**Physics Optional-UPSC Syllabus**

##### 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 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.

**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; 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.

##### 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 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