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# UPSC Mains Exam Syllabus - Physics Optional

## UPSC Mains Exam Syllabus - Physics Optional

## 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-Morley 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) Geometrical Optics: Laws of reflection and refraction from Fermat’s
principle; Matrix method in paraxial optics-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) 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;
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, polarization; Solutions to
boundary-value problems-conducting 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; Biot-Savart
law, Ampere’s law, Faraday’s law, Lenz’ law; Self-and mutual-inductances; 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, Stefan- Boltzmann law,
Wien’s displacement law and Rayleigh-Jeans’ 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; Maxwell-Boltzman 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 applