Department of Physics
Ghazi University DG Khan
Subject Name:
Optics
Subject Code:
PHY – 508
Semester/ Section:
6th (Morning)
Session:
2021-2025
Credit Hours:
3 (3-0)
Notes Title:
Mid Term Notes Spring 2024
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
Table of Contents
CHAPTER 1: INTRODUCTION TO OPTICS
4
1.1 HISTORICAL OVERVIEW
1.2 OPTICS IN PHYSICS
OPTICS:
BRANCHES OF OPTICS:
I. PHYSICAL OPTICS:
CLASSIFICATION:
II. GEOMETRICAL OPTICS:
1.3 LAWS OF GEOMETRICAL OPTICS
REFRACTIVE INDEX (N):
TYPES OF REFLECTION:
A) REGULAR REFLECTION:
B) IRREGULAR REFLECTION:
LENSES:
I. CONVEX LENS:
II. CONCAVE LENS:
TERMS RELATED TO LENSES & MIRRORS:
I. CENTER OF CURVATURE:
II. PRINCIPAL AXIS:
III. OPTICAL CENTER C:
IV. PRINCIPAL FOCUS:
MIRRORS:
1) PLANE MIRROR:
2) SPHERICAL MIRROR:
STOPS:
I. APERTURE STOP:
II. FIELD STOP:
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4
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4
5
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5
5
6
7
7
7
7
7
8
9
9
9
9
10
10
10
10
11
11
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1.4 ABERRATIONS (‫)دھندال پن‬
A. CHROMATIC ABERRATIONS:
B. SPHERICAL ABERRATIONS:
1.5 COMA
1.6 ASTIGMATISM
1.7 TOTAL INTERNAL REFLECTION
1.8 OPTICAL FIBER
CONSTRUCTION OF OPTICAL FIBER:
FIBER MATERIAL AND MANUFACTURING:
KINDS OF OPTICAL FIBER:
A) MONO-MODE OPTICAL FIBER:
B) MULTI-MODE OPTICAL FIBER:
ADVANTAGES OF OPTICAL FIBER:
DISADVANTAGES OF OPTICAL FIBER:
USES OF OPTICAL FIBER:
11
12
13
14
15
15
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17
18
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20
20
CHAPTER 2: WAVEFRONT SPLITTING INTERFEROMETER
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OPTICS (PHYS-508)
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5.0 BASICS
WAVEFRONT:
HUYGEN’S PRINCIPLE:
5.1 THE YOUNG’S DS EXPERIMENT
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OPTICS (PHYS-508)
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Mid Term Notes Spring 2024
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BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
CHAPTER 1: INTRODUCTION TO OPTICS
1.1 Historical Overview
Nature of Light:
17th Century
❖ In 17th century, two theories were introduced.
❖ First is the corpuscular (particle) nature of light by Isaac Newton.
❖ He gave laws of reflection and refraction.
❖ Second is the wave nature of light by Huygens.
19th Century
❖ Two important incidents were made in 19th century.
❖ In 1802, Thomas Youngs performed experiment of interference of light which proved that light has
wave nature.
❖ In 1865, Maxwell performed experiment. Electromagnetism is based upon Maxwell’s equations.
❖ In this era, speed of light was calculated experimentally as c = 3 x 108 m/s.
❖ Maxwell noticed that the speed of light waves is equal to the speed of light, so he called light waves
as electromagnetic waves (EM waves).
20th Century
❖ Max Planck and Einstein performed experiments.
❖ In 1901, Max Planck gave the concept of Quanta (smallest unit of Energy) which means energy of
light is quantized.
❖ In 1905, Einstein proposed that energy of light is in discrete packets called as photons (known as
photon theory) which is based upon Photoelectric effect and Compton effect.
❖ Photoelectric and Compton effects both, show particle (corpuscular) nature of light.
❖ In conclusion, Light has dual nature (both wave and particle).
1.2 Optics in Physics
Optics:
The study of behavior (interaction) and properties of light is called as Optics.
It also includes the study of eye itself because human eye forms an image with a lens. It is also
concerned with light production and its phenomenon like reflection, refraction, diffraction and dispersion etc.
along with properties.
Branches of Optics:
There are two branches of Optics.
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OPTICS (PHYS-508)
BS Physics 6th Semester
i.
Physical Optics
ii.
Geometrical Optics
i.
Physical Optics:
Section: Morning
Mid Term Notes Spring 2024
It covers the wave or particle nature of light. It is based on the nature of light. Interference,
diffraction, polarization, Maxwell’s equation etc. indicates that light is an EM wave.
Classification:
It has three types.
i.
Geometrical Optics: Rectilinear Propagation, Refraction, Reflection of light.
ii.
Wave Optics: Interference, Differential polarization, Dispersion of light.
iii.
Quantum Mechanics: Orbits, Energy levels, Lasers, Holography, Spectrum.
ii.
