14

PHYSICS-DSC 4A: WAVES AND OPTICS

Superposition of Two Collinear Harmonic oscillations: Linearity and Superposition

Principle. (1) Oscillations having equal frequencies and (2) Oscillations having different

frequencies (Beats). (4 Lectures)

Superposition of Two Perpendicular Harmonic Oscillations: Graphical and

Analytical Methods. Lissajous Figures with equal an unequal frequency and their uses.

 (2 Lectures)

Waves Motion- General: Transverse waves on a string. Travelling and standing waves

on a string. Normal Modes of a string. Group velocity, Phase velocity. Plane waves.

Spherical waves, Wave intensity. (7 Lectures)

Fluids: Surface Tension: Synclastic and anticlastic surface - Excess of pressure -

Application to spherical and cylindrical drops and bubbles - variation of surface tension

with temperature - Jaegar’s method. Viscosity: Viscosity - Rate flow of liquid in a

capillary tube - Poiseuille’s formula - Determination of coefficient of viscosity of a

liquid - Variations of viscosity of a liquid with temperature lubrication. Physics of low

(Credits: Theory-04, Practicals-02)

Theory: 60 Lectures

Superposition of Two Collinear Harmonic oscillations: Linearity and Superposition

Principle. (1) Oscillations having equal frequencies and (2) Oscillations having different

frequencies (Beats). (4 Lectures)

Superposition of Two Perpendicular Harmonic Oscillations: Graphical and

Analytical Methods. Lissajous Figures with equal an unequal frequency and their uses.

 (2 Lectures)

Waves Motion- General: Transverse waves on a string. Travelling and standing waves

on a string. Normal Modes of a string. Group velocity, Phase velocity. Plane waves.

Spherical waves, Wave intensity. (7 Lectures)

Fluids: Surface Tension: Synclastic and anticlastic surface - Excess of pressure -

Application to spherical and cylindrical drops and bubbles - variation of surface tension

with temperature - Jaegar’s method. Viscosity: Viscosity - Rate flow of liquid in a

capillary tube - Poiseuille’s formula - Determination of coefficient of viscosity of a

liquid - Variations of viscosity of a liquid with temperature lubrication. Physics of low

pressure - production and measurement of low pressure - Rotary pump - Diffusion pump

- Molecular pump - Knudsen absolute gauge - penning and pirani gauge – Detection of

leakage. (6 Lectures)

Sound: Simple harmonic motion - forced vibrations and resonance - Fourier’s Theorem

- Application to saw tooth wave and square wave - Intensity and loudness of sound -

Decibels - Intensity levels - musical notes - musical scale. Acoustics of buildings:

Reverberation and time of reverberation - Absorption coefficient - Sabine’s formula -

measurement of reverberation time - Acoustic aspects of halls and auditoria.

 (6 Lectures)

Wave Optics: Electromagnetic nature of light. Definition and Properties of wave front.

Huygens Principle. (3 Lectures)

Interference: Interference: Division of amplitude and division of wavefront. Young’s

Double Slit experiment. Lloyd’s Mirror and Fresnel’s Biprism. Phase change on

reflection: Stokes’ treatment. Interference in Thin Films: parallel and wedge-shaped

films. Fringes of equal inclination (Haidinger Fringes); Fringes of equal thickness

(Fizeau Fringes). Newton’s Rings: measurement of wavelength and refractive index.

 (10 Lectures)

Michelson’s Interferometer: Idea of form of fringes (no theory needed), Determination

of wavelength, Wavelength difference, Refractive index and Visibility of fringes.

 (3 Lectures)

15

Diffraction: Fraunhofer diffraction: Single slit; Double Slit. Multiple slits & Diffraction

grating. Fresnel Diffraction: Half-period zones. Zone plate. Fresnel Diffraction pattern

of a straight edge, a slit and a wire using half-period zone analysis. (14 Lectures)

Polarization: Transverse nature of light waves. Plane polarized light – production and

analysis. Circular and elliptical polarization. (5 Lectures)

Reference Books:

 Fundamentals of Optics, F A Jenkins and H E White, 1976, McGraw-Hill

 Principles of Optics, B.K. Mathur, 1995, Gopal Printing

 Fundamentals of Optics, H.R. Gulati and D.R. Khanna, 1991, R. Chand

Publication

 University Physics. FW Sears, MW Zemansky and HD Young 13/e, 1986.

Addison-Wesley

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PHYSICS LAB-DSC 4A LAB: WAVES AND OPTICS

60 Lectures

1. To investigate the motion of coupled oscillators

2. To determine the Frequency of an Electrically Maintained Tuning Fork by

Melde’s Experiment and to verify λ2

 – T Law.

3. To study Lissajous Figures

4. Familiarization with Schuster`s focussing; determination of angle of prism.

5. To determine the Coefficient of Viscosity of water by Capillary Flow Method

(Poiseuille’s method). 

6. To determine the Refractive Index of the Material of a given Prism using Sodium

Light.

7. To determine Dispersive Power of the Material of a given Prism using Mercury

Light

8. To determine the value of Cauchy Constants of a material of a prism.

9. To determine the Resolving Power of a Prism.

10. To determine wavelength of sodium light using Fresnel Biprism.

11. To determine wavelength of sodium light using Newton’s Rings.

12. To determine the wavelength of Laser light using Diffraction of Single Slit.

13. To determine wavelength of (1) Sodium & (2) spectrum of Mercury light using

plane diffraction Grating

14. To determine the Resolving Power of a Plane Diffraction Grating.

15. To measure the intensity using photosensor and laser in diffraction patterns of

single and double slits.

Reference Books:

 Advanced Practical Physics for students, B.L. Flint & H.T. Worsnop, 1971, Asia

Publishing House.

16

 Advanced level Physics Practicals, Michael Nelson and Jon M. Ogborn, 4th

Edition, reprinted 1985, Heinemann Educational Publishers

 A Text Book of Practical Physics, Indu Prakash and Ramakrishna, 11th Edition,

2011, Kitab Mahal, New Delhi.

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Discipline Specific Elective

Select two papers

PHYSICS- DSE: DIGITAL AND ANALOG CIRCUITS AND

INSTRUMENTATION

(Credits: Theory-04, Practicals-02)

Theory: 60 Lectures

UNIT-1: Digital Circuits

Difference between Analog and Digital Circuits. Binary Numbers. Decimal to Binary

and Binary to Decimal Conversion, AND, OR and NOT Gates (Realization using Diodes

and Transistor). NAND and NOR Gates as Universal Gates. XOR and XNOR Gates.

 (4 Lectures)

De Morgan's Theorems. Boolean Laws. Simplification of Logic Circuit using Boolean

Algebra. Fundamental Products. Minterms and Maxterms. Conversion of a Truth Table

into an Equivalent Logic Circuit by (1) Sum of Products Method and (2) Karnaugh Map.

 (5 Lectures)

Binary Addition. Binary Subtraction using 2's Complement Method).Half Adders and

Full Adders and Subtractors, 4-bit binary Adder-Subtractor. (4 Lectures)

UNIT-2: Semiconductor Devices and Amplifiers:

Semiconductor Diodes: p and n type semiconductors. Barrier Formation in PN Junction

Diode. Qualitative Idea of Current Flow Mechanism in Forward and Reverse Biased

Diode. PN junction and its characteristics. Static and Dynamic Resistance. Principle and

structure of (1) LEDs (2) Photodiode (3) Solar Cell.

 (5 Lectures)

Bipolar Junction transistors: n-p-n and p-n-p Transistors. Characteristics of CB, CE and

CC Configurations. Active, Cutoff, and Saturation Regions. Current gains α and β.

Relations between α and β. Load Line analysis of Transistors. DC Load line and Q-

point. Voltage Divider Bias Circuit for CE Amplifier. h-parameter Equivalent Circuit.

