) = sin – 1 (0.27) = 15.66
2
1
1 )
2
(
. 

 n
A
N
Acceptance angle = 2a = 31.33

 A silica optical fiber has a core
refractive index of 1.50 and a cladding
refractive index of 1.47. Determine (i)
the critical angle at the core – cladding
interface, (ii) the N.A for the fiber and
(iii) the acceptance angle for the fiber.

n1 = 1.50 ; n2 = 1.47








 
1
2
1
sin
n
n
c

The critical angle

5
.
78
50
.
1
47
.
1
sin 1








=
2
1
2
2
2
1 )
(
. n
n
A
N 

The numerical aperture
30
.
0
)
47
.
1
50
.
1
( 2
1
2
2


The acceptance angle = 2a = 2 sin – 1 (N.A) = 2 sin – 1 (0.30) =
34.9
Critical angle = 78.5º ; N.A = 0.30 ; Acceptance angle =
34.9

Exercise (1) : Calculate the numerical aperture
and acceptance angle of fiber with a core index of
1.52 and a cladding index of 1.50.
= 0.246 and
a = sin – 1 (N.A) = 1414;
Acceptance angle = 2a = 2828
2
1
2
2
2
1 )
(
. n
n
A
N 


Exercise (2) : The relative refractive index difference
for an optical fiber is 0.05. If the entrance end of the
fiber is facing the air medium and refractive index of
core is 1.46, estimate the numerical aperture
46
.
0
N.A 

Introduction :
 In the early stages of development, fiber communication
promised extremely high data rates, which would allow large
masses of data to be transmitted quickly.
 It also had the potential for transmission over long distances
without the need to amplify and retransmit along the way.
 Recent developments have exceeded the hope of those
involved in the technology.

 The bandwidth of the fiber optic
communication system, which determines
the maximum data rate, depends on the
major components of the system.
 Fig. shows the block diagram of fiber optic
communication system.
 The information signal to be transmitted may
be voice, video or computer data.

 The first step is to convert the information into a
form compatible with the communications
medium.
 This is usually done by converting continuous
analog signals such as voice and video (TV)
signals into a series of digital pulses.
 An Analog – to – Digital (A/D) converter is used
for this purpose. Computer data is already in the
digital form.

 These digital pulses are then used to flash a
powerful light source (i.e.) off and on very rapidly.
 In a simple low – cost system that transmits over
short distances, the light source is usually a light
emitting diode (LED).
 This is a semiconductor device that puts out a low
– intensity red light beam. Other colours are also
used.

 Infrared beams like those used in TV remote
controls are also used in transmission.
 Another commonly used light source is the
solid state laser.
 This is also a semiconductor device that
generates an extremely intense single
frequency light beam.

 The light beam pulses are then fed into a
fiber – optic cable where they are transmitted
over long distances.
 At the receiving end, a light sensitive device
known as a photocell or light detector is used
to detect the light pulses.
 This photocell or photo detector converts the
light pulses into an electrical signal.
 The electrical pulses are amplified and
reshaped back into digital form.

 Both the light sources at the sending end and the
light detectors on the receiving end must be
capable of operating at the same data rate.
 The circuitry that drives the light source and the
circuitry that amplifies and processes the
detected light must both have suitable high-
frequency response.
 The fiber itself must not distort the high-speed
light pulses used in the data transmission.
 They are fed to a decoder, such as a Digital – to –
Analog converter (D/A), where the original voice
or video is recovered.

 In very long transmission systems, repeater units
must be used along the way.
 Since the light is greatly attenuated when it travels
over long distances, at some point it may be too weak
to be received reliably.
 To overcome this problem, special relay stations are
used to pick up light beam, convert it back into
electrical pulses that are amplified and then
retransmit the pulses on another beam.
 Several stages of repeaters may be needed over very
long distances.
 But despite the attenuation problem, the loss is less
than the loss that occurs with the electric cables.

 Transmission loss is low.
 Fiber is lighter and less bulky than equivalent copper cable.
 More information can be carried by each fiber than by equivalent copper
cables.
 There is complete electrical isolation between the sender and the receiver.
 There is no interference in the transmission of light from electrical
disturbances or electrical noise.
 The fiber itself can withstand environmental conditions such as salt,
pollution and radiation with no resulting corrosion and minimal nuclear
radiation effects, so it is more reliable.
 The transmission is more secure and private

 Optical fibers can be used as sensors for the
measurement mechanical force, pressure, electric
field, electric current, magnetic field, temperature,
nuclear radiations, density etc.
 In computers, fibers are used to exchange the
information between different terminals in a
network.
 The optical fibers are used in industrial
automation, security alarm system and process
control.

 The fiber optic cables are widely used in
electronic fields to produce required delay.
 It is possible to study interior of the lungs and
other parts of the body that can not be viewed
directly (endoscopy).
 The fiber optical system widely used in defence
services because high privacy is maintained.

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