Geometrical Optics:
The branch of optics which deals with the formation of images is called as geometrical optics. It is
based on the relationship between angles and lenses that is described by the light rays. With the
help of few rules of geometry, we can explain the formation of images by devices like lenses,
mirrors, cameras, telescopes, and mirror telescope. The study of reflection and refraction of rays
of light without reference to the physical nature or wave nature of light. It deals with the ray
treatment of light.
It is related to the study of optical phenomenon without taking into account nature of light. It
is used to design, manufacture materials for optical devices.
1.3 Laws of Geometrical Optics
The laws explained on the basis of geometrical optics are called laws of geometrical optics.
These laws are;
1. Law of rectilinear propagation
2. Law of reflection
3. Law of refraction
1. Law of Rectilinear Propagation:
In a homogenous medium, light travels along straight paths.
i.
ii.
iii.
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Remember!
A medium whose all parts exactly alike (same) is called as homogenous medium. i.e., glass.
A medium whose all parts exactly not alike (same) is called as heterogenous medium. i.e., a
mixture of mud and stones.
A straight line showing the path of light in a medium is called as ray.
OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
2. Law of Reflection:
Bouncing back of light in the same medium is known
as reflection of light.
It has two postulates.
i.
The incident ray, the normal and reflected ray,
at the point of incidence, all lie in the same
plane.
ii.
The angle of incidence = The angle of
Reflection.
Reflection occurs due to repulsive nature of the medium.
3. Law of Refraction:
When a ray of light moves from one medium to another medium, it deviates from the actual path. The
bending of light due to change of medium is called as refraction of light.
Refraction occurs due to attractive nature of the medium.
It has two postulates.
i.
The incident ray, the normal and refracted ray, at
the point of incidence, all lie in the same plane.
ii.
The ratio of sine of angle of incidence and
Remember!
A beam is a stream of light energy and
is represented by a number of rays
which is either diverging, converging or
parallel.
refraction is always equal to a constant as given
below,
𝑺𝒊𝒏 𝒊
= 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕
𝑺𝒊𝒏 𝒓
𝑺𝒊𝒏 𝒊
Where 𝑺𝒊𝒏 𝒓 is known as refractive index (n) of 2nd medium w.r.t to the 1st medium.
𝑺𝒊𝒏 𝒊
𝒏𝟐
=𝒏=
𝑺𝒊𝒏 𝒓
𝒏𝟏
It is also called as Snell’s Law.
Refractive Index (n):
It is the ratio of speed of light in a vacuum to the speed of light in a medium.
𝑹𝒆𝒇𝒓𝒂𝒄𝒕𝒊𝒗𝒆 𝑰𝒏𝒅𝒆𝒙 =
𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝒍𝒊𝒈𝒉𝒕 𝒊𝒏 𝑽𝒂𝒄𝒖𝒖𝒎 𝒄
=
𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝒍𝒊𝒈𝒉𝒕 𝒊𝒏 𝑴𝒆𝒅𝒊𝒖𝒎 𝒗
For Example,
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Material
Refractive index of the material (n)
Air
1
Glass
1.5
OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Water
Mid Term Notes Spring 2024
1.33
Types of Reflection:
a) Regular Reflection:
The reflection of light in one only one direction is called
as regular reflection. In a regular reflection ∠𝒊 = ∠𝒓. The
smooth surface reflects the rays of light in one direction.
It is shown in the above diagram.
b) Irregular Reflection:
The reflection of light in many directions is called
irregular refraction as shown in the below diagram. A
rough surface reflects the light rays in many directions.
This type is important in our life due to brightness appear
in the rooms, cavities, or shadow places.
In geometrical optics we use ray approximation of light to describe phenomenon reflection,
refraction, diffraction and interference etc. A ray is a geometrical representation of light.
Lenses:
Lens is a refracting device, that reconfigure a transmitted energy distribution. It is a transparent material in
which one surface is curved. Lens are used in phenomena of refraction.
There are two types of lenses.
i.
Convex Lens (Converging Lens)
ii.
Concave Lens (Diverging Lens)
i.
Convex Lens:
➢ It is a reflecting material; light passes through it. It is used for objects which are nearby.
➢ These lenses are thicker at midpoints and thinner at edges.
➢ These lenses made waves to converge to central axis (by bending at second interference)
and are called as converging lens.
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OPTICS (PHYS-508)
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Section: Morning
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➢ It is used in telescopes, eye lens, magnifying glasses.
➢ For hyper phobia (far-sightedness), convex lens is used.
➢ The lens which causes incident parallel rays to converge at a point is known as convex lens
or converging lens.
➢ The nature of focal length is positive for convex lens.
➢ There are three kinds of convex lens.
ii.
i.
Double Convex lens (diagram a)
ii.
Plano Convex lens (diagram b)
iii.
Concavo-Convex lens (diagram c)
Concave Lens:
➢ These lenses are thinner at midpoint and thicker at
edge.
➢ These lenses made waves to diverge from central axis
(by bending at second interference) so called
diverging lenses. It is used in binoculars, eyeglasses, telescopes and flash light etc.
➢ The lens which causes the incident parallel rays of light to diverge from a point is called
concave or diverging lens.
➢ Concave lens is thinner at the center and thicker at the
edges.