Analysis of a single-stage CE amplifier using Hybrid Model. Input and Output

17

Impedance. Current, Voltage and Power Gains. Class A, B, and C Amplifiers.

 (12 Lectures)

UNIT-3: Operational Amplifiers (Black Box approach):

Characteristics of an Ideal and Practical Op-Amp (IC 741), Open-loop& Closed-loop

Gain. CMRR, concept of Virtual ground. Applications of Op-Amps: (1) Inverting and

Non-inverting Amplifiers, (2) Adder, (3) Subtractor, (4) Differentiator, (5) Integrator,

(6) Zero Crossing Detector. (13 Lectures)

Sinusoidal Oscillators: Barkhausen's Criterion for Self-sustained Oscillations.

Determination of Frequency of RC Oscillator (5 Lectures)

UNIT-4: Instrumentations:

Introduction to CRO: Block Diagram of CRO. Applications of CRO: (1) Study of

Waveform, (2) Measurement of Voltage, Current, Frequency, and Phase Difference.

 (3 Lectures)

Power Supply: Half-wave Rectifiers. Centre-tapped and Bridge Full-wave Rectifiers

Calculation of Ripple Factor and Rectification Efficiency, Basic idea about capacitor

filter, Zener Diode and Voltage Regulation (6 Lectures)

Timer IC: IC 555 Pin diagram and its application as Astable & Monostable

Multivibrator (3 Lectures)

Reference Books:

 Integrated Electronics, J. Millman and C.C. Halkias, 1991, Tata Mc-Graw Hill.

 Electronic devices and circuits, S. Salivahanan and N. Suresh Kumar, 2012, Tata

Mc-Graw Hill.

 Microelectronic Circuits, M.H. Rashid, 2ndEdn.,2011, Cengage Learning.

 Modern Electronic Instrumentation & Measurement Tech., Helfrick&Cooper,1990,

PHI Learning

 Digital Principles & Applications, A.P. Malvino, D.P. Leach & Saha, 7th Ed.,2011,

Tata McGraw Hill

 Microelectronic circuits, A.S. Sedra, K.C. Smith, A.N. Chandorkar, 2014, 6th Edn.,

Oxford University Press.

 Fundamentals of Digital Circuits, A. Anand Kumar, 2nd Edition, 2009, PHI Learning

Pvt. Ltd.

 OP-AMP and Linear Digital Circuits, R.A. Gayakwad, 2000, PHI Learning Pvt. Ltd.

PRACTICALS - DSE LAB: DIGITAL AND ANALOG CIRCUITS

AND INSTRUMENTS

60 Lectures

1. To measure (a) Voltage, and (b) Frequency of a periodic waveform using a CRO

2. To verify and design AND, OR, NOT and XOR gates using NAND gates.

3. To minimize a given logic circuit.

4. Half adder, Full adder and 4-bit Binary Adder.

18

5. Adder-Subtractor using Full Adder I.C.

6. To design an astable multivibrator of given specifications using 555 Timer.

7. To design a monostable multivibrator of given specifications using 555 Timer.

8. To study IV characteristics of PN diode, Zener and Light emitting diode

9. To study the characteristics of a Transistor in CE configuration.

10. To design a CE amplifier of a given gain (mid-gain) using voltage divider bias.

11. To design an inverting amplifier of given gain using Op-amp 741 and study its

frequency response.

12. To design a non-inverting amplifier of given gain using Op-amp 741 and study

its Frequency Response.

13. To study a precision Differential Amplifier of given I/O specification using Op-

amp.

14. To investigate the use of an op-amp as a Differentiator

15. To design a Wien Bridge Oscillator using an op-amp.

Reference Books:

 Basic Electronics: A text lab manual, P.B. Zbar, A.P. Malvino, M.A. Miller, 1994,

Mc-Graw Hill.

 Electronics: Fundamentals and Applications, J.D. Ryder, 2004, Prentice Hall.

