Physics major syllabus gauhati university(G.U): CBCS for Honors

Physics major syllabus gauhati university(G.U): CBCS for Honors: We are all aware that Gauhati University has recently changed its syllabus and made some drastic changes. And new syllabus is very important in order to get good marks. so our team has bought lastes G.U syllabus for CBCS. CBSC is the new form o syllabus by gauhati university.Also get free career guide for the field of physics.

Part I

Physics major syllabus gauhati university:First Semester

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1. PHY-HC-1016

Mathematical Physics 1

Course Outcome: On successful completion of the course students will be able to understand vector

and its applications in various fields, differential equations and its applications, different coordinate

systems, concept of probability and error. Students will also able to solve numerical problems using

computer programming.

1.1 Theory

1.1.1 Vector Calculus

Revision: Properties of vectors under rotations. Scalar product and its invariance under rotations. Vector

prod- uct, Scalar triple product and their interpretation in terms of area and volume respectively. Scalar

and Vector fields. Vector Differentiation: Directional derivatives and normal derivative. Gradient of a

scalar field and its geometrical interpretation. Divergence and curl of a vector field. Del and Laplacian

operators. Vector identities. Vector Integration: Ordinary Integrals of Vectors. Multiple integrals,

Jacobian. Notion of infinitesimal line, surface and volume elements. Line, surface and volume integrals

of Vector fields. Flux of a vector field. Gauss’ divergence theorem, Green’s and Stokes Theorems and

their applications (no rigorous proofs).

1.1.2 First and Second order Differential Equations

First Order and Second Order Differential equations: First Order Differential Equations and Integrating

Factor. Homogeneous Equations with constant coefficients. Wronskian and general solution. Calculus

of functions of more than one variable: Partial derivatives, exact and inexact differentials. Integrating

factor, with simple illustration.

1.1.3 Orthogonal Curvilinear Coordinates

Orthogonal Curvilinear Coordinates. Derivation of Gradient, Divergence, Curl and Laplacian in Carte-sian, Spherical and Cylindrical Coordinate Systems.

1.1.4 Dirac Delta function and its Properties

Definition of Dirac delta function. Representation as limit of a Gaussian function and rectangular

function. Prop- erties of Dirac delta function.

1.1.5 Introduction to Probability

1.1.5 Unit V : Independent random variables: Probability distribution functions; binomial, Gaussian and

Poisson, with examples. Mean and variance.

1.1.6 Theory of Errors

1.1.6 Unit VI : Systematic and Random Errors. Propagation of Errors. Normal Law of Errors. Standard

and Probable Error. Least-squares fit.

1.2 Lab

1.2.1 Aim

The aim of this Lab 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
• The course will consist of lectures (both theory and practical) in the 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 any one operating system Linux or Microsoft Windows

Introduction and Overview Computer architecture and organization, memory and Input/output de-

Vices.Basics of scientific computing Binary and decimal arithmetic, Floating point numbers, algorithms,

Sequence, Se- lection and Repetition, single and double precision arithmetic, underflow & overflow- em-

phasize the importance of making equations in terms of dimensionless variables, Iterative methods

Review of C & C++ Programming fundamentals Introduction to Programming, constants, vari-

ables and data types, operators and Expressions I/O statements, scan f and print f, c in and c out, Manipulators for data formatting, Control statements (decision making and looping statements) (if statement. if-else Statement. Nested if Structure. else-if Statement. Ternary Operator. goto Statement. Switch Statement. Unconditional and Conditional Looping. While Loop. do-while Loop. for Loop. break and continue Statements. Nested Loops), Arrays (1D & 2D) and strings, user defined functions, Structures and Unions, Idea of classes and objects.Programs Sum & average of a list of numbers, largest of a given list of numbers and its location in the list, sorting of numbers in ascending descending order, Binary search ,Random number generation Area of circle, area of square, volume of sphere, value of pi (π) Solution of Algebraic and Transcendental equations by Newton Raphson methods Solution of linear and quadratic equation, solving α = tan α, I = I0(sin α/α).in optics Interpolation by Newton Gre- gory Forward and Backward difference formula Evaluation of trigonometric functions e.g. sin θ, cos θ,tan θ etc. Numerical Integration (Trapezoidal and Simpson rules), Monte Carlo method Given Position with equidistant time data to calculate velocity and acceleration and vice versa. Find the area of B-H Hysteresis loop Solution of Ordinary Differential Equations (ODE) First order Differential equation Eu-ler, modified Euler and Runge-Kutta (RK) second and fourth order methods First order differential equation (a) Radioactive decay (b) Newton’s law of cooling.

2. PHY-HC-1026

Mechanics

Course Outcome: On successful completion of the course students will be able understand Inertial and

non inertial reference frames, Newtonian motion, Galilean transformations, projectile motion, work and

energy, Elastic and inelastic collisions, motion under central force, simple harmonic oscillations, special

theory of relativity. Students will be able to measure different physical constants using formula taught

in theory.

2.1 Theory

2.1.1 Fundamentals of Dynamic

Reference frames. Inertial frames; Review of Newton’s Laws of Motion. Galilean transformations;

Galilean invari- ance. Momentum of variable mass system: motion of rocket. Motion of a projectile in

Uniform gravitational field Dynamics of a system of particles. Centre of Mass. Principle of conservation

of momentum. Impulse.

2.1.2 Work and Energy

Work and Kinetic Energy Theorem. Conservative and non-conservative forces. Potential Energy. Energy

diagram. Stable and unstable equilibrium. Elastic potential energy. Force as gradient of potential energy.

Work & Potential energy. Work done by non-conservative forces. Law of conservation of Energy.

2.1.3 Collisions

Elastic and inelastic collisions between particles. Centre of Mass and Laboratory frames.

2.1.4 Rotational Dynamics

Angular momentum of a particle and system of particles. Torque. Principle of conservation of angular

momentum. Rotation about a fixed axis. Moment of Inertia. Calculation of moment of inertia for rect-

angular, cylindrical and spherical bodies. Kinetic energy of rotation. Motion involving both translation

and rotation.

2.1.5 Elasticity

Relation between Elastic constants. Twisting torque on a Cylinder or Wire. Cantilever.

2.1.6 Fluid Motion

Kinematics of Moving Fluids: Poiseuille’s Equation for Flow of a Liquid through a Capillary Tube.

2.1.7 Gravitation and Central Force Motion

Law of gravitation. Gravitational potential energy. Inertial and gravitational mass. Potential and

field due to spherical shell and solid sphere. Motion of a particle under a central force field. Two-

body problem and its reduction to one-body problem and its solution. The energy equation and energy

diagram. Kepler’s Laws.

2.1.8 Oscillations

SHM: Simple Harmonic Oscillations. Differential equation of SHM and its solution. Kinetic energy,

potential energy, total energy and their time-average values. Damped oscillation. Forced oscillations:

Transient and steady states; Resonance, sharpness of resonance; power dissipation and Quality Factor.

Compound Pendulum.