➢ For myopia (nearsightedness), concave lenses are used.
➢ The nature of focal length is negative for convex lens.
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OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
➢ There are three types of concave lens.
i.
Double concave lens (diagram d)
ii.
Plano concave lens (diagram e)
iii.
Convex concave lens (diagram f)
Terms Related to Lenses & Mirrors:
I.
Center of Curvature:
It is the center of the sphere of which the mirror forms the part. It is represented by C.
II.
Principal Axis:
➢ The line passing through the center of lens is called principal axis or The straight line joining
the pole (P) and the center of curvature.
➢ It is normal for the mirror at its pole.
➢ Each of two surfaces of spherical lens is a section of a sphere.
➢ The line passing through the two centers of curvature of the lens is called the principal axis.
➢ The middle point of the spherical mirror is called as pole denoted by P.
III.
Optical Center C:
A point on the principal axis t the center of lens is called as optical center, denoted by C as given.
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OPTICS (PHYS-508)
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IV.
Section: Morning
Mid Term Notes Spring 2024
Principal Focus:
For Convex Lens; The light rays traveling parallel to the principal axis of a convex lens after refraction
meet at a point on the principle axis is called principle focus or focal point F.
For Concave Lens: The parallel rays appear to come from a point behind the lens called principle
focus F.
Focal Length (f): The distance between optical center and principal focus is called focal length.
Mirrors:
It is a piece of glass whose one side is highly polished surface which reflects 80 to 90% of light. It has
two kinds: plane and spherical mirrors.
1) Plane Mirror:
A mirror whose surface is flat is called as plane mirror.
2) Spherical Mirror:
A mirror whose polished reflecting surface is part of hollow surface is called spherical mirror. One
side of spherical mirror is opaque and other is polished reflecting surface (Spherical mirror uses
reflection of light). Types of spherical mirrors are;
a) Convex Mirror
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OPTICS (PHYS-508)
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Section: Morning
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b) Concave Mirror
i.
Convex Mirror: (Opaque)
These mirrors have reflecting outer curved surface. These mirrors form only virtual image.
ii.
Concave Mirror: (Opaque)
These mirrors have reflecting inner curvature surface. These mirrors form both virtual and real
images.
Stops:
Stops is an optical instrument (lens, mounting, diaphragm or some similar objects) which limits the rays that
can be transmitted through the instrument.
It may be used to eliminate unwanted rays which produce aberrations. There are two properties of
stops that are important.
i.
Aperture Stop:
The stop which controls the quantity of transmitted light is called as aperture stop.
ii.
Field Stop:
The stop which controls the field of view is called as field stop.
In a camera, photographic film acts as a field stop. In the telescope, the field stop is usually the rim of
the lens or diaphragm in the telescope tube.
1.4 Aberrations (‫)دھندال پن‬
It is the property of the optical instruments such as lens that causes the light to be spread over some region of
space, rather than to be focused at a point. It caused the image to be formed by lens, is distorted and blurred.
The departure of actual image from the predictions is called as aberrations. Generally, it has some
types, given as,
A. Chromatic Aberrations
a. Longitudinal Chromatic Aberrations
b. Lateral Chromatic Aberrations
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OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
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B. Monochromatic Aberrations
a) Spherical Aberrations
b) Coma
c) Astigmatism
d) Curvature of Field
e) Distortion
A. Chromatic Aberrations:
Aberrations caused by the variation of refractive index with wavelength are called as chromatic
aberrations. Distorted and blurred image will be formed due to this.
Explanation:
If the ray of white light passes through the lens, the white light dispersed into its constituent
seven colors. Red rays are brought to focus at Fr, and blue rays are brought to focus at Fb as shown in
given figure. Due to this defect, image will be colored and not well defined. This type of defect is
called chromatic aberration.
If refractive index of blue is nb, and for red it is nr, focal length of blue is fb and for red, it is fr, then,
𝒏 𝒃 > 𝒏𝒓
That’s why the fb < fr.
Removal of Chromatic Aberration:
This defect can be removed by using a combination of convex and concave lens made of two different
materials having unequal dispersive powers. This lens is given such suitable shapes that the dispersion
by one lens is exactly equal and opposite to that produce by the other. The focal length of lenses are
also unequal in numerical values. So that the focal length of the combination has a finite value, as
shown in below figure.
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OPTICS (PHYS-508)
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Section: Morning
Mid Term Notes Spring 2024
B. Spherical Aberrations:
The rays refracting from different regions of lens don’t come to same focus but are focused at different
points. OR
The aberrations caused by the large apertures of the lens is called as spherical aberrations. Spherical
aberrations for converging lens is positive while it is negative for diverging lens.
Explanation:
When the beam of parallel rays is allowed to fall on convex lens, after reflection it will be
focused at single point by the lens only if the aperture of the lens is small. Otherwise, the lens will
refract the outer rays slightly more than the central rays as shown in the given figure. The image
produced will not be well defined and sharp. This lens defect is called as spherical aberration.
