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GALGOTIAS COLLEGE OF ENGINEERING& TECHNOLOGY
Galgotias College of Engineering and Technology, Greater Noida
Vision of Institute
To be a leading educational institution recognized for excellence in engineering education &
research producing globally competent and socially responsible technocrats.
Mission of Institute
- To provide state of art infrastructural facilities that support achieving academic excellence.
- To provide a work environment that is conducive for professional growth of faculty and
staff.
- To collaborate with industry for achieving excellence in research, consultancy and
entrepreneurship development.
Program Outcomes (PO’s) relevant to the course:
PO1 Engineering knowledge : Apply the knowledge of mathematics, science, engineering fundamentals,
and an engineering specialization to the solution of complex engineering problems.
PO2 Problem analysis : Identify, formulate, review research literature, and analyze complex engineering
problems reaching substantiated conclusions using first principles of mathematics, natural sciences,
and engineering sciences.
PO3 Design/development of solutions : Design solutions for complex engineering problems and design
system components or processes that meet the specified needs with appropriate consideration for
the public health and safety, and the cultural, societal, and environmental considerations.
PO4 Conduct investigations of complex problems : Use research-based knowledge and research
methods including design of experiments, analysis and interpretation of data, and synthesis of the
information to provide valid conclusions
PO5 Modern tool usage : Create, select, and apply appropriate techniques, resources, and modern
engineering and it tools including prediction and modeling to complex engineering activities with an
understanding of the limitations.
PO6 The engineer and society : Apply reasoning informed by the contextual knowledge to assess
societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to the
professional engineering practice.
PO7 Environment and sustainability : Understand the impact of the professional engineering solutions
in societal and environmental contexts, and demonstrate the knowledge of, and need for
sustainable development.
PO8 Ethics : Apply ethical principles and commit to professional ethics and responsibilities and norms of
the engineering practice..
PO9 Individual and team work : : Function effectively as an individual, and as a member or leader in
diverse teams, and in multidisciplinary settings
PO10 Communications : Communicate effectively on complex engineering activities with the engineering
community and with society at large, such as, being able to comprehend and write effective reports
and design documentation, make effective presentations, and give and receive clear instructions.
PO11 Project management and finance : : Demonstrate knowledge and understanding of the engineering
and management principles and apply these to one’s own work, as a member and leader in a team,
to manage projects and in multidisciplinary environments.
PO12 Life-long learning: Recognize the need for, and have the preparation and ability to engage in
independent and life-long learning in the broadest context of technological change.
DR. A. P. J. ABDUL KALAM TECHNICAL UNIVERSITY, LUCKNOW
SYLLABUS(Engg. Physics-KAS101T/201T)
B. TECH. FIRST/SECOND SEMESTER-2021-
SN Units COs
1 Relativistic Mechanics
Frame of reference, Inertial & non-inertial frames, Galilean transformations, Michelson- Morley experiment, Postulates of special theory of relativity, Lorentz transformations, Length contraction, Time dilation, Velocity addition theorem, Variation of mass with velocity, Einstein‟s mass energy relation, Relativistic relation between energy and momentum, Massless particle.
CO1: Understand the basics of relativistic mechanics.(K2)
2 Electromagnetic Field Theory
Continuity equation for current density, Displacement current, Modifying equation for the curl of magnetic field to satisfy continuity equation, Maxwell‟s equations in vacuum and in non conducting medium, Energy in an electromagnetic field, Poynting vector and Poynting theorem, Plane electromagnetic waves in vacuum and their transverse nature. Relation between electric and magnetic fields of an electromagnetic wave, Energy and momentum carried by electromagnetic waves, Resultant pressure, Skin depth.
CO2: Derive the expression for EM- wave using Maxwell’s equations.(K1)
3 Quantum Mechanics
Black body radiation, Stefan‟s law, Wien‟s law, Rayleigh-Jeans law and Planck‟s law, Wave particle duality, Matter waves, Time-dependent and time-independent Schrodinger wave equation, Born interpretation of wave function, Solution to stationary state Schrodinger wave equation for one-Dimensional particle in a box, Compton effect.
CO3: Understand the concepts of quantum mechanics.(K2)
4 Wave Optics
Coherent sources, Interference in uniform and wedge shaped thin films, Necessity of extended sources, Newton‟s Rings and its applications. Fraunhoffer diffraction at single slit and at double slit, absent spectra, Diffraction grating, Spectra with grating, Dispersive power, Resolving power of grating, Rayleigh‟s criterion of resolution, Resolving power of grating.