2.1.9 Non-Inertial Systems

Non-inertial frames and fictitious forces. Uniformly rotating frame. Laws of Physics in rotating coordi-

nate systems. Centrifugal force. Coriolis force and its applications.

2.1.10 Special Theory of Relativity

Michelson-Morley Experiment and its outcome. Postulates of Special Theory of Relativity. Lorentz

Transformations. Simultaneity and order of events. Lorentz contraction. Time dilation. Relativistic

transformation of velocity, frequency and wave number. Relativistic addition of velocities. Variation of

mass with velocity. Massless Particles. Mass-energy Equivalence. Relativistic Doppler effect. Relativistic

Kinematics. Transformation of Energy and Momentum.

2.2 Lab

A minimum of seven experiments to be done.

1. Measurements of length (or diameter) using vernier caliper, screw gauge, Spherometer and travel-

ling micro- scope.

2. To study the Motion of Spring and calculate (a) Spring constant and (b) Rigidity modulus.
3. To determine the Moment of Inertia of a cylinder about two different axes of symmetry by torsional

oscillation method.

4. To determine Coefficient of Viscosity of water by Capillary Flow Method (Poiseuille’s method).
5. To determine the Young’s Modulus of the material of a wire by Searle’s apparatus.
6. To determine the Modulus of Rigidity of a Wire Static method.
7. To determine the value of g using Bar Pendulum.
8. To determine the value of g using Kater’s Pendulum.
9. To determine the height of a building using a Sextant.
10. To determine g and velocity for a freely falling body using Digital Timing Technique.

Part II

Physics major syllabus gauhati university:Second Semester

3. PHY-HC-2016

Electricity & Magnetism

Course Outcome: After successful completion of this course, students will be able to Understand

electric and magnetic fields in matter, Dielectric properties of matter magnetic properties of matter,

electromagnetic induction, applications of Kirchhoff’s law in different circuits, applications of network theorem in circuits. Students will be able to apply the theory in laboratory to measure different electrical parameters associated with electrical circuits.

3.1 Theory

3.1.1 Electric Field and Electric Potential

Electric field: Electric field lines. Electric flux. Gauss’ Law with applications to charge distributions

with spherical, cylindrical and planar symmetry. Conservative nature of Electrostatic Field. Electrostatic Potential. Laplace’s and Poisson equations. The Unique- ness Theorem. Potential and Electric Field of a dipole. Force and Torque on a dipole. Electrostatic energy of system of charges. Electrostatic energy of a charged sphere. Conductors in an electrostatic Field. Surface charge and force on a conductor. Capacitance of a system of charged conductors. Parallel-plate capacitor. Capacitance of an isolated conductor. Method of Images and its application to:

(1) Plane Infinite Sheet and

(2) Sphere.

3.1.2 Dielectric Properties of Matter

Electric Field in matter. Polarization, Polarization Charges. Electrical Susceptibility and Dielectric

Constant. Capacitor (parallel plate, spherical, cylindrical) filled with dielectric. Displacement vector D~ .

Relations between E~ , P~ and D~ . Gauss’ Law in dielectrics.Physics major syllabus gauhati university

3.1.3 Magnetic Field

Magnetic Force on a point charge, definition and properties of magnetic field B~ . Curl and Divergence.

Vector potential A~. Magnetic Force on (1) a current carrying wire (2) between current elements. Torque

on a current loop in a uniform magnetic field. Biot-Savart’s law and its simple application : straight

wire and circular loop. Current loop as a magnetic dipole and its dipole moment (analogy with electric

dipole ) Ampere’s circuital law and its application to

(1) Solenoid

(2) Torus.

3.1.4 Magnetic Properties of Matter

Magnetization vector (M~ ). Magnetic Intensity (H~ ). Magnetic Susceptibility and permeability. Relation

between B~ , H~ , M~ . Ferromagnetism. B-H curve and hysteresis.

3.1.5 Electromagnetic Induction

Faraday’s Law. Lenz’s Law. Self Inductance and Mutual Inductance. Reciprocity Theorem. Energy

stored in a Magnetic Field. Introduction to Maxwell’s Equations. Charge Conservation and Displacement

current.

3.1.6 Electrical Circuits

AC Circuits: Kirchhoff’s laws for AC circuits. Complex Reactance and Impedance. Series LCR Circuit:

(1) Resonance,

(2) Power Dissipation and

(3) 13 Quality Factor,

and (4) Band Width. Parallel LCR

Circuit.

3.1.7 Network Theorems

Ideal Constant-voltage and Constant-current Sources. Network Theorems: Thevenin theorem, Norton

theorem, Superposition theorem, Reciprocity theorem, Maximum Power Transfer theorem. Applications to dc circuits.

3.1.8 Ballistic Galvanometer

Torque on a current Loop. Ballistic Galvanometer: Current and Charge Sensitivity. Electromagnetic

damping. Logarithmic damping. CDR.

3.2 Lab

A minimum of seven experiments to be done.

1. Use a Multimeter for measuring (a) Resistances, (b) AC and DC Voltages, (c) DC Current, (d)

Capacitances and (e) Checking electrical fuses.

2. To study the characteristics of a series RC Circuit.
3. To determine an unknown Low Resistance using Potentiometer.
4. To determine an unknown Low Resistance using Carey Foster’s Bridge.
5. To compare capacitances using De’Sauty’s bridge.
6. Measurement of field strength B~ and its variation in a solenoid (determine dB/dx).
7. To verify the Thevenin and Norton theorems.
8. To verify the Superposition, and Maximum power transfer theorems.
9. To determine self inductance of a coil by Anderson’s bridge.
10. To study response curve of a Series LCR circuit and determine its (a) Resonant frequency, (b)

Impedance at resonance, (c) Quality factor Q, and (d) Band width.

11. To study the response curve of a parallel LCR circuit and determine its (a) Anti- resonant frequency

and (b) Quality factor Q.

12. Measurement of charge and current sensitivity and CDR of Ballistic Galvanometer.
13. Determine a high resistance by leakage method using Ballistic Galvanometer.
14. To determine self-inductance of a coil by Rayleigh’s method.
15. To determine the mutual inductance of two coils by Absolute method.

4. PHY-HC-2026

Waves & Optics

Course Outcome: After successful completion of this course, students will be able to understand

superposition of harmonic oscillations, different types of wave motions, superposition of harmonic waves, interference and interferometer, diffraction, holography. Students will be able to study phenomena like interference and diffraction to measure different properties of the source.

4.1 Theory

4.1.1 Superposition of Collinear Harmonic Oscillations

Linearity and Superposition Principle. Superposition of two collinear oscillations having

(1) Equal frequencies and

(2) Different frequencies (Beats). Superposition of N collinear Harmonic Oscillations with

(1) Equal phase differences and (2) equal frequency differences.

4.1.2 Superposition of Two Perpendicular Harmonic Oscillations

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

4.1.3 Wave Motion

Plane and Spherical Waves. Longitudinal and Transverse Waves. Plane Progressive (Travelling) Waves.