Removal of Spherical Aberration:
➢ The optical instruments using lenses are provided with stop which allow the central rays to
pass through the lens. In this way, the effective aperture of the lens remain small and spherical
aberration minimized.
➢ Spherical aberration can also be reduced by taking the suitable values of radii of curvature of
surface of lens or using two lenses by keeping at suitable distance from each other.
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OPTICS (PHYS-508)
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Mid Term Notes Spring 2024
1.5 Coma
Spherical Aberration and Off-Axis Aberrations:
Off-axis points experience various aberrations such as coma, astigmatism, curvature of field, and distortion,
in addition to spherical aberration. Initial off-axis aberration encountered is coma, while spherical aberration
primarily effects on-axis points.
Effect of Coma:
Coma leads to differential magnification across the lens, causing rays near the axis to focus at a different point
compared to marginal rays. This results in different parts of the lens contributing to the image formation with
varying magnifications.
Meridional Plane Rays:
Rays depicted in the meridional plane (containing the optical axis and the object point) illustrate the effect of
coma. Complete understanding of image formation requires consideration of all rays, not just those in the
meridional plane.
Three-Dimensional Perspective:
Three-dimensional perspective shows rays hitting the lens at equal distances from the center. Rays intersecting
the lens diametrically opposite converge to a single point on the paraxial image plane, while other pairs of
rays focus to different points forming a circle on the image plane.
Radius and Center Shift:
Coma is measured by the radius of the circle formed by the foci of different ray pairs. As the radius
(represented as 'h') of the zone increases, the center of the circle shifts away from the ideal image point,
indicating more pronounced coma.
Composite Image Appearance:
Composite image of a point object exhibits a comet-like appearance due to the effect of coma. The overall
image shape resembles a comet, with the center of the circle of foci determining the extent of coma present.
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OPTICS (PHYS-508)
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Mid Term Notes Spring 2024
1.6 Astigmatism
Astigmatism in Optical Systems:
When an optical system is free from spherical aberration and coma, but suffers from astigmatism, it images
sharply those object points lying on or near the axis. However, for points far away from the axis, the image of
a point becomes elongated rather than a point, indicating the presence of astigmatism.
Meridional and Sagittal Planes:
The plane containing the axis and the object point is termed the meridional plane. Perpendicular to the
meridional plane, the plane containing the axis is termed the sagittal plane.
Image Formation in Astigmatism:
In the presence of astigmatism only, rays in the meridional plane converge at a different point compared to
those in the sagittal plane. For instance, rays PA and PB converge at point T, while rays PC and PD converge
at a different point S, distinct from T.
Focal Lines:
Due to the differing convergence points of rays in the meridional and sagittal planes, focal lines are formed.
The focal line T, normal to the meridional plane, is termed the tangential focus. Similarly, the focal line at S,
lying in the tangential plane, is termed the sagittal focal line.
Measurement of Astigmatism:
The distance between the tangential focus (T) and the sagittal focus (S) serves as a measure of the extent of
astigmatism present in the optical system.
Note: Please label points in the above diagram by yourself.
1.7 Total Internal Reflection
Refraction at Interface:
When light passes from a denser medium to a rarer medium, it bends away from the normal.
Increasing Angle of Incidence:
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OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
The angle of refraction 𝜽𝒓 is always greater than the angle of incidence 𝜽𝒊 . As the angle of incidence increases,
the corresponding angle of refraction also increases.
Critical Angle:
The angle of incidence at which the angle of refraction becomes 90° is termed the critical angle 𝜽𝒄 . Denoted
by 𝜽𝒄 , it marks a threshold beyond which total internal reflection occurs.
Total Internal Reflection:
Total internal reflection happens when the angle of incidence exceeds the critical angle. This phenomenon
occurs only when light travels from a denser medium to a rarer medium. Instead of refracting into the rarer
medium, the light is entirely reflected back into the denser medium.
Characteristics of Total Internal Reflection:
Total internal reflection redirects the light back into the denser medium, with an angle of reflection equal to
the angle of incidence. This process is illustrated in given figure, where the light instead of refracting is
reflected back into the same medium when the angle of incidence 𝜽𝒊 surpasses the critical angle.
Relation between “𝜽𝒄 ” and “n”:
According to Snell’s law,
𝒏𝟏 𝑺𝒊𝒏 𝜽𝒊 = 𝒏𝟐 𝑺𝒊𝒏 𝜽𝒓
where n1 is the refractive index of the first medium and n2 is the refractive index of the second medium. When
angle of incidence is equal to critical angle the angle of refraction will equal to 90°. The refractive index of
air is equal to 1. Putting the values in above equation we get,
𝒏𝟏 𝑺𝒊𝒏 𝜽𝒄 = 𝟏 × 𝑺𝒊𝒏 𝟗𝟎𝒐
𝒏𝟏 =
𝟏
𝑺𝒊𝒏 𝜽𝒄
𝒘𝒉𝒆𝒓𝒆
𝒏=
𝒄
𝒗
Above equation shows that the refractive index is a way of measuring the speed of light in a material. Light
travel faster in a vacuum.
