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Physics (Optional) Syllabus for Preliminary Examination
1. Mechanics and Waves
Dimensional analysis. Newtons laws of motion and applications, variable
mass systems, projectiles. Rotational dynamics-kinetic energy, angular
momentum, theorems of moment of intertia and calculations in simple cases.
Conservative forces, frictional forces. Gravitaional poten
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tial and intensity
due to spherical objects. Central forces, Keplers problem, escape velocity
and artificial satellites (including GPS). Streamline motion, viscosity,
Poiseuilles equation. Applications of Bernoullis equation and Stokes law.
Special relativity and Lorentz transformation-length contraction, time
dilation, mass-energy relation.
Simple harmonic motion, Lissajous figures. Damped oscillation, forced
oscillation and resonance. Beats, Phase and group velocities. Stationary
waves, vibration of strings and air columns, longitudinal waves in solids.
Doppler effect. Ultrasonics and applications. 2. Geometrical and Physical Optics.
Laws of reflection and refraction from Fermats principle. Matrix method in
paraxial optics- thin lens formula, nodal planes, system of two thin lenses.
Chromatic and spherical aberrations. Simple optical instruments-magnifier,
eyepieces, telescopes and microscopes.
Huygens principle-reflection and refraction of waves. Interference of
light-Youngs experiment, Newtons rings, interference by thin films,
Michelson interferometer. Fraunhofer diffraction-single slit, double slit,
diffraction grating, resolving power. Fresnel diffraction-half-period zones
and zone plate. Production and detection of linearly, circularly and
elliptically polarised light. Double refraction, quarter-waves plates and
half-wave plates. Polarizing sheets. Optical activity and applications.
Rayleigh scattering and applications.
Elements of fibre optics-attenuation; pulse dispersion in step index and
parabolic index fibres; material dispersion. Lasers, characteristics of
laser light-spatial and temporal coherence. Focussing of laser beams and
applciations. 3. Heat and Thermodynamics
Thermal equilibrium and temperature. The zeroth law of thermodynamics. Heat
and the first law of thermodynamics. Efficiency of Carnot engines. Entropy
and the second law of thermodynamics. Kinetic theory and the equation of
state of an ideal gas. Mean free path, distribution of molecular speeds and
energies. Trasport phenomena. Andrews experiements-van der Waals equation
and applications. Joule-Kelvin effect and applications. Brownian motion.
Thermodynamic potentials-Maxwell relations. Phase transitions. Kirchhoffs
laws. Black-body radiation-Stefan-Boltzmann law, spectral radiancy, Wien
displacement law, application to the cosmic microwave background radiation,
Planck radiation law. 4. Electricity and Magnetism
Electric charge, Coulombs law, electric field, Gauss law. Electric
potential, van de Graff accelerator. Capacitors, dielectrics and
polarization. Ohms law, Kirchhoffs first and second rules, resistors in
series and parallel, applications to two-loop circuits. Magnietic
field-Gausslaw for magnetism, atomic and nuclear magnetism, magnetic
susceptibility, classification of magnetic materials. Cirulating charges,
cyclotron, synchrotron. Hall effect. Biot-Savart law, Amperes law,
Faradays law of induction., Lenzs law. Inductance. Alternating current
circuits-RC, LR, single-loop LRC circuits, impedance, resonance, power in AC
circuits. Displacement current, Maxwells equations (MKS units),
electromagnetic waves, energy transport and Poynting vector. 5. Atomic and Nuclear Physics
Photoelectric effect, Einsteins photon theory. Bohrs theory of hydrogen
atom. Stern-Gerlach experiment, quantisation of angular momentum, electron
spin. Pauli exclusion principle and applications. Zeeman effect. X-ray
spectrum, Braggs law, Bohrs theory of the Mosley plot. Compton effect,
Compton wavelength. Wave nature of matter, de Broglie wavelength,
wave-particle duality. Heisenbergs uncertainty relationships.