Wave Equation. Particle and Wave Velocities. Differential Equation. Pressure of a Longitudinal Wave.

Energy Transport. Intensity of Wave. Water Waves: Ripple and Gravity Waves.

4.1.4 Velocity of Waves

Velocity of Transverse Vibrations of Stretched Strings. Velocity of Longitudinal Waves in a Fluid in a

Pipe. Newton’s Formula for Velocity of Sound. Laplace’s Correction.

4.1.5 Superposition of Two Harmonic Waves

Standing (Stationary) Waves in a String: Fixed and Free Ends. Analytical Treatment. Phase and Group

Velocities. Changes with respect to Position and Time. Energy of Vibrating String. Transfer of Energy.

Normal Modes of Stretched Strings. Plucked and Struck Strings. Melde’s Experiment. According to Physics major syllabus gauhati university Longitudinal

Standing Waves and Normal Modes. Open and Closed Pipes. Superposition of N Harmonic Waves.

4.1.6 Wave Optics

Electromagnetic nature of light. Definition and properties of wave front. Huygens Principle. Temporal

and Spatial Coherence.

4.1.7 Interference

Division of amplitude and wave front. 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.

4.1.8 Interferometer

Michelson Interferometer-(1) Idea of form of fringes (No theory required), (2) Determination of Wave-

length, (3) Wavelength Difference, (4) Refractive Index. 5. Visibility of fringes. Fabry-Perot interferom-

eter.

4.1.9 Diffraction

Fresnel and Fraunhofer diffraction. Fresnel’s Half-Period Zones for Plane Wave. Explanation of Recti-

linear Propagation of Light. Theory of a Zone Plate: Multiple Foci of a Zone Plate. Fresnel diffraction

pattern of a straight edge and at a circular aperture . Resolving Power of a telescope.

4.1.10 Fraunhofer Diffraction

Single slit. Double slit . Multiple slits. Diffraction grating . Resolving power of grating.

4.1.11 Holography

Principle of Holography. Recording and Reconstruction Method. Theory of Holography as Interference

between two Plane Waves. Point source holograms.

4.2 Lab

A minimum of seven experiments to be done.

1. To determine the frequency of an electric tuning fork by Melde’s experiment and verify λ 2 −T law.
2. To study Lissajous Figures.
3. Familiarization with: Schuster’s focusing, determination of angle of prism.
4. To determine refractive index of the Material of a prism using sodium source.
5. To determine the dispersive power and Cauchy constants of the material of a prism using mercury

source.

6. To determine wavelength of sodium light using Fresnel Biprism.
7. To determine wavelength of sodium light using Newton’s Rings.
8. To determine the thickness of a thin paper by measuring the width of the interference fringes

produced by a wedge-shaped Film.

9. To determine wavelength of (1) Na source and (2) spectral lines of Hg source using plane diffraction

grating.

10. To determine dispersive power and resolving power of a plane diffraction grating.

Part III

Physics major syllabus gauhati university:Third Semester

5. PHY-HC-3016

Mathematical Physics II

5.1 Theory

5.1.1 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, Hermite and Laguerre Differential Equations.

Properties of Legendre Polynomials: Rodrigues Formula, Generating Function, Orthogonality. Simple

recurrence relations. Expansion of function in a series of Legendre Polynomials.

5.1.2 Partial Differential Equations

Solutions to partial differential equations, using separation of variables: Laplace’s Equation in problems

of rect- angular, cylindrical and spherical symmetry. Wave equation and its solution for vibrational

modes of a stretched string, rectangular and circular membranes. Diffusion Equation.

5.1.3 Some Special Integrals

Beta and Gamma Functions and Relation between them. Expression of Integrals in terms of Gamma

Functions.

5.1.4 Matrix

Matrix algebra using index notation, Properties of matrices, Special matrix with their proper- ties:

Transpose matrix, complex conjugate matrix, Hermitian matrix, Anti-Hermitian matrix, special square

matrix, unit matrix, diagonal matrix, co-factor matrix, adjoint of a matrix, self- adjoint matrix, symmetric matrix, anti-symmetric matrix, unitary matrix, orthogonal matrix, trace of a matrix, inverse matrix.

Determinant, Rank, Eigen value, Eigen vector and diagonalisation of matrix.

5.1.5 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.

Application to square and triangular waves.

5.2 Lab

5.2.1 Aim

The aim of this Lab is to use the computational methods to solve physical problems. Course will consist

of lectures (both theory and practical) in the Lab. Evaluation done not on the programming but on the

basis of formulating the problem. Introduction to Numerical computation softwares Introduction to Scilab/Mathematica/Matlab, Advantages and disadvantages, Scilab / Mathematica / Matlab environment, Command window, Figure window, Edit window, Variables and arrays, Initialising variables in Scilab / Mathematica / Matlab, Multidimensional ar- rays, Subarray, Special values, Displaying output data, data file, Scalar and array operations, Hierarchy of operations, Built in Scilab / Mathematica / Matlab functions, Introduction to plotting, 2D and 3D plotting. Curve fttting, Least square ftt, Goodness of ftt, standard deviation Ohms law to calculate R, Hooke’s law to calculate spring constant. Solution of Linear system of equations Solution of Linear system of equations by Gauss elimination method and Gauss Seidal method. Diagonalisation of matrices, Inverse of a matrix, Eigen vectors, eigenvalues prob- lems. Solution of mesh equations of electric circuits (3 meshes) Solution of coupled spring mass systems (3 masses). Generation of Special functions Generation of Special functions using User defined functions in Scilab / Math- ematica / Matlab. Generating and plotting Legendre Polynomials Generating and plotting Hermite function.Physics major syllabus gauhati university.

First order ODE Solution of first order Differential equation Euler, modified Euler and Runge-Kutta

second order methods. First order differential equation (a) Current in RC, LC circuits with DC source

(b) Classical equations of motion.

Second order ODE Second order differential equation. Fixed difference method. Second order Differential Equation

(a) Harmonic oscillator (no friction)

(b) Damped Harmonic oscillator

(c) Over damped

(d) Critical damped. Partial Differential Equation (PDE) Solution of Partial Differential Equation:

(a) Wave equation (b) Heat equation.

6. PHY-HC-3026

Thermal Physics

6.1 Theory

6.1.1 Introduction to Thermodynamics

6.1.2 Zeroth and First Law of Thermodynamics

Extensive and intensive Thermodynamic Variables, Thermodynamic Equilibrium, Zeroth Law of Thermodynamics & Concept of Temperature, Concept of Work & Heat, State Functions, First Law of Thermo  dynamics and its differential form, Internal Energy, First Law & various processes, Applications of First Law: General Relation between CP and CV, Work Done during Isothermal and Adiabatic Processes,Compressibility and Expansion Co-efficient.

6.1.3 Second Law of Thermodynamics

Reversible and Irreversible process with examples. Conversion of Work into Heat and Heat into Work.