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OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
The speed of light in a vacuum is about 300, 000 km/s. The refractive index of medium is calculated
by dividing the speed of light in a vacuum by the speed of light in the medium. The refractive index of vacuum
is 1.
Medium
Refractive Index (n)
Medium
Refractive Index (n)
Air
1.000293
Crown Glass
1.53
Hydrogen
1.000132
Flint Glass
1.62
Water
1.33
Plexiglas
4.49
Ice
1.309
Diamond
2.42
1.8 Optical Fiber
Composition and Structure:
- Optical fibers are composed of flexible, transparent materials such as extruded glass (silica) or plastic.
- They are slightly thicker than a human hair.
Working Principle:
- Optical fibers function as waveguides or "light pipes" to transmit light between two ends of the fiber.
- The principle of operation is based on the total internal reflection of light.
Fiber Optics:
- The applied science and engineering field concerned with the design and application of optical fibers is
known as fiber optics.
- Fiber optics technology utilizes the properties of optical fibers for various applications.
Applications:
- Optical fibers find extensive use in fiber-optic communications.
- They enable transmission over longer distances and at higher bandwidth (data rates) compared to wire
cables.
- Fiber optics technology is rapidly replacing conventional methods of communication that utilize metal
wire.
Construction of Optical Fiber:
Core Composition:
- The internal part of the fiber, called the core, is made of transparent material, typically silica.
Page | 17 OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
- It serves as the pathway for transmitting the signal.
Cladding:
- The core is enveloped by an outer layer with a high refractive index, known as cladding.
Buffer Layer:
- Surrounding the cladding is a plastic layer called the buffer.
- Buffers provide mechanical isolation, protection from physical damage, and fiber identification.
Strength Material:
- Kevlar is used as a layer to strengthen the fiber and prevent breakage when pulled through tubes or under
stress.
PVC Outer Jacket:
- The fiber assembly is further protected by an outer jacket made of PVC (polyvinyl chloride).
Cable Formation:
- Multiple fibers are bundled together and enveloped in a PVC Nylon layer to form a cable.
Optical Fiber Diameter:
- The outer diameter of the wire typically ranges from 100 to 300 micrometers (𝝁m), while the inner diameter
is between 50 to 100 𝝁m.
- The diameter of the cable is determined by the number of optical fibers it contains.
Fiber Material and Manufacturing:
The raw material for optical fiber is silica glass. To make the refractive index or the material varying
germanium, phosphorus, boron and Florence are added. From core to the outer surface germanium and
phosphorus increases the refractive index whereas boron and Florence decreases the refractive index. Standard
optical fibers are made by first constructive a large-diameter
"perform" with a carefully controlled refractive index profile,
and then "pulling" the perform to form the long, thin optical
fiber.
Kinds of Optical Fiber:
Optical waves are propagated through the core of the optical
fiber. The propagation of the optical signal through the fiber is
due to the phenomenon of total internal. reflection. Many
signals can be transmitted through the fiber at the same time.
The number of signals which can be transmitted through the
fiber depends upon the wavelength of the wave and the
difference of the refractive index between the core and the outer surface of the fiber.
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OPTICS (PHYS-508)
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a) Mono-Mode Optical Fiber:
If only one wave can be transmitted through a fiber, then it is called mono mode fiber or single mode
fiber. Mono mode optical fiber has very narrow core as compared to multi-mode optical fiber. Laser
as monochromatic light is used for data propagations.
b) Multi-Mode Optical Fiber:
The fiber through which a number of signals can be transmitted simultaneously is called multi-mode
optical fiber or MMF. Multi-mode fiber is of two types; step index fiber and graded index fiber.
i.
Step-Index Fiber:
In step index fiber the refractive index of the fiber is constant. So, the total internal
reflection takes place at the edge of the core. It also used for the single signals.
ii.
Graded Index Fiber:
In a graded index fiber, the refractive index is not constant, it decreases gradually from
core to the outer surface therefore the signals instead of reflecting from the outer surface
of the fiber refract inside the fiber shown in given figure.
Advantages of Optical Fiber:
The advantages and disadvantages of an optical fiber can be estimated by its comparison with the metal wire
used for the same purpose. The advantages of optical fiber are as follows.
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OPTICS (PHYS-508)
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Signal Transmission:
Metal wire: Electrical signals; Optical fiber: Light signals.
Energy losses: Greater in metal wire than in optical fiber.
Attenuation (‫)فیفخت‬:
Optical fiber: Far less attenuation than electrical copper cables.
Frequency Range:
Optical fiber can transmit a wider frequency range than metal wire.
Weight:
Metal wires are heavier due to the greater density of copper compared to silica in optical fibers. Optical fibers
are lightweight.
Raw Material Availability:
Raw material for optical fibers (silica) is abundant and easily available.
Temperature Sensitivity:
Optical fiber is less affected by temperature changes compared to metal wire.
Interference:
Metal wires can be affected by electric and magnetic fields, while optical fibers are not.
