## PHYSICS

**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 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.

**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) 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.

**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, polarisation. Solutions to boundaryvalue 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. Selfand 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.

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

**5. 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; 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; ClausiusClapeyron 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.

**PAPER‐II**

**1. Quantum Mechanics :**

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.

**2. Atomic and Molecular Physics :**

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.

**3. Nuclear and Particle 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.

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; 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 superconductivity.

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.