Schroedingers equation-eigenvalues and eigenfunctions of (i) particle in a
box, (ii) simple harmonic oscillator and (iii) hydrogen atom. Potential step
and barrier penetration. Natural and artificial radioactivity. Binding
energy of nuclei, nuclear fission and fusion. Classification of elementary
particles and their interactions. 6. Electronics
Diodes in half-waves and full-wave rectification, qualitative ideas of
semiconductors, p type and n type semiconductors, junction diode, Zener
diode, transistors, binary numbers, Logic gates and truth tables, Elements
of microprocessors and computers.
Physics (Optional) Syllabus for Main Examination
Paper-I
Section-A
1. Classical Mechanics (a) Particle dynamics
Centre of mass and laboratory coordinates, conservation of linear and
angular momentum. The rocket equation. Rutherford scattering, Galilean
transformation, intertial and non-inertial frames, rotating frames,
centrifugal and Coriolis forces, Foucault pendulum. (b) System of particles
Constraints, degrees of freedom, generalised coordinates and momenta.
Lagranges equation and applications to linear harmonic oscillator, simple
pendulum and central force problems. Cyclic coordinates, Hamilitonian
Lagranges equation from Hamiltons principle. (c) Rigid body dynamics
Eulerian angles, inertia tensor, principal moments of inertia. Eulers
equation of motion of a rigid body, force-free motion of a rigid body.
Gyroscope. 2. Special Relativity, Waves & Geometrical Optics
(a) Special Relativity
Michelson-Morley experiment and its implications. Lorentz
transformations-length contraction, time dilation, addition of velocities,
aberration and Doppler effect, mass-energy relation, simple applications to
a decay process. Minkowski diagram, four dimensional momentum vector.
Covariance of equations of physics.
(b) Waves
Simple harmonic motion, damped oscillation, forced oscillation and
resonance. Beats. Stationary waves in a string. Pulses and wave packets.
Phase and group velocities. Reflection and Refraction from Huygens
principle.
(c) Geometrical Optics
Laws of relfection and refraction from Fermats principle. Matrix method in
paraxial optic-thin lens formula, nodal planes, system of two thin lenses,
chromatic and spherical aberrations. 3. Physical Optics
(a) Interference
Interference of light-Youngs experiment, Newtons rings, interference by
thin films, Michelson interferometer. Multiple beam interference and
Fabry-Perot interferometer. Holography and simple applications.
(b) Diffraction
Fraunhofer diffraction-single slit, double slit, diffraction grating,
resolving power. Fresnel diffraction: - half-period zones and zones plates.
Fresnel integrals. Application of Cornus spiral to the analysis of
diffraction at a straight edge and by a long narrow slit. Diffraction by a
circular aperture and the Airy pattern.
(c) Polarisation and Modern Optics
Production and detection of linearly and circularly polarised light. Double
refraction, quarter wave plate. Optical activity. Principles of fibre optics
attenuation; pulse dispersion in step index and parabolic index fibres;
material dispersion, single mode fibres. Lasers-Einstein A and B
coefficients. Ruby and He-Ne lasers. Characteristics of laser light-spatial
and temporal coherence. Focussing of laser beams. Three-level scheme for
laser operation.
Section-B 4. Electricity and Magnetism
(a) Electrostatics and Magnetostatics
Laplace ad Poisson equations in electrostatics and their applications.
Energy of a system of charges, multipole expansion of scalar potential.
Method of images and its applications. Potential and field due to a dipole,
force and torque on a dipole in an external field. Dielectrics,
polarisation. Solutions to bounary-value problems-conducting and dielectric
spheres in a uniform electric field. Magentic shell, uniformly magnetised
sphere. Ferromagnetic materials, hysteresis, energy loss.
(b) Current Electricity
Kirchhoffs laws and their applications. Biot-Savart law, Amperes law,
Faradays law, Lenz law. Self-and mutual-inductances. Mean and rms values
in AC circuits. LR CR and LCR circuits- series and parallel resonance.
Quality factor. Principal of transformer. 5. Electromagnetic Theory & Black Body Radiation
(a) Electromagnetic Theory
Displacement current and Maxwells equatons. Wave equations in vacuum,
Poynting theorem. Vector and scalar potentials. Gauge invariance, Lorentz
and Coulomb gauges. Electromagnetic field tensor, covariance of Maxwells
equations. Wave equations in isotropic dielectrics, reflection and
refraction at the boundary of two dielectrics. Fresnels relations. Normal
and anomalous dispersion. Rayleigh scattering.