Heat Engines. Carnot’s Cycle, Carnot engine & efficiency. Refrigerator & coefficient of performance,

2nd Law of Thermodynamics: Kelvin-Planck and Clausius Statements and their Equivalence. Carnot’s

Theorem. Applications of Second Law of Thermodynamics: Thermodynamic Scale of Temperature and

its Equivalence to Perfect Gas Scale.

6.1.4 Entropy

Concept of Entropy, Clausius Theorem. Clausius Inequality, Second Law of Thermodynamics in terms

of Entropy. Entropy of a perfect gas. Principle of Increase of Entropy. Entropy Changes in Reversible

and Irreversible processes with examples. Entropy of the Universe. Entropy Changes in Reversible and

Irreversible Processes. Principle of Increase of Entropy. Temperature–Entropy diagrams for Carnot’s

Cycle. Third Law of Thermodynamics. Unattainability of Absolute Zero.

6.1.5 Thermodynamic Potentials

Thermodynamic Potentials: Internal Energy, Enthalpy, Helmholtz Free Energy, Gibb’s Free Energy.

Their Definitions, Properties and Applications. Surface Films and Variation of Surface Tension with

Temperature. Magnetic Work, Cooling due to adiabatic demagnetization, First and second order Phase Transitions with examples, Clausius Clapeyron Equation and Ehrenfest equations.

6.1.6 Maxwell’s Thermodynamic Relations

Derivations and applications of Maxwell’s Relations, Maxwell’s Relations:

(1) Clausius Clapeyron equation,

(2) Values of Cp-Cv,

(3) TdS Equations,

(4) Joule-Kelvin coefficient for Ideal and Van der Waal Gases,

(5) Energy equations,

(6) Change of Temperature during Adiabatic Process.

6.1.7 Kinetic Theory of Gases

6.1.8 Distribution of Velocities

Maxwell-Boltzmann Law of Distribution of Velocities in an Ideal Gas and its Experimental Verification.

Doppler Broadening of Spectral Lines and Stern’s Experiment. Mean, RMS and Most Probable Speeds.

Degrees of Freedom. Law of Equipartition of Energy (No proof required). Specific heats of Gases.

6.1.9 Molecular Collisions

Mean Free Path. Collision Probability. Estimates of Mean Free Path. Transport Phenomenon in Ideal

Gases: (1) Viscosity, (2) Thermal Conductivity and (3) Diffusion. Brownian Motion and its Significance.

6.1.10 Real Gases

Behaviors of Real Gases: Deviations from the Ideal Gas Equation. The Virial Equation. Andrew’s

Experiments on CO2 Gas. Critical Constants. Continuity of Liquid and Gaseous State. Vapour and Gas.

Boyle Temperature. Van der Waal’s Equation of State for Real Gases. Values of Critical Constants. Law

of Corresponding States. Comparison with Experimental Curves. P-V Diagrams. Joule’s Experiment.

Free Adiabatic Expansion of a Perfect Gas. Joule-Thomson Porous Plug Experiment. Joule- Thomson

Effect for Real and Van der Waal Gases. Temperature of Inversion. Joule- Thomson Cooling.

6.2 Lab

1. To determine Mechanical Equivalent of Heat, J, by Callender and Barne’s constant flow method.
2. To determine the Coefficient of Thermal Conductivity of Cu by Searle’s Apparatus.
3. To determine the Coefficient of Thermal Conductivity of Cu by Angstrom’s Method.
4. To determine the Coefficient of Thermal Conductivity of a bad conductor by Lee and Charlton’s disc method.
5. To determine the Temperature Coefficient of Resistance by Platinum Resistance Thermometer

(PRT).

6. To study the variation of Thermo-emf of a Thermocouple with Difference of Temperature of its

Two Junctions.

7. To calibrate a thermocouple to measure temperature in a specified Range using

(1) Null Method,

(2) Direct measurement using Op-Amp difference amplifier and to determine Neutral Temperature.

PHY-HC-3036

7.1 Theory

7.1.1 Introduction to CRO

Block Diagram of CRO. Electron Gun, Deflection System and Time Base. Deflection Sensitivity. Applications of CRO: (1) Study of Waveform, (2) Measurement of Voltage, Current, Frequency, and Phase Difference.

7.1.2 Integrated Circuits (qualitative treatment only)

Active & Passive components. Discrete components. Wafer. Chip. Advantages and drawbacks of ICs.

Scale of integration: SSI, MSI, LSI and VLSI (basic idea and definitions only). Classification of ICs.

Examples of Linear and Digital lCs.

7.1.3 Digital Circuits

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

Decimal Conversion. BCD, Octal and Hexadecimal numbers. AND, OR and NOT Gates (realization

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

7.1.4 Boolean Algebra

De Morgan’s Theorems. Boolean Laws. Simplification of Logic Circuit using Boolean Algebra. Funda-

mental Products. Idea of Minterms and Maxterms. Conversion of a Truth table into Equivalent Logic Circuit by

(1) Sum of Products Method and

(2) Karnaugh Map.

7.1.5 Data Processing Circuits

Basic idea of Multiplexers, De-multiplexers, Decoders, Encoders.

7.1.6 Arithmetic Circuits

Binary Addition. Binary Subtraction using 2’s Complement. Half and Full Adders. Half & Full Sub-

tractors, 4-bit binary Adder/Subtractor.

7.1.7 Sequential Circuits

SR, D, and JK Flip-Flops. Clocked (Level and Edge Triggered) Flip-Flops. Preset and Clear operations. Race- around conditions in JK Flip-Flop. M/S JK Flip-Flop.

7.1.8 Timers: IC 555

Block diagram and applications: Astable multivibrator and Monostable multivibrator.

7.1.9 Shift Registers

Serial-in-Serial-out, Serial-in-Parallel-out, Parallel-in-Serial-out and Parallel-in-Parallel-out Shift Registers (only up to 4 bits).

7.1.10 Counters (4 bits)

Ring Counter, Asynchronous counters, Decade Counter. Synchronous Counter.

7.1.11 Computer Organization

Input/Output Devices. Data storage (idea of RAM and ROM). Computer memory. Memory organization

& addressing.

7.1.12 Intel 8085 Microprocessor Architecture

Main features of 8085. Block diagram. Components. Pin-out diagram. Buses. Registers. ALU. Memory.

Stack memory. Timing & Control circuitry.

7.1.13 Introduction to Assembly Language 1 byte, 2 byte, & 3 byte instructions.

7.2 Lab

A minimum of seven experiments to be done.

