PAPER  I
1. (a) Mechanics of Particles:
Laws of motion; conservation of energy and momentum, applications to rotating frames, centripetal and Coriolis accelerations; Motion under a central force; Conservation of angular momentum, Kepler’s laws; Fields and potentials; Gravitational field and potential due to spherical bodies, Gauss and Poisson equations, gravitational selfenergy; Twobody problem; Reduced mass; Rutherford scattering; Centre of mass and laboratory reference frames.
(b) Mechanics of Rigid Bodies:
System of particles; Centre of mass, angular momentum, equations of motion; Conservation theorems for energy, momentum and angular momentum; Elastic and inelastic collisions; Rigid body; Degrees of freedom, Euler’s theorem, angular velocity, angular momentum, moments of inertia, theorems of parallel and perpendicular axes, equation of motion for rotation; Molecular rotations (as rigid bodies); Di and triatomic molecules; Precessional motion; top, gyroscope.
(c) Mechanics of Continuous Media:
Elasticity, Hooke’s law and elastic constants of isotropic solids and their interrelation; Streamline (Laminar) flow, viscosity, Poiseuille’s equation, Bernoulli’s equation, Stokes’ law and applications.
(d) Special Relativity:
MichelsonMorley experiment and its implications; Lorentz transformationslength contraction, time dilation, addition of relativistic velocities, aberration and Doppler effect, massenergy relation, simple applications to a decay process; Four dimensional momentum vector; Covariance of equations of physics.
2. Waves and Optics:
(a) 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.
(b) Geometrical Optics:
Laws of reflection and refraction from Fermat's principle; Matrix method in paraxial opticsthin lens formula, nodal planes, system of two thin lenses, chromatic and spherical aberrations.
(c) Interference:
Interference of lightYoung's experiment, Newton's rings, interference by thin films, Michelson interferometer; Multiple beam interference and FabryPerot interferometer.
(d) Diffraction:
Fraunhofer diffractionsingle slit, double slit, diffraction grating, resolving power; Diffraction by a circular aperture and the Airy pattern; Fresnel diffraction: halfperiod zones and zone plates, circular aperture.
(e) Polarization and Modern Optics:
Production and detection of linearly and circularly polarized 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; LasersEinstein A and B coefficients; Ruby and HeNe lasers; Characteristics of laser lightspatial and temporal coherence; Focusing of laser beams; Threelevel scheme for laser operation; Holography and simple applications.
3. Electricity and Magnetism:
(a) Electrostatics and Magnetostatics:
Laplace and 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, polarization; Solutions to boundaryvalue problemsconducting and dielectric spheres in a uniform electric field; Magnetic shell, uniformly magnetized sphere; Ferromagnetic materials, hysteresis, energy loss.
(b) Current Electricity:
Kirchhoff's laws and their applications; BiotSavart law, Ampere's law, Faraday's law, Lenz' law; Selfand mutualinductances; Mean and r m s values in AC circuits; DC and AC circuits with R, L and C components; Series and parallel resonances; Quality factor; Principle of transformer.
(c) Electromagnetic Waves and Blackbody Radiation:
Displacement current and Maxwell's equations; Wave equations in vacuum, Poynting theorem; Vector and scalar potentials; Electromagnetic field tensor, covariance of Maxwell's equations; Wave equations in isotropic dielectrics, reflection and refraction at the boundary of two dielectrics; Fresnel's relations; Total internal reflection; Normal and anomalous dispersion; Rayleigh scattering; Blackbody radiation and Planck’s radiation law, StefanBoltzmann law, Wien’s displacement law and RayleighJeans’ law.
4. Thermal and Statistical Physics:
(a) Thermodynamics:
Laws of thermodynamics, reversible and irreversible processes, entropy; Isothermal, adiabatic, isobaric, isochoric processes and entropy changes; Otto and Diesel engines, Gibbs' phase rule and chemical potential; van der Waals equation of state of a real gas, critical constants; MaxwellBoltzman distribution of molecular velocities, transport phenomena, equipartition and virial theorems; DulongPetit, Einstein, and Debye's theories of specific heat of solids; Maxwell relations and applications; Clausius Clapeyron equation; Adiabatic demagnetisation, JouleKelvin effect and liquefaction of gases.
(b) Statistical Physics:
Macro and micro states, statistical distributions, MaxwellBoltzmann, BoseEinstein and FermiDirac distributions, applications to specific heat of gases and blackbody radiation; Concept of negative temperatures.
PAPER  II
1. Quantum Mechanics:
Waveparticle dualitiy; Schroedinger equation and expectation values; Uncertainty principle; Solutions of the onedimensional Schroedinger equation for a free particle (Gaussian wavepacket), particle in a box, particle in a finite well, linear harmonic oscillator; Reflection and transmission by a step potential and by a rectangular barrier; Particle in a three dimensional box, density of states, free electron theory of metals; Angular momentum; Hydrogen atom; Spin half particles, properties of Pauli spin matrices.
2. Atomic and Molecular Physics:
SternGerlach experiment, electron spin, fine structure of hydrogen atom; LS coupling, JJ coupling; Spectroscopic notation of atomic states; Zeeman effect; FrankCondon principle and applications; 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 and EPR; Elementary ideas about Lamb shift and its significance.
3. Nuclear and Particle Physics:
Basic nuclear propertiessize, binding energy, angular momentum, parity, magnetic moment; Semiempirical mass formula and applications, mass parabolas; Ground state of deuteron, magnetic moment and noncentral forces; Meson theory of nuclear forces; Salient features of nuclear forces; Shell model of the nucleus  successes and limitations; Violation of parity in beta decay; Gamma decay and internal conversion; Elementary ideas about Mossbauer spectroscopy; Qvalue of nuclear reactions; Nuclear fission and fusion, energy production in stars; Nuclear reactors.
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.
4. Solid State Physics, Devices and Electronics:
Crystalline and amorphous structure of matter; Different crystal systems, space groups; Methods of determination of crystal structure; Xray diffraction, scanning and transmission electron microscopies; Band theory of solids  conductors, insulators and semiconductors; Thermal properties of solids, specific heat, Debye theory; Magnetism: dia, para and ferromagnetism; Elements of superconductivity, Meissner effect, Josephson junctions and applications; Elementary ideas about high temperature superconductivity.
Intrinsic and extrinsic semiconductors; pnp and npn transistors; Amplifiers and oscillators; Opamps; FET, JFET and MOSFET; Digital electronicsBoolean identities, De Morgan's laws, logic gates and truth tables; Simple logic circuits; Thermistors, solar cells; Fundamentals of microprocessors and digital computers.