Overheating and Crosstalk:
Overheating is possible in metal wires but not in optical fibers. Crosstalk is possible in metal wires if they
touch, while it's not an issue in optical fibers since the signal stays within the fiber.
Disadvantages of Optical Fiber:
Following are the disadvantages of the optical fiber as compared to the metal wire.
1. Through the raw material of an optical fiber is abundant, but the manufacturing cost of the optical fiber
is very high.
2. Strength of the metal wire is much greater than the optical fiber, which is easily breakable.
3. Remote power feeding is not possible in case of optical fiber.
4. Its splicing (joining) is very difficult.
Uses of Optical Fiber:
Communication Advantages:
- Optical fibers enable long-distance transmission with higher bandwidths compared to wire cables. They
offer lower signal loss and immunity to electromagnetic interference.
Illumination and Imaging:
- Used for illumination and image transmission, especially in confined spaces.
- Fiber bundles facilitate imaging devices like endoscopes for internal examinations, telecommunication etc.
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OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
Replacement:
- Replacing metal wires in various telecommunications applications such as telephone cables, TV channels,
video phones, fax, and telex.
Medical Applications:
- Utilized in surgery for laser transmission, such as kidney stone treatment, using coherent fiber bundles and
endoscopes.
- Transmission of lasers into machinery for fault detection in industrial settings.
Light Guides:
- Serve as light guides in medical and other applications requiring bright light without a clear line-of-sight
path.
- In some buildings, optical fibers route sunlight from the roof to interior spaces for illumination.
THE END OF CHAPTER 1
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OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
CHAPTER 2: WAVEFRONT SPLITTING INTERFEROMETER
2.0 Basics
Wavefront:
A wavefront is an imaginary surface or line that connects all the points of a wave that have the same phase/
mod of vibration.
The distance between two consecutive crests/ troughs is known as wavelength denoted by λ. It has two types.
i.
Plane Wavefronts
ii.
Spherical Wavefronts
i.
Plane Wavefronts:
In optics, plane wavefronts refer to the surfaces perpendicular to the direction of propagation of a
plane wave. A plane wave is a type of wave where the wave fronts are flat and parallel to each
other. These wavefronts propagate uniformly through space, meaning that at any given moment,
each point along a wavefront is in phase with the corresponding point on adjacent wavefronts.
ii.
Spherical Wavefronts:
In optics, spherical wavefronts refer to the surfaces that propagate outward from a point source of
light or other electromagnetic radiation. Unlike plane wavefronts, which are flat and parallel to
each other, spherical wavefronts are curved and expand outward in all directions from the source.
Spherical wavefronts are commonly encountered in situations where light originates from a
localized source or diverges from a point due to scattering, reflection, or refraction. They play a
Page | 22 OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
fundamental role in understanding phenomena such as wavefront propagation, diffraction, and
interference in optical systems.
Remember!
Distance in plane,
S=vt
Distance in Sphere,
r=ct
or
r = c ∆t
We can also change spherical wavefronts into plane wavefronts by using convex lens.
Huygen’s Principle:
Huygens' principle is a fundamental concept in wave optics that was proposed by Dutch physicist Christiaan
Huygens in the 17th century. It describes how waves propagate through a medium. Huygens' principle states:
"When a wavefront propagates through a medium, each point on the wavefront becomes a source of secondary
wavelets that spread out in all directions. The new wavefront at any later time is the envelope tangent to the
secondary wavelets at that time."
The two postulates of Huygens' principle for wavefronts are:
❖ Every point on a given wavefront can be considered as a point source of secondary spherical wavelets
that propagate outward in all directions with the same speed as the wavefront.
❖ The new position of the wavefront at a later time is determined by the envelope (or tangent) of all these
secondary wavelets. In other words, the new wavefront is formed by connecting the points where the
secondary wavelets are just touching each other, forming a coherent continuation of the original
wavefront.
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OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
Interference of Light Waves:
Interference of light waves occurs when coherent waves overlap, leading to constructive or destructive
interference. Constructive interference strengthens waves when peaks align, while destructive interference
weakens them when peaks align with troughs. This creates light and dark interference patterns. It's crucial in
optics for phenomena like thin film interference, diffraction, and interferometry.
The two waves must have,
➢ Same frequency
➢ Same Wavelength
➢ Travelling in Same Medium
Types of Interference:
(1) Constructive Interference:
Constructive interference occurs when the peaks of two or more waves align with each other, resulting
in an increase in the overall amplitude of the resulting wave. This reinforcement of waves leads to a
constructive interference pattern, where the combined wave has a greater intensity than the individual
waves.
(2) Destructive Interference:
Destructive interference occurs when the peak of one wave aligns with the trough of another wave,
resulting in cancellation or reduction of the overall amplitude of the resulting wave. This leads to
regions where the waves effectively cancel each other out, producing a decrease or elimination of
intensity in the interference pattern.
Conditions For interference of Waves:
Light must have,
❖ Monochromatic having one wavelength.
❖ Coherent (In-phase or Constant Phase Difference).