1. To measure (a) Voltage, and (b) Time period of a periodic waveform using CRO.
2. To test a Diode and Transistor using a Multimeter.
3. To design a switch (NOT gate) using a transistor.
4. To verify and design AND, OR, NOT and XOR gates using NAND gates.
5. To design a combinational logic system for a specified Truth Table.
6. To convert a Boolean expression into logic circuit and design it using logic gate ICs.
7. Half Adder, Full Adder and 4-bit binary Adder.
8. Half Subtractor, Full Subtractor, Adder-Subtractor using Full Adder IC.
9. To build Flip-Flop (RS, Clocked RS, D-type and JK) circuits using NAND gates.
10. To build JK Master-slave flip-flop using Flip-Flop ICs .
11. To build a 4-bit Counter using D-type/JK Flip-Flop ICs and study timing diagram.
12. To make a 4-bit Shift Register (serial and parallel) using D-type/JK Flip-Flop ICs.
13. To design an astable multivibrator of given specifications using 555 Timer.
14. To design a monostable multivibrator of given specifications using 555 Timer. 15. Write the following programs using 8085 Microprocessor

(a) Addition and subtraction of numbers using direct addressing mode

(b) Addition and subtraction of numbers using indirect addressing mode

(c) Multiplication by repeated addition

(d) Division by repeated subtraction

(e) Handling of 16-bit Numbers

(f) Use of CALL and RETURN Instruction

(g) Block data handling

Part IV

Physics major syllabus gauhati university:Fourth Semester

8. PHY-HC-4016

Mathematical Physics III

8.1 Theory

8.1.1 Complex Analysis

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

functions. Singular functions: poles and branch points, order of singularity.

8.1.2 Complex Integration

Integration of a function of a complex variable. Cauchys Integral formula. Simply and multiply

connected region. Laurent and Taylors expansion. Residues and Residue Theorem with numerical

application.

8.1.3 Fourier Transforms

Fourier Transforms: Fourier Integral theorem. Fourier Transform. Examples. Fourier trans- form of trigonometric, Gaussian functions Representation of Dirac delta function as a Fourier Integral. Fourier

Transform of derivatives, Inverse Fourier transform, Convolution theorem (Statement only). Properties

Of Fourier transforms (translation, change of scale, complex conjugation).

8.1.4 Laplace Transforms

Laplace Transform (LT) of Elementary functions. Properties of LTs: Change of Scale Theorem, Shifting

Theorem. LTs of 1st and 2nd order Derivatives and Integrals of Functions, Derivatives and Integrals

of LTs. LT of Unit Step function, Dirac Delta function, Periodic Functions. Convolution Theorem

(Statement only). Inverse LT. Application of Laplace Transforms to 2nd order Differential Equations: Damped Harmonic Oscillator.

8.1.5 Tensor Algebra

Introduction to tensor, Transformation of co-ordinates, Einsteins summation convention. contravariant

and co- variant tensor, tensorial character of physical quantities, symmetric and antisymmetric tensors,

kronecker delta, Levi-Civita tensor. Quotient law of tensors, Raising and lowering of indices Rules for

combination of tensors- addition, subtraction, outer multiplication, contraction and inner multiplications.

8.2 Lab

1. Solve differential equation

dx

dy = e

−x with y = 0 for x = 0

dx

dy + e

−x

y = x

d

2x

dy2

+ 2

dy

dxe

−x

y = −y

d

2x

dy2

+ e

−t

dy

dxe

−x

y = −y

2. Dirac Delta Function

Evaluate the integral I

I =

1

√

2πσ2

Z

exp

−

(x − 2)2

2σ

2

(x + 3)dx, forσ = 1, 0.1, 0.01

and show the I → 5

3. Fourier Series

Make a program to evaluate

X∞

n=1

(0.2)n

Evaluate the Fourier coefficients of a given periodic function (square wave)

4. Frobenius method and Special functions

Evaluate

Z 1

−1

Pn(μ)Pm(μ)dμ = δn,m.

Plot Pn(x), jν(x) and show the recursion relation.

5. Calculation of error for each data point of observations recorded in experiments done in previous

semesters (choose any two).

6. Calculation of least square fitting manually without giving weightage to error. Confirmation of

least square fitting of data through computer program.

7. Evaluation of trigonometric functions e.g. sin θ, given Bessel’s function at N points find its value

at an intermediate point.

8. Integrate

1

(x

2 + 1)

numerically in a given interval.

9. Compute the nth roots of unity forn = 2, 3, and 4.
10. Find the two square roots of 5 + 12j.
11. Integral transform

Evaluate FFT of e

−x

2

.

12. Solve Kirchoff’s Current law for any node of an arbitrary circuit using Laplace’s transform.

9. PHY-HC-4026

Elements of Modern Physics

9.1 Theory

9.1.1 Quantum Theory and Blackbody Radiation

Quantum theory of light; photo-electric effect and Compton scattering. De Broglie wavelength and

matter waves; Davisson-Germer experiment. Wave description of particles by wave packets. group and

phase velocities and relation between them. Two-slit experiment with electrons. Probability. wave

amplitude and wave functions.

9.1.2 Uncertainty and Wave-Particle Duality

Position measurement : gamma ray microscope thought experiment; wave-particle duality, Heisenberg

uncertainty principle (Uncertainty relations involving Canonical pair of variables): Derivation from wave

packets, impossibility of a particle following a trajectory; estimating minimum energy of a confined

particle using uncertainty principle; energy-time uncertainty principle- application to virtual particles

and range of an interaction.

9.1.3 Schrödinger Equation

Two slit interference experiment with photons, atoms and particles; linear superposition principle as a consequence; Matter waves and wave amplitude; Schrödinger equation for non- relativistic particles; momentum and energy operators; stationary states; physical interpretation of a wave function, probabilities and normalization; probability and probability current densities in one dimension.

9.1.4 One-dimensional Box and Step Barrier

One dimensional infinitely rigid box- energy eigenvalues and eigen functions, normalization; quantum dot as example; quantum mechanical scattering and tunnelling in one dimension-across a step potential and rectangular potential barrier.

9.1.5 Structure of the Atomic Nucleus

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, N Z graph,

liquid drop model: semi-empirical mass formula and binding energy, nuclear shell model (qualitative

discussions) and magic numbers.

9.1.6 Radioactivity

Alpha decay. Beta decay energy released, spectrum and Pauli’s prediction of neutrino. Gamma ray

emission, energy- momentum conservation: electron-positron pair creation by gamma photons in the

vicinity of a nucleus.

9.1.7 Fission and Fusion

Mass deficit, Einstein’s mass-energy equivalence principle and generation of nuclear energy. Fission –

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

235. Fusion and thermonuclear reactions driving stellar energy (brief qualitative discussions).

9.1.8 Lasers

Einstein’s A and B coefficients. Metastable states. Spontaneous and Stimulated emissions. Optical

Pumping and Population Inversion. Three-Level and Four-Level Lasers. Ruby Laser and He-Ne Laser.

Basic lasing.

9.2 Lab

A minimum of seven experiments to be done..

1. Measurement of Planck’s constant using black body radiation and photo-detector. Photo-electric Effect.
2. Photo current versus intensity and wavelength of light; maximum energy of photo-electrons versus

frequency of light.

