Physics Optional syllabus

(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 self-energy;
• Two-body 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 tri-atomic molecules;
• Precessional motion;
• top, gyroscope.

(c) Mechanics of Continuous Media

• Elasticity, Hooke’s law and elastic constants of isotropic solids and their inter-relation;
• Streamline (Laminar) flow, viscosity, Poiseuille’s equation, Bernoulli’s equation, Stokes’ law and applications.

(d) Special Relativity

• Michelson-Morely experiment and its implications;
• Lorentz transformations length contraction, time dilation, addition of relativistic velocities, aberration and Doppler effect, mass-energy relation, simple applications to a decay process.
• Four dimensional momentum vector; Covariance of equations of physics.

(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) Geometrial Optics

• Laws of reflection and refraction from Fermat’s principle;
• Matrix method in paraxial optic-thin lens formula, nodal planes, system of two thin lenses, chromatic and spherical aberrations.

(c) Interference

• Interference of light -Young’s experiment, Newton’s rings, interference by thin films, Michelson interferometer;
• Multiple beam interference and Fabry Perot interferometer.

(d) Diffraction

• Fraunhofer diffraction single slit, double slit, diffraction grating, resolving power;
• Diffraction by a circular aperture and the Airy pattern;
• Fresnel diffraction: half-period zones and zone plates, circular aperture.

(e) Polarisation 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 fibers;
• Lasers-Einstein A and B coefficients.
• Ruby and He-Ne lasers.
• Characteristics of laser light-spatial and temporal coherence;
• Focusing of laser beams.
• Three-level scheme for laser operation;
• Holography and simple applications.

(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, polarisation.
• Solutions to boundary-value problems-conducting and dielectric spheres in a uniform electric field;
• Magnetic shell, uniformly magnetised sphere;
• Ferromagnetic materials, hysteresis, energy loss.

(b) Current Electricity

• Kirchhoff’s laws and their applications.
• Biot-Savart law, Ampere’s law, Faraday’s law, Lenz’ law. Self-and mutual- inductances;
• Mean and rms values in AC circuits;
• DC and AC circuits with R, L and C components;
• Series and parallel resonance;
• Quality factor;
• Principle of transformer.

• 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- Stefan- Boltzmann law, Wien’s displacement law and Rayleigh-Jeans law.

(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;
• Maxwell-Boltzmann distribution of molecular velocities, transport phenomena, equipartition and virial theorems;
• Dulong-Petit, Einstein, and Debye’s theories of specific heat of solids;
• Maxwell relations and application;
• Clausius-Clapeyron equation. Adiabatic demagnetisation, Joule-Kelvin effect and liquefaction of gases.

(b) Statistical Physics

• Macro and micro states, statistical distributions, Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Distributions, applications to specific heat of gases and blackbody radiation;
• Concept of negative temperatures.

• Wave-particle duality;
• Schroedinger equation and expectation values;
• Uncertainty principle;
• Solutions of the one-dimensional Schroedinger equation for free particle (Gaussian wave-packet), 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.

• Stern-Gerlach experiment, electron spin, fine structure of hydrozen atom;
• L-S coupling, J-J coupling: Spectroscopic notation of atomic states;
• Zeeman effect;
• Franck- Condon principle and applications;
• Elementary theory of rotational, vibrational 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.

• 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.
• 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.

• Crystalline and amorphous structure of matter;
• Different crystal systems, space groups;
• Methods of determination of crystal structure;
• X-ray diffraction, scanning and transmission electron microscopies;
• Band theory of solids-conductors, insulators and semi-conductors;
• Thermal properties of solids, specific heat, Debye theory;
• Magnetism: dia, para and ferromagnetism;
• Elements of super-conductivity, Meissner effect, Josephson junctions and applications;
• Elementary ideas about high temperature super- conductivity.
• Intrinsic and extrinsic semi-conductors- p-n-p and n-p-n transistors;
• Amplifiers and oscillators.
• Op-amps;
• FET, JFET and MOSFET;
• Digital electronics-Boolean identities, De Morgan’s laws, Logic gates and truth tables.
• Simple logic circuits;
• Thermistors, solar cells;
• Fundamentals of microprocessors and digital computers.