Page | 24
OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
2.1 The Young’s DS Experiment
Young's double slit experiment uses two coherent sources of light placed at a small distance apart, usually
only a few orders of magnitude greater than the wavelength of light is used.
Experimental Setup:
Young in 1801, for studying Interference, effects of light, screen having 2 slits is illuminated by a beam of
monochromatic light. The portion of the wave front incident on the slits behaves as a source of secondary
wavelets (Huygens's principle). The secondary wavelets leaving slits are coherent superpositions of slits of
the wavelets result in a series of bright and dark fringes which are observed on a second screen placed at some
parallel screen.
Minima and Maxima Fringes:
Let us now consider the formation of bright and dark fringes. As pointed out earlier the two slits behave as
coherent sources of secondary wavelets. The wavelets arrive at the screen in such a way that at same points
crests fall on crests and troughs resulting in constructive interference and bright fringes are formed. There are
some points on the screen where crests meet troughs giving rise to destructive interference and the dark fringes
are formed. The bright fringes are termed as maxima and dark fringes are termed as minima.
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OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
In order to derive equations for maxima and minima. an arbitrary point P is taken as the screen on one
side of the central point O. AP and BP are the paths of rays reaching point P. The line AD is drawn such that
AP = DB. The separation between the centers of the two slits is AB = d. The distance of the screen from the
slits is CO = L. The angle between CP and CO is 0, as shown in above figure.
Path Difference:
The path difference between the wavelets leaving the slits and arriving at P is BD. The no. of
wavelengths contained within BD that determines whether bright or dark fringes will appear at P. If the point.
P is to have bright fringe; the path difference BD must be an integral multiple of wavelengths. Thus,
𝑩𝑫 = 𝒎𝝀
∴ 𝒎 = 𝟎, 𝟏, 𝟐, 𝟑, …
𝑺𝒊𝒏𝒄𝒆
𝑩𝑫 = 𝒅 𝒔𝒊𝒏 𝜽
𝑺𝒐
𝒎𝝀 = 𝒅 𝐬𝐢𝐧 𝜽
(𝑬𝒒. 𝟏)
For different values of m (order of a fringe),
m = 0,
d sin θ = m λ = 0 (Central Maxima)
m = 1,
d sin θ = m λ = λ (1st Maxima)
m = 2,
d sin θ =m λ = 2 λ (2nd Maxima)
The bright fringe is located on the other side of O. If a dark fringe appears at the point B. The path
difference BD must contain half-Integral number of wavelengths.
𝑩𝑫 = (𝟐𝒎 + 𝟏)
𝟏
𝑩𝑫 = (𝒎 + ) 𝝀
𝟐
𝒔𝒐
𝝀
𝟐
𝟏
𝒅 𝐬𝐢𝐧 𝜽 = (𝒎 + ) 𝝀
𝟐
(𝑬𝒒. 𝟐)
For different values of m (order of a fringe),
m=0,
m=1,
m=2,
1
1
λ
d sin θ = (m+ ) λ = ( ) λ =
2
2
2
1
1
3λ
d sin θ = (m+ ) λ = (1+ ) λ =
2
2
2
1
1
5λ
d sin θ = (m+ ) λ = (2+ ) λ =
2
2
2
(1st Minima)
(2nd Minima)
(3rd Minima)
Position of Maxima:
The 1st and 2nd dark fringe appear at m = 0 and m = 1. As the angle 𝜽 is small, then;
𝐬𝐢𝐧 𝜽 ≈ 𝐭𝐚𝐧 𝜽 ≈ 𝜽
𝒚
𝒎𝝀
= 𝐬𝐢𝐧 𝜽 =
𝑳
𝒅
𝒎𝝀
𝒐𝒓
𝒚=
𝑳
𝒅
𝐭𝐚𝐧 𝜽 =
𝒚 𝒎𝝀
=
𝑳
𝒅
Page | 26
OPTICS (PHYS-508)
(𝑬𝒒. 𝟑)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
Position of Dark Fringe:
If P is to have dark fringe, then,
𝟏 𝝀𝑳
𝒚 = (𝒎 + )
𝟐 𝒅
(𝑬𝒒. 𝟒)
In order to determine the distance between the adjacent fringes on the screen mth and (m+1)th fringes are
considered. For the mth order:
𝒚𝒎 =
𝒎𝝀
𝑳
𝒅
Distance between Consecutive Maxima:
(Width of Maxima)
We know that the mth order maxima is equal to;
𝒚𝒎 =
𝒎𝝀𝑳
𝒅
− (𝒊)
The next maxima fringe is;
𝒚𝒎+𝟏 =
(𝒎 + 𝟏)𝝀𝑳
𝒅
− (𝒊𝒊)
Subtract equation (i) from equation (ii);
(𝒎 + 𝟏)𝝀𝑳 𝒎𝝀𝑳
−
𝒅
𝒅
𝝀𝑳 𝝀𝑳
∆𝒚 = (𝒎 + 𝟏 − 𝒎)
=
𝒅
𝒅
𝒚𝒎+𝟏 − 𝒚𝒎 =
Distance between two Consecutive Minima:
For minima,
𝟏 𝝀𝑳
𝒚𝒎 = (𝒎 + )
− (𝒊𝒊𝒊)
𝟐 𝒅
𝟏 𝝀𝑳
𝒚𝒎+𝟏 = (𝒎 + 𝟏 + )
− (𝒊𝒗)
𝟐 𝒅
Subtract equation (iii) from equation (iv),
𝟏 𝝀𝑳
𝟏 𝝀𝑳
𝒚𝒎+𝟏 − 𝒚𝒎 = (𝒎 + 𝟏 + )
− (𝒎 + )
𝟐 𝒅
𝟐 𝒅
𝟏
𝟏 𝝀𝑳 𝝀𝑳
∆𝒚 = (𝒎 + 𝟏 + − 𝒎 − )
=
𝟐
𝟐 𝒅
𝒅
Fringe Size (∆y):
Its formula shows that,
∆𝒚 ∝ 𝝀 ,
Page | 27
OPTICS (PHYS-508)
∆𝒚 ∝ 𝑳 ,
∆𝒚 ∝
𝟏
𝒅
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
Fringe Spacing:
Above relations reveal that fringe spacing increase if red light (long wavelength) is used as compared to blue
light (short wavelength).