3. To determine work function of material of filament of directly heated vacuum diode.
4. To determine the Planck’s constant using LEDs of at least 4 different colours.
5. To determine the wavelength of H – α emission line of hydrogen atom.
6. To determine the ionization potential of mercury.
7. To determine the absorption lines in the rotational spectrum of iodine vapour.
8. To determine the value of e/m by (a) magnetic focusing or (b) bar magnet.
9. To setup the Millikan oil drop apparatus and determine the charge of an electron.
10. To show the tunneling effect in tunnel diode using I — V characteristics.
11. To determine the wavelength of laser source using diffraction of single slit.
12. To determine the wavelength of laser source using diffraction of double slits.
13. To determine (1) wavelength and (2) angular spread of He-Ne laser using plane diffraction grating.

Gauhati High Court question paper

10. PHY-HC-4036

Analog Systems & Applications

10.1 Theory

10.1.1 Semiconductor Diodes

P and N type semiconductors. Energy Level Diagram. Conductivity and Mobility, Concept of Drift

velocity. PN Junction Fabrication (Simple Idea). Barrier Formation in PN Junction Diode. Static and

Dynamic Resistance. Current Flow Mechanism in Forward and Reverse Biased Diode. Drift Velocity.

Derivation for Barrier Potential, Barrier Width and Current for Step Junction. Current flow mechanism

in Forward and Reverse Biased Diode.

10.1.2 Two-terminal Devices and their Applications

(1) Rectifier Diode: Half- wave Rectifiers. Centre-tapped and Bridge Full-wave Rectifiers, Calculation

of Ripple Factor and Rectification Efficiency, C-filter (2) Zener Diode and Voltage Regulation. Principle

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

10.1.3 Bipolar Junction Transistors

n-p-n and p-n-p Transistors. Characteristics of CB, CE and CC Configurations. Current gains α and

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

Mechanism of Current Flow. Active, Cutoff and Saturation Regions.

10.1.4 Amplifiers

Transistor Biasing and Stabilization Circuits. Fixed Bias and Voltage Divider Bias. Transistor as 2-port

Network. h-parameter Equivalent Circuit. Analysis of a single-stage CE amplifier using Hybrid Model.

Input and Output Impedance. Current, Voltage and Power Gains. Classification of Class A, B & C

Amplifiers.

10.1.5 Coupled Amplifier

Two stage RC-coupled amplifier and its frequency response.

10.1.6 Feedback in Amplifiers

Effects of Positive and Negative Feedback on Input Impedance, Output Impedance, Gain, Stability, Distortion and Noise.

10.1.7 Sinusoidal Oscillators

Barkhausen’s Criterion for self-sustained oscillations. RC Phase shift oscillator, determination of Frequency. Hartley & Colpitts oscillators.

10.1.8 Operational Amplifiers (Black Box approach)

Characteristics of an Ideal and Practical Op-Amp. (IC 741) Open-loop and Closed-loop Gain. Frequency

Response. CMRR. Slew Rate and concept of Virtual ground.

10.1.9 Applications of Op-Amps

(1) Inverting and non-inverting amplifiers, (2) Adder, (3) Subtractor, (4) Differentiator, (5) Integrator,

(6) Log am- plifier, (7) Zero crossing detector (8) Wein bridge oscillator. (9 Lectures) Conversion: Re-

sistive network (Weighted and R — 2R Ladder). Accuracy and Resolution. A/D Conversion (successive approximation).

10.2 Lab

A minimum of eight experiments to be done.

1. To study V — I characteristics of PN junction diode, and Light emitting diode.
2. To study the V — I characteristics of a Zener diode and its use as voltage regulator.
3. Study of V — I & power curves of solar cells, and find maximum power point & efficiency.
4. To study the characteristics of a Bipolar Junction Transistor in CE configuration.
5. To study the various biasing configurations of BJT for normal class A operation.
6. To design a CE transistor amplifier of a given gain (mid-gain) using voltage divider bias.
7. To study the frequency response of voltage gain of a RC-coupled transistor amplifier.
8. To design a Wien bridge oscillator for given frequency using an op-amp.
9. To design a phase shift oscillator of given specifications using BJT.
10. To study the Colpitt’s oscillator.
11. To design a digital to analog converter (DAC) of given specifications.
12. To study the analog to digital convertor (ADC) IC.
13. To design an inverting amplifier using Op-amp (741/351) for dc voltage of given gain .
14. To design inverting amplifier using Op-amp (741/351) and study its frequency response.
15. To design non-inverting amplifier using Op-amp (741/351) & study its frequency response.
16. To study the zero-crossing detector and comparator.
17. To add two dc voltages using Op-amp in inverting and non-inverting mode.
18. To design a precision Differential amplifier of given I/O specification using Op-amp.
19. To investigate the use of an op-amp as an Integrator.
20. To investigate the use of an op-amp as a Differentiator.

Part V

Physics major syllabus gauhati university:Fifth Semester

11. PHY-HC-5016

Quantum Mechanics & Applications

11.1 Theory

11.1.1 Time Dependent Schrödinger Equation (Lectures 06)

Time dependent Schrödinger equation and dynamical evolution of a quantum state, properties of wave

function. Interpretation of wave function. Probability and probability current densities in three dimen-

sions. Conditions for physical acceptability of wave functions. Normalization. Linearity and Superposi-

tion Principles. Eigenvalues and eigenfunctions. Position, momentum and energy operators; commutator

of position and momentum operators. Expectation values of position and momentum. wave function of

a free particle.

11.1.2 Time Independent Schrödinger Equation (Lectures 10)

Hamiltonian, stationary states and energy eigenvalues; expansion of an arbitrary wave function as a linear

com- bination of energy eigenfunctions; General solution of the time dependent Schrödinger equation in

terms of linear combinations of stationary states; Application to spread of Gaussian wave-packet for a

free particle in one di- mension; wave packets, Fourier transforms and momentum space wave function;

Position-momentum uncertainty principle.

11.1.3 Bound States

Continuity of wave function, boundary condition and emergence of discrete energy levels; application

to one- dimensional problem-square well potential; Quantum mechanics of simple harmonic oscillator-

energy levels and energy eigenfunctions using Frobenius method; Hermite polynomials; ground state, zero point energy & uncertainty principle.

11.1.4 Hydrogen-like Atoms

Time independent Schrödinger equation in spherical polar coordinates; separation of variables for second order partial differential equation; angular momentum operator & quantum numbers; Radial wave,functions from Frobenius method; shapes of the probability densities for ground & first excited states;Orbital angular momentum quantum numbers l and m; s, p, d, . . . shells.

11.1.5 Atoms in Electric & Magnetic Fields

Electron angular momentum. Space quantization. Electron Spin and Spin Angular Momentum. Larmor’s

Theorem. Spin Magnetic Moment. Stern-Gerlach Experiment. Electron Magnetic Moment and Magnetic

Energy, Gyromag- netic Ratio and Bohr Magneton. Zeeman Effect: Normal and Anomalous Zeeman

Effect. Paschen-Back Effect and Stark Effect (Qualitative Discussion only).

11.1.6 Many Electron Atoms

Pauli’s Exclusion Principle. Symmetric & Antisymmetric W ave Functions. Periodic table. Fine structure. Spin orbit coupling. Spectral Notations for Atomic States. Total angular momentum. Vector

Model. Spin-orbit coupling in atoms: L S and J J couplings. Hund’s Rule. Term symbols. Spectra of

Hydrogen and Alkali Atoms (Na etc.).