 OP-Amps and Linear Integrated Circuit, R. A. Gayakwad, 4th edition, 2000, Prentice

Hall.

 Electronic Principle, Albert Malvino, 2008, Tata Mc-Graw Hill.

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PHYSICS- DSE: ELEMENTS OF MODERN PHYSICS

(Credits: Theory-04, Practicals-02)

Theory: 60 Lectures

Planck’s quantum, Planck’s constant and light as a collection of photons; Photo-electric

effect and Compton scattering. De Broglie wavelength and matter waves; Davisson-

Germer experiment. (8 Lectures)

Problems with Rutherford model- instability of atoms and observation of discrete atomic

spectra; Bohr's quantization rule and atomic stability; calculation of energy levels for

hydrogen like atoms and their spectra. (4 Lectures)

Position measurement- gamma ray microscope thought experiment; Wave-particle

duality, Heisenberg uncertainty principle- impossibility of a particle following a

trajectory; Estimating minimum energy of a confined particle using uncertainty

principle; Energy-time uncertainty principle. (4 Lectures)

Two slit interference experiment with photons, atoms and particles; linear superposition

principle as a consequence; Matter waves and wave amplitude; Schrodinger equation for

non-relativistic particles; Momentum and Energy operators; stationary states; physical

19

interpretation of wavefunction, probabilities and normalization; Probability and

probability current densities in one dimension. 11 Lectures)

One dimensional infinitely rigid box- energy eigenvalues and eigenfunctions,

normalization; Quantum dot as an example; Quantum mechanical scattering and

tunnelling in one dimension - across a step potential and across a rectangular potential

barrier. (12 Lectures)

Size and structure of atomic nucleus and its relation with atomic weight; Impossibility of

an electron being in the nucleus as a consequence of the uncertainty principle. Nature of

nuclear force, NZ graph, semi-empirical mass formula and binding energy.

 (6 Lectures)

Radioactivity: stability of nucleus; Law of radioactive decay; Mean life & half-life; 

decay; decay - energy released, spectrum and Pauli's prediction of neutrino; -ray

emission. (11 Lectures)

Fission and fusion - mass deficit, relativity and generation of energy; Fission - nature of

fragments and emission of neutrons. Nuclear reactor: slow neutrons interacting with

Uranium 235; Fusion and thermonuclear reactions.

 (4 Lectures)

Reference Books:

 Concepts of Modern Physics, Arthur Beiser, 2009, McGraw-Hill

 Modern Physics, John R. Taylor, Chris D. Zafiratos, Michael A.Dubson,2009, PHI

Learning

 Six Ideas that Shaped Physics: Particle Behave like Waves, Thomas A. Moore,

2003, McGraw Hill

 Quantum Physics, Berkeley Physics Course Vol.4. E.H. Wichman, 2008, Tata

McGraw-Hill Co.

 Modern Physics, R.A. Serway, C.J. Moses, and C.A.Moyer, 2005, Cengage

Learning

 Modern Physics, G. Kaur and G.R. Pickrell, 2014, McGraw Hill

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PRACTICALS -DSE-1 LAB: ELEMENTS OF MODERN PHYSICS

60 Lectures

1. To determine value of Boltzmann constant using V-I characteristic of PN diode.

2. To determine work function of material of filament of directly heated vacuum

diode.

3. To determine value of Planck’s constant using LEDs of at least 4 different

colours.

4. To determine the ionization potential of mercury.

5. To determine the wavelength of H-alpha emission line of Hydrogen atom.

6. To determine the absorption lines in the rotational spectrum of Iodine vapour.

20

7. To study the diffraction patterns of single and double slits using laser source and

measure its intensity variation using Photosensor and compare with incoherent

source – Na light.

8. Photo-electric effect: photo current versus intensity and wavelength of light;

maximum energy of photo-electrons versus frequency of light

9. To determine the value of e/m by magnetic focusing.

10. To setup the Millikan oil drop apparatus and determine the charge of an electron.

Reference Books:

 Advanced Practical Physics for students, B.L. Flint & H.T. Worsnop, 1971, Asia

Publishing House.