(b) Blackbody radiation
Balckbody radiation and Planck radiation law- Stefan-Boltzmann law, Wien
displacement law and Rayleigh-Jeans law. Planck mass, Planck length, Planck
time,. Planck temperature and Planck energy. 6. Thermal and Statistical Physics
(a) Thremodynamics
Laws of thermodynamics, reversible and irreversible processes, entropy.
Isothermal, adiabatic, isobaric, isochoric processes and entropy change.
Otto and Diesel engines, Gibbs phase rule and chemical potential. van der
Waals equation of state of a real gas, critical constants. Maxwell-Boltzman
distribution of molecular velocities, transport phenomena, equipartition and
virial theorems. Dulong-Petit, Einstein, and Debyes theories of specific
heat of solids. Maxwell relations and applications. Clausius- Clapeyron
equation. Adiabatic demagnetisation, Joule-Kelvin effect and liquefaction of
gases.
(b) Statistical Physics
Saha ionization formula. Bose-Einstein condenssation. Thermodynamic
behaviour of an ideal Fermi gas, Chandrasekhar limit, elementary ideas about
neutron stars and pulsars. Brownian motion as a random walk, diffusion
process. Concept of negative temperatures.
Paper-II Section-A
1. Quantum Mechanics I
Wave-particle dualitiy. Schroedinger equation and expectation values.
Uncertainty principle. Solutions of the one-dimensional Schroedinger
equation free particle (Gaussian wave-packet), particle in a box, particle
in a finite well, linear harmonic oscillator. Reflection and transmission by
a potential step and by a rectangular barrier. Use of WKB formula for the
life-time calcuation in the alpha-decay problem. 2. Quantum Mechanics II & Atomic Physics
(a) Quantum Mechanics II
Particle in a three dimensional box, density of states, free electron theory
of metals. The angular meomentum problem. The hydrogen atom. The spin half
problem and properties of Pauli spin matrices.
(b) Atomic Physics
Stern-Gerlack experiment, electron spin, fine structure of hydrogen atom.
L-S coupling, J-J coupling. Spectroscopic notation of atomic states. Zeeman
effect. Frank-Condon principle and applications. 3. Molecular Physics
Elementary theory of rotational, vibratonal and electronic spectra of
diatomic molecules. Raman effect and molecular structure. Laser Raman
spectroscopy Importance of neutral hydrogen atom, molecular hydrogen and
molecular hydrogen ion in astronomy Fluorescence and Phosphorescence.
Elementary theory and applications of NMR. Elementary ideas about Lamb shift
and its significance.
Section-B 4. Nuclear Physics
Basic nuclear properties-size, binding energy, angular momentum, parity,
magnetic moment. Semi-empirical mass formula and applications. Mass
parabolas. Ground state of a deuteron magnetic moment and non-central
forces. Meson theory of nuclear forces. Salient features of nuclear forces.
Shell model of the nucleus-success and limitations. Violation of parity in
beta decay. Gamma decay and internal conversion. Elementary ideas about
Mossbauer spectroscopy. Q-value of nuclear reactions. Nuclear fission and
fusion, energy production in stars. Nuclear reactors. 5. Particle Physics & Solid State Physics
(a) Particle Physics
Classification of elementary particles and their interactions. Conservation
laws. Quark structure of hadrons. Field quanta of electroweak and strong
interactions. Elementary ideas about Unification of Forces. Physics of
neutrinos.
(b) Solid State Physics
Cubic crystal structure. Band theory of solids- conductors, insulators and
semiconductors. Elements of superconductivity, Meissner effect, Josephson
junctions and applications. Elementary ideas about high temperature
superconductivity. 6. Electronics
Intrinsic and extrinsic semiconductors-p-n-p and n-p-n
transistors.Amplifiers and oscillators. Op-amps. FET, JFET and MOSFET.
Digital electronics-Boolean identities, De Morgans laws, Logic gates and
truth tables., Simple logic circuits. Thermistors, solar cells. Fundamentals
of microprocessors and digital computers.