11.2 Lab

Use C/C++/Scilab/FORTRAN/Mathematica for solving the following problems based on Quantum Mechanics.

1. Solve the s-wave Schrödinger equation for the ground state and the first excited state of the

hydrogen atom

d

2y

dx2

= A(r)u(r), A(r) = 2m

̄h

2

e

2

r

,

were, m is the reduced mass of the electron. Obtain the energy eigenvalues and plot the corre-

sponding wave functions. Remember that the ground state energy of the hydrogen atom is ≈ −13.6

eV. Take e = 3.795 (eVA ̊),  ̄hc = 1973(eV A ̊) and m = 0.511 × 106

eV /c2

.

2. Solve the s-wave radial Schrödinger equation for an atom

d

2y

dx2

= A(r)u(r), A(r) = 2m

̄h

2

where m is the reduced mass of the system (which can be chosen to be the mass of an electron),

for the screened Coulomb potential

V (r) = −

e

2

r

e

−r/a

Find the energy (in eV) of the ground state of the atom to an accuracy of three significant digits.

Also, plot the corresponding wave function. Take e = 3.795 (eVA ̊), and a = 3A,  ̊ 5A,  ̊ and7A ̊ in the

units of  ̄hc= 1973 (eVA ̊). m = 0.511×106

eV/c2

. The ground state energy is expected to be above

−12 eV in all three cases.

3. Solve the s-wave radial Schrödinger equation for a particle of mass m

d

2y

dx2

= A(r)u(r), A(r) = 2m

̄h

2

The anharmonic potential

V (r) = 1

2

kr2 +

1

3

br3

for the ground state energy (in MeV) of particle to an accuracy of three significant digits. Also,

plot the corresponding wave function. Choose m = 940 MeV/c2

, k = 100 MeV fm−2

, b = 0, 10,

30 MeV fm−3

. In these units, c ̄h = 197.3 MeV fm. The ground state energy I is expected to lie in

between 90 and 110 MeV for all three cases.

4. Solve the s-wave radial Schrödinger equation for the vibration of hydrogen molecule

d

2y

dx2

= A(r)u(r), A(r) = 2μ

̄h

2

where μ is the reduced mass of the two-atom system for the Morse potential

V (r) = D(e

−2αr0

− e

−αr0

), r0 =

r − r0

r

.

Find the lowest vibrational energy (in MeV) of the molecule to an accuracy of thee significant

digits. Also plot the corresponding wave function. Take m = 940×106

eV/c2

, D = 0.755501eV, α

= 1.44, and r0 = 0.131349A ̊.

43

Laboratory based experiments (Optional)

5. Study of electron spin resonance – determine magnetic field as a function of the resonance frequency.
6. Study of Zeeman effect – with external magnetic field; hyperfine splitting.
7. To show the tunneling effect in tunnel diode using I ! V characteristics.
8. Quantum efficiency of CCDs.

12. PHY-HC-5026

Solid State Physics

12.1 Theory

12.1.1 Crystal Structure

Amorphous and Crystalline Materials. Lattice Translation Vectors. Symmetry operations, Lattice with

a Basis – Central and Non-Central Elements. Unit Cell. Miller Indices. Reciprocal Lattice. Types of

Lattices. Brillouin Zones. Diffraction of X-rays by Crystals. Bragg’s Law. Atomic and Geometrical

Factor.

12.1.2 Elementary Lattice Dynamics

Lattice Vibrations and Phonons: Linear Monoatomic and Diatomic Chains. Acoustical and Optical

Phonons. Qualitative Description of the Phonon Spectrum in Solids. Dulong and Petit’s Law, Einstein

and Debye theories of specific heat of solids. T 3 law.

12.1.3 Magnetic Properties of Matter

Dia, Para, Ferri, and Ferromagnetic Materials. Classical Langevin Theory of Dia and Paramagnetic

Domains. Quantum Mechanical Treatment of Paramagnetism. Curie’s law, Weiss’s Theory of Ferromag-

netism and Ferromag- netic Domains. Discussion of B — H Curve. Hysteresis and Energy Loss.

12.1.4 Dielectric Properties of Materials, Polarization. Local Electric Field at an Atom. Depolarization Field. Electric Susceptibility. Polariz ability. Clausius Mosotti Equation. Classical Theory of Electric Polarizability. Normal and Anomalous Dispersion. Cauchy and Sellmeir relations. Langevin-Debye equation. Complex Dielectric Constant.

Optical Phenomena. Application: Plasma Oscillations, Plasma Frequency, Plasmons, T0 modes.

12.1.5 Ferroelectric Properties of Materials

Structural phase transition, Classification of crystals, Piezoelectric effect, Pyroelectric effect, Ferroelectric effect, Electrostrictive effect, Curie-Weiss Law, Ferroelectric domains, PE hysteresis loop.

12.1.6 Free Electron Theory of Metals

electrical and thermal conductivity of metals, Wiedemann-Franz law. Elementary band theory: Kronig

Penny model. Band Gap. Conductor, Semiconductor (P and N type) and insulator. Conductivity of

Semiconductor, mobility, Hall Effect. Measurement of conductivity (4-probe method) & Hall coefficient.

12.1.7 Superconductivity

Experimental Results. Critical Temperature. Critical magnetic field. Meissner effect. Type I and type

II Super- conductors, London’s Equation and Penetration Depth. Isotope effect. Idea of BCS theory

(No derivation).

12.2 Lab

A minimum of five experiments to be done.

1. Measurement of susceptibility of paramagnetic solution (Quinck’s Tube Method).
2. To measure the Magnetic susceptibility of Solids.
3. To determine the Coupling Coefficient of a Piezoelectric crystal.
4. To measure the Dielectric Constant of a dielectric Materials with frequency.
5. To determine the complex dielectric constant and plasma frequency of metal using Surface Plasmon

resonance (SPR).

6. To determine the refractive index of a dielectric layer using SPR.
7. To study the PE Hysteresis loop of a Ferroelectric Crystal.
8. To draw the BH curve of Fe using Solenoid & determine energy loss from Hysteresis.
9. To measure the resistivity of a semiconductor (Ge) with temperature by four-probe method (room

temperature to 150C) and to determine its band gap.

10. To determine the Hall coefficient of a semiconductor sample.

Part VI

Physics major syllabus gauhati university:Sixth Semester

49

13. PHY-HC-6016

Electromagnetic Theory

13.1 Theory

13.1.1 Maxwell Equations

Review of Maxwell’s equations. Displacement Current. Vector and Scalar Potentials. Gauge Trans-

formations: Lorentz and Coulomb Gauge. Boundary Conditions at Interface between Different Media.

Wave Equations. Plane Waves in Dielectric Media. Poynting Theorem and Poynting Vector. Electro-

magnetic (EM) Energy Density. Physical Concept of Electromagnetic Field Energy Density, Momentum

Density and Angular Momentum Density.