CO4: Describe the different phenomena of light and its applications.(K1)
5 Fiber Optics & Laser
Fibre Optics: Introduction to fibre optics, Acceptance angle, Numerical aperture, Normalized frequency, Classification of fibre, Attenuation and Dispersion in optical fibres. Laser: Absorption of radiation, Spontaneous and stimulated emission of radiation, Einstein‟s coefficients, Population inversion, Various levels of Laser, Ruby Laser, He-Ne Laser, Laser applications.
CO5: Comprehend the concepts and applications of fiber optics and LASER.(K2)
S.No Unit Name Source name Study Material/ Web Link
1 Unit-I-RELATIVISTIC MECHANICS NPTEL
https://www.digimat.in/nptel/courses/video/115101011/L .html http://nptel.ac.in/courses/115101011/ https://nptel.ac.in/courses/122107035/31-
2 Unit-2-ELECTROMAGNETIC FIELD THEORYNPTEL
https://nptel.ac.in/courses/115/101/115101005/ https://www.digimat.in/nptel/courses/video/115101005/L .html https://www.digimat.in/nptel/courses/video/115105104/L .html
3 Unit-3-QUANTUM MECHANICS NPTEL
https://www.digimat.in/nptel/courses/video/115102023/L .html http://nptel.ac.in/courses/122101002/downloads/lec-26.pdf https://nptel.ac.in/courses/122/105/122105023/
4 Uniy-4-WAVE OPTICS NPTEL
https://nptel.ac.in/courses/122107035/ http://nptel.ac.in/courses/122105023/
5 Unit-5 LASER & FIBER OPTICS NPTEL
http://nptel.ac.in/courses/122101002/downloads/lec-28.pdf https://www.digimat.in/nptel/courses/video/115107095/L .html
Syudy Material/WebLink
COURSE OUTCOMES (COs): Engineering Physics (KAS-101T/201T),
YEAR OF STUDY: 2021-
Course outcomes Statement (On completion of this course, the student will be able to - )
CO1 Understand the basics of relativistic mechanics.(K2)
CO2 Derive the expression for EM-wave^ using^ Maxwell’s^ equations.(K1)
CO3 Understand the concepts of quantum mechanics.(K2)
CO4 Describe the different phenomena of light and its applications.(K1)
CO5 Comprehend the concepts and applications of fiber optics and LASER.(K2)
Mapping of Course Outcomes with Program Outcomes (CO-PO Mapping)
- Slight ( low) 2. Moderate ( medium) 3. Substantial (high)
COs/POs PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO CO1 3 3 3 CO2 3 3 3 3 CO3 3 3 3 CO4 2 3 CO5 3 3 3
KAS-
101 T/201T
Contents Beyond the Syllabus: Physics (KAS101T/KAS201T)
Session -2021-
S.No. Contents Beyond the Syllabus
Delivery Details
(Board/PPTs
Teaching)
Perfectly Elastic Collision of Two Particles PPT
E M wave spectrum and its uses PPT
Tunneling Effect PPT
Young’s double Slits PPT
Holography(Construction and reconstruction of 3D
image)
PPT
Engineering Physics KAS 101T/201T
Module- 1 - Relativistic Mechanics CO
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1.1 Introduction of Newtonian Mechanics
The universe, in which we live, is full of dynamic objects. Nothing is static here Starting from giant stars to tiny electrons, everything is dynamic. This dynamicity of universal objects leads to variety of interactions, events and happenings. The curiosity of human being/scientist to know about these events and laws which governs them. Mechanics is the branch of Physics which is mainly concerned with the study of mobile bodies and their interactions.
A real breakthrough in this direction was made my Newton in 1664 by presenting the law of linear motion of bodies. Over two hundred years, these laws were considered to be perfect and capable of explaining everything of nature.
1.2 Frames of Reference
The dynamicity of universal objects leads to variety of interactions between these objects leading to
various happenings. These happenings are termed as events. The relevant data about an event is recorded
by some person or instrument, which is known as “Observer ”.
The motion of material body can only described relative to some other object. As such, to locate the
position of a particle or event, we need a coordinate system which is at rest with respect to the observer.
Such a coordinate system is referred as frame of reference or observers frame of reference.
“A reference frame is a space or region in which we are making observation and measuring physical(dynamical) quantities such as velocity and
acceleration of an object(event).” or
“A frame of reference is a three dimensional coordinate system relative to which described the position and motion(velocity and acceleration) of a body(object)”
Fig.1.1 represents a frame of reference(S), an object be
situated at point P have co-ordinate i.e.
P( ), measured by an Observer(O). Where be the time
of measurement of the co-ordinate of an object. Observers in
different frame of references may describe same event in
different way.
Example- takes a point on the rim of a moving wheel of cycle. for an observer sitting at the center of the
wheel, the path of the point will be a circle. However, For an observer standing on the ground the path of
the point will appear as cycloid.
Fig 1.1: frame of reference
Engineering Physics KAS 101T/201T
Module- 1 - Relativistic Mechanics CO
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b) Transformation in velocities components:
The conversion of velocity components measured in frame F into their equivalent components in the frame F' can be known by differential Equation (1) with respect to time we get,
u'x= = (^ )
hence u'x= ux-V
Similarly, from Equation (3) and (4) we can write
u'y= uy and u'z= uz
In vector form,
Hence transformation in velocity is variant only along the direction of motion of the frame and remaining dimensions( along y and z) are unchanged under Galilean Transformation.
c) Transformation in acceleration components:
The acceleration components can be derived by differentiating velocity equations with respect to time,
a'x= ( )
a'x= ax
In vector form a' = a
This shows that in all inertial reference frames a body will be observed to have the same acceleration. Hence acceleration are invariant under Galilean Transformation.
Failures of Galilean transformation:
According to Galilean transformations the laws of mechanics are invariant. But under Galilean transformations, the fundamental equations of electricity and magnetism have very different forms. Also if we measure the speed of light c along x-direction in the frame F and then in the frame F' the value comes to be c' = c – vx. But according to special theory of relativity the speed of light c is same in all inertial frames.
1.4 Michelson-Morley Experiment
“The objective of Michelson - Morley experiment was to detect the existence of stationary medium ether (stationary frame of reference i.e. ether frame.)”, which was assumed to be required for the propagation of the light in the space.
u'=u – v
Engineering Physics KAS 101T/201T
Module- 1 - Relativistic Mechanics CO
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In order to detect the change in velocity of light due to relative motion between earth and hypothetical medium ether, Michelson and Morley performed an experiment which is discussed below. The experimental arrangement is shown in Fig
Light from a monochromatic source S, falls on the semi-silvered glass plate G inclined at an angle 45° to the beam. It is divided into two parts by the semi silvered surface, one ray 1 which travels towards mirror M 1 and other is transmitted, ray 2 towards mirror M 2. These two rays fall normally on mirrors M 1 and M 2 respectively and are reflected back along their original paths and meet at point G and enter in telescope. In telescope interference pattern is obtained.
If the apparatus is at rest in ether, the two reflected rays would take equal time to return the glass plate G. But actually the whole apparatus is moving along with the earth with a velocity say v. Due to motion of earth the optical path traversed by both the rays are not the same. Thus the time taken by the two rays to travel to the mirrors and back to G will be different in this case.
Let the mirrors M 1 and M 2 are at equal distance l from the glass plate G. Further let c and v be the velocities at light and apparatus or earth respectively. It is clear from Fig. that the reflected ray 1 from glass plate G strikes the mirror M 1 at A' and not at A due to the motion of the earth.
The total path of the ray from G to A' and back will be GA'G'.
∴ From Δ GA'D (GA')^2 =(AA')^2 + (A'D)^2 ...(1) As (GD =AA')
If t be the time taken by the ray to move from G to A', then from Equation (1), we have
(c t)^2 =(v t)^2 + (l)^2
Hence t= (^) √
If t 1 be the time taken by the ray to travel the whole path GA'G', then
Engineering Physics KAS 101T/201T
Module- 1 - Relativistic Mechanics CO
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But the experimental were detecting no fringe shift. So there was some problem in theory calculation and is a negative result. The conclusion drawn from the Michelson-Morley experiment is that, there is no existence of stationary medium ether in space.
Negative results of Michelson - Morley experiment
- Ether drag hypothesis: In Michelson - Morley experiment it is explained that there is no relative motion between the ether and earth. Whereas the moving earth drags ether alone with its motion so the relative velocity of ether and earth will be zero.
- Lorentz-Fitzgerald Hypothesis: Lorentz told that the length of the arm (distance between the pale and the mirror M 2 ) towards the transmitted side should be L(√1 – v^2 /c^2 ) but not L. If this is taken then theory and experimental will get matched. But this hypothesis is discarded as there was no proof for this.
- Constancy of Velocity of light: In Michelson - Morley experiment the null shift in fringes was observed. According to Einstein the velocity of light is constant it is independent of frame of reference, source and observer.
Einstein special theory of Relativity (STR)
Einstein gave his special theory of relativity (STR) on the basis of M-M experiment
Einstein’s First Postulate of theory of relativity:
All the laws of physics are same (or have the same form) in all the inertial frames of reference moving with uniform velocity with respect to each other. (This postulate is also called the law of equivalence ).
Einstein’s second Postulate of theory of relativity:
The speed of light is constant in free space or in vacuum in all the inertial frames of reference moving with uniform velocity with respect to each other. (This postulate is also called the law of constancy ).