The fringe spacing varies directly with distance L between the slits and screen and inversely with the
separation d of the slits.
2.2 Interference in Thin Films
Interference in thin films is a phenomenon where light waves reflected from the top and bottom surfaces of a
thin film, like soap bubbles or oil on water, interfere with each other. This can create a pattern of colorful
bands or fringes. It’s used in designing anti-reflective coatings and is also the principle behind Newton’s rings
experiment.
The thickness of the film relative to the wavelength of light is the other crucial factor in thin film interference.
For example, oil-water surface, surface of soap bubbles etc. The Path Difference (P.D) depends upon three
factors;
➢ Nature of the Film
➢ Thickness of the Film
➢ Angle of Incidence
Newton Rings:
Remember!
The Wavelength of light is
400-800 nm or it can be
written as 400 x 10-9 m or also
4 x 102 x 10-9 m which gives 4
x 10-7 m.
Newton’s rings are a series of concentric circular rings consisting of bright- and dark-colored fringes. When a
plano-convex lens lies on top of a plane lens or glass sheet, a small layer of air is formed between the two
lenses. Newton’s rings are formed by the interference phenomenon when monochromatic and coherent rays
of light are reflected from the top and bottom surfaces of this air film. The film’s thickness varies from zero
at the point of contact to a finite value in the wedge-shaped region. The phenomenon of the formation of
Newton’s rings can be explained based on the wave theory of light.
An air film of varying thickness is formed between the lens and the glass sheet.
Page | 28
OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
❖ When a ray falls on the surface of the lens, it is reflected as well as refracted.
❖ When the refracted ray strikes the glass sheet, it undergoes a phase change of 180° on reflection.
❖ Interference occurs between two waves that interfere constructively if the path difference between
them is (m+1/2) λ and destructively if the path difference between them is m λ, thereby producing
alternate bright and dark rings.
Experimental Setup
Apparatus:
The apparatus consists of the following components.
o Nearly monochromatic source of light (sodium light)
o Plano-convex lens
o Optically flat glass plates
o Convex lens
o Traveling microscope
Diagram:
Explanation:
The experimental setup for Newton’s ring is shown in the figure above. The convex surface of a plano-convex
lens having a long focal length (large radius of curvature) is placed in contact with a plane glass plate and
clamped together. Light from a monochromatic source (e.g., sodium lamp) is allowed to fall on a convex lens
through a wide slit, which renders it into a nearly parallel beam.
Page | 29
OPTICS (PHYS-508)
BS Physics 6th Semester
Section: Morning
Mid Term Notes Spring 2024
At first, light falls on a glass plate inclined at an angle of 45° to the vertical before reaching the lensplate system at the bottom. Light is reflected from the upper surface of the glass plate and the lower surface
of the lens. Due to the air film formed by the glass plate and lens, interference fringes are formed, which are
observed directly through a traveling microscope. The rings are concentric circles. A dark central spot is
obtained when viewed by reflection.
IMPORTANT SHORT QUESTIONS
Q.1. Why are Newton’s rings circular?
Ans. The plano-convex lens is circular. All the bright and dark fringes are the loci of the points of the film
of equal thickness. As the equally thick films are formed along the diameter of the circular shape, the
fringe pattern is also circular.
Q.2. Why is the center of Newton’s rings dark?
Ans. At the point of contact of the lens with the glass plate, the thickness of the air film is minimal
compared to the wavelength of light. Therefore, the path difference introduced between the interfering
waves is zero, the condition of minimum intensity. Consequently, the interfering waves at the center are
opposite in phase and interfere destructively.
Q.3. Why is sodium light used in Newton’s ring experiment?
Ans. Sodium light is used in Newton’s rings experiment because it is monochromatic, and the two spectral
lines of sodium can be resolved without difficulty.
THE END OF MID TERM SYLLABUS
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OPTICS (PHYS-508)