13.1.2 EM Wave Propagation in Unbounded Media

Plane EM waves through vacuum and isotropic dielectric medium, transverse nature of plane EM waves,

refractive index and dielectric constant, wave impedance. Propagation through conducting media, re-

laxation time, skin depth. Wave propagation through dilute plasma, electrical conductivity of ionized

gases, plasma frequency, refractive index, skin depth, application to propagation through ionosphere.

13.1.3 EM Wave in Bounded Media

Boundary conditions at a plane interface between two media. Reflection & Refraction of plane waves

at plane interface between two dielectric media-Laws of Reflection & Refraction. Fresnel’s Formulae

for perpendicular & parallel polarization cases, Brewster’s law. Reflection & Transmission coefficients.

Total internal reflection, evanescent waves. Metallic reflection (normal Incidence).

13.1.4 Polarization of Electromagnetic Waves

Description of Linear, Circular and Elliptical Polarization. Propagation of E.M. Waves in Anisotropic

Media. Symmetric Nature of Dielectric Tensor. Fresnel’s Formula. Uniaxial and Biaxial Crystals. Light

Propagation in Uniaxial Crystal. Double Refraction. Polarization by Double Refraction. Nicol Prism.

Ordinary & extraordinary refractive indices. Production & detection of Plane, Circularly and Elliptically

Polarized Light. Phase Retardation Plates: Quarter-Wave and Half-Wave Plates. Babinet Compensator

and its Uses. Analysis of Polarized Light.

13.1.5 Rotatory Polarization

Optical Rotation. Biot’s Laws for Rotatory Polarization. Fresnel’s Theory of optical rotation. Calcu-

lation of angle of rotation. Experimental verification of Fresnel’s theory. Specific rotation. Laurent’s

half-shade polarimeter.

13.1.6 Wave Guides

Planar optical wave guides. Planar dielectric wave guide. Condition of continuity at interface. Phase

shift on total reflection. Eigenvalue equations. Phase and group velocity of guided waves. Field energy

and Power transmission.

13.1.7 Optical Fibres

Numerical Aperture. Step and Graded Indices (Definitions Only). Single and Multiple Mode Fibres

(Concept and Definition Only).

13.2 Lab

A minimum of seven experiments to be done.

1. To verify the law of Malus for plane polarized light.
2. To determine the specific rotation of sugar solution using Polarimeter.
3. To analyze elliptically polarized Light by using a Babinet’s compensator.
4. . To study dependence of radiation on angle for a simple Dipole antenna.
5. To determine the wavelength and velocity of ultrasonic waves in a liquid (Kerosene Oil, Xylene,

etc.) by studying the diffraction through ultrasonic grating.

6. To study the reflection, refraction of microwaves.
7. To study Polarization and double slit interference in microwaves.
8. To determine the refractive index of liquid by total internal reflection using Wollaston’s air-film.
9. To determine the refractive Index of (1) glass and (2) a liquid by total internal reflection using a

Gaussian eyepiece.

10. To study the polarization of light by reflection and determine the polarizing angle for air-glass

interface.

11. To verify the Stefan’s law of radiation and to determine Stefan’s constant.
12. To determine the Boltzmann constant using V — I characteristics of PN junction diode.
13. PHY-HC-6026

Physics major syllabus gauhati university:Statistical Mechanics

14.1 Theory

14.1.1 Classical Statistics

Macrostate & Microstate, Elementary Concept of Ensemble, Phase Space, Entropy and Thermodynamic

Probability, Maxwell-Boltzmann Distribution Law, Partition Function, Thermodynamic Functions of an

Ideal Gas, Classical Entropy Expression, Gibbs Paradox, Sackur Tetrode equation, Law of Equipartition

of Energy (with proof) – Applications to Specific Heat and its Limitations, Thermodynamic Functions

of a Two-Energy Levels System, Negative Temperature.

14.1.2 Classical Theory of Radiation

Properties of Thermal Radiation. Blackbody Radiation. Pure temperature dependence. Kirchhoff’s law.

Stefan- Boltzmann law: Thermodynamic proof. Radiation Pressure. Wien’s Displacement law. Wien’s

Distribution Law. Saha’s Ionization Formula. Rayleigh-Jean’s Law. Ultraviolet Catastrophe.

14.1.3 Quantum Theory of Radiation

Spectral Distribution of Black Body Radiation. Planck’s Quantum Postulates. Planck’s Law of Black-

body Radi- ation: Experimental Verification. Deduction of (1) Wien’s Distribution Law, (2) Rayleigh-

Jeans Law, (3) Stefan- Boltzmann Law, (4) Wien’s Displacement law from Planck’s law.

14.1.4 Bose-Einstein Statistics

B-E distribution law, Thermodynamic functions of a strongly Degenerate Bose Gas, Bose Einstein con-

densation, properties of liquid He (qualitative description), Radiation as a photon gas and Thermody-

namic functions of photon gas. Bose derivation of Planck’s law.

14.1.5 Fermi-Dirac Statistics

Fermi-Dirac Distribution Law, Thermodynamic functions of a Completely and strongly Degenerate Fermi

Gas, Fermi Energy, Electron gas in a Metal, Specific Heat of Metals, Relativistic Fermi gas, White Dwarf

Stars, Chandrasekhar Mass Limit.

14.2 Lab

Use C/C++/Scilab/other numerical simulations for solving the problems based on Statistical Mechanics.

1. Computational analysis of the behavior of a collection of particles in a box that satisfy Newtonian

mechanics and interact via the Lennard-Jones potential, varying the total number of particles N

and the initial conditions:

(a) Study of local number density in the equilibrium state (i) average; (ii) fluctuations.

(b) Study of transient behaviour of the system (approach to equilibrium).

(c) Relationship of large N and the arrow of time.

(d) Computation of the velocity distribution of particles for the system and comparison with the

Maxwell velocity distribution.

(e) Computation and study of mean molecular speed and its dependence on particle mass.

(f) Computation of fraction of molecules in an ideal gas having speed near the most probable speed

2. Computation of the partition function Z(β) for examples of systems with a finite number of single

particle levels (e.g., 2 level, 3 level, etc.) and a finite number of non-interacting particles N under

Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics: (a) Study of how Z(β), average

energy hEi , energy fluctuation ∆E, specific heat at constant volume Cv, depend upon the tem-

perature, total number of particles N and the spectrum of single particle states.

(b) Ratios of occupation numbers of various states for the systems considered above.

(c) Computation of physical quantities at large and small temperature T and comparison of various

statistics at large and small temperature T .

3. Plot Planck’s law for Black Body radiation and compare it with Raleigh-Jeans Law at high tem-

perature and low temperature.

4. Plot Specific Heat of Solids (a) Dulong-Petit law, (b) Einstein distribution function, (c) Debye

distribution function for high temperature and low temperature and compare them for these two

cases.

5. Plot the following functions with energy at different temperatures

(a) Maxwell-Boltzmann distribution

(b) Fermi-Dirac distribution

(c) Bose-Einstein distribution