 Advanced level Physics Practicals, Michael Nelson and Jon M. Ogborn, 4th

Edition, reprinted 1985, Heinemann Educational Publishers

 A Text Book of Practical Physics, Indu Prakash and Ramakrishna, 11th Edition,

2011, Kitab Mahal, New Delhi.

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PHYSICS-DSE: MATHEMATICAL PHYSICS

(Credits: Theory-04, Practicals-02)

Theory: 60 Lectures

The emphasis of the course is on applications in solving problems of interest to

physicists. The students are to be examined entirely on the basis of problems, seen and

unseen.

Calculus of functions of more than one variable: Partial derivatives, exact and inexact

differentials. Integrating factor, with simple illustration. Constrained Maximization

using Lagrange Multipliers. (6 Lectures)

Fourier Series: Periodic functions. Orthogonality of sine and cosine functions, Dirichlet

Conditions (Statement only). Expansion of periodic functions in a series of sine and

cosine functions and determination of Fourier coefficients. Complex representation of

Fourier series. Expansion of functions with arbitrary period. Expansion of non-periodic

functions over an interval. Even and odd functions and their Fourier expansions.

Application. Summing of Infinite Series. (10 Lectures)

Frobenius Method and Special Functions: Singular Points of Second Order Linear

Differential Equations and their importance. Frobenius method and its applications to

differential equations. Legendre, Bessel, Hermite and Laguerre Differential Equations.

Properties of Legendre Polynomials: Rodrigues Formula, Orthogonality. Simple

recurrence relations. (16 Lectures)

Some Special Integrals: Beta and Gamma Functions and Relation between them.

Expression of Integrals in terms of Gamma Functions. Error Function (Probability

Integral). (4 Lectures)

21

Partial Differential Equations: Solutions to partial differential equations, using

separation of variables: Laplace's Equation in problems of rectangular, cylindrical and

spherical symmetry. (10 Lectures)

Complex Analysis: Brief Revision of Complex Numbers and their Graphical

Representation. Euler's formula, De Moivre's theorem, Roots of Complex Numbers.

Functions of Complex Variables. Analyticity and Cauchy-Riemann Conditions.

Examples of analytic functions. Singular functions: poles and branch points, order of

singularity, branch cuts. Integration of a function of a complex variable. Cauchy's

Inequality. Cauchy’s Integral formula.

 (14 Lectures)

Reference Books:

 Mathematical Methods for Physicists: Arfken, Weber, 2005, Harris, Elsevier.

 Fourier Analysis by M.R. Spiegel, 2004, Tata McGraw-Hill.

 Mathematics for Physicists, Susan M. Lea, 2004, Thomson Brooks/Cole.

 An Introduction to Ordinary Differential Equations, Earl A Coddington, 1961, PHI

Learning.

 Differential Equations, George F. Simmons, 2006, Tata McGraw-Hill.

 Essential Mathematical Methods, K.F. Riley and M.P. Hobson, 2011, Cambridge

University Press

 Partial Differential Equations for Scientists and Engineers, S.J. Farlow, 1993, Dover

Publications.

 Mathematical methods for Scientists and Engineers, D.A. McQuarrie, 2003, Viva

Books.

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PRACTICALS -DSE LAB: MATHEMATICAL PHYSICS

60 Lectures

The aim of this course is not just to teach computer programming and numerical

analysis but to emphasize its role in solving problems in Physics.

 Highlights the use of computational methods to solve physical problems

 Use of computer language as a tool in solving physics problems (applications)

 The course will consist of lectures (both theory and practical) in the Computer

Lab

 Evaluation done not on the programming but on the basis of formulating the

problem

 Aim at teaching students to construct the computational problem to be solved

 Students can use anyone operating system Linux or Microsoft Windows

Topics Description with Applications

Introduction and Overview Computer architecture and organization, memory and

Input/output devices