1.5 Lorentz Transformation Equations
Consider the two observers O and O' at the origin of the inertial frame of reference F and F' respectively as shown in Fig. Let at time t = t' = 0, the two coordinate systems coincide initially. Let a pulse of light is flashed at time t = 0 from the origin which spreads out in the space and at the same time the frame F' starts moving with constant velocity v along positive X-direction relative to the frame F. This pulse of light reaches at point P, whose coordinates of position and time are (x, y, z, t) and (x',y', z', t') measured by the observer O and O' respectively. Therefore the transformation equations of x and x' can be given as,
x'=k (x – v t)………………………....(1)
Where k is the proportionality constant and is independent of x and t.
Engineering Physics KAS 101T/201T
Module- 1 - Relativistic Mechanics CO
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The inverse relation can be given as,
x=k (x' + v t') ………………… (2)
As t and t' are not equal, substitute the value of x' from Equation (1) in Equation (2)
x=k [k (x – vt) + vt'] or =(^ )
t'= or t'= ( ) ………………………....(3)
According to second postulate of special theory of relativity the speed of light c remains constant. Therefore the velocity of pulse of light which spreads out from the common origin observed by observer O and O' should be same.
∴ x=c t and x' = ct'………………………………………...(4)
Substitute the values of x and x' from Equation (4) in Equation (1) and (2) we get
ct'=k (x – v t) = k (ct – v t) or ct'=kt (c – v) ................................(5)
and similarly ct=k t' (c + v) ................................(6)
Multiplying Equation (5) and (6) we get,
c^2 t t'=k^2 t t' (c^2 – v^2 ) hence
after solving k= √
Hence equation (7) substitute in equation (1), then Lorentz transformation in position will be
x'= √
, y=y', z'=z
Calculation of Time: equation (7) substitute in equation (3),
t'= ( )
From equation ( 7),
or,
then above equation becomes
t'= =
or, t'= ( )
Engineering Physics KAS 101T/201T
Module- 1 - Relativistic Mechanics CO
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Hence L=Lo √^ ………………….(3)
From this equation. Thus the length of the rod is contracted by a factor √^ as measured by observer in
stationary frame F.
Special Case:
If v <<< c, then v^2 /c^2 will be negligible in Lo√^ and it can be neglected
Then equation (3) becomes L = LO.
Percentage of length contraction=
1.6.2 Time dilation
Let there are two inertial frames of references F and F'. F is the stationary frame of reference and F' is the moving frame of reference. At time t=t’=0 that is in the start, they are at the same position that is Observers O and O’ coincides. After that F' frame starts moving with a uniform velocity v along x axis.
Let a clock is placed in the frame F'. The time coordinate of the initial time of the clock will be t 1 according to the observer in S and the time coordinate of the final tick (time) will be will be t 2 according to same observer.
The time coordinate of the initial time of the clock will be t' 1 according to the observer in F' and the time coordinate of the final tick (time) will be will be t' 2 according to same observer.
Therefore the time of the object as seen by observer O' in F' at the position x’ will be
to = t’ 2 – t’ 1 ……………………………….(1)
The time t’ is called the proper time of the event. The apparent or dilated time of the same event from frame S at the same position x will be
t = t 2 – t 1 ……………………………….(2)
Now use Lorentz inverse transformation equations for, that is
t 1 = √
t 2 = √
Engineering Physics KAS 101T/201T
Module- 1 - Relativistic Mechanics CO
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By putting equations (3) and (4) in equation (2) and solving, we get
t = √
Substitute equation (1) in above equation,
t = √
This is the relation of the time dilation.
Special Case:
If v <<< c, then v^2 /c^2 will be negligible in √
and it can be neglected
Then t = to
Experimental evidence: The time dilation is real effect can be verified by the following experiment. In 1971 NASA conducted one experiment in which J.C. Hafele, as astronomer and R.F. Keating, a physicist circled the earth twice in a jet plane, once from east to west for two days and then from west to east for two days carrying two cesium-beam atomic clocks capable of measuring time to a nanosecond. After the trip the clocks were compared with identical clocks. The clocks on the plane lost 59 10 ns during their eastward trip and gained 273 7 ns during the westward trip.This results shows that time dilation is real effect.
1.6.3 Relativistic Addition of Velocities
One of the consequences of the Lorentz transformation equations is the counter-intuitive “velocity addition theorem”. Consider an inertial frame S’^ moving with uniform velocity v relative to stationary observer S along the positive direction of X- axis. Suppose a particle is also moving along the positive direction of X-axis. If the particle moves through a distance dx in time interval dt in frame S, then velocity of the particle as measured by an observer in this frame is given by
(1)
To an observer in S’ frame, let the velocity be (by definition)
(2)
Now, we have the Lorentz transformation equations:
√( )
and √( )
Taking differentials of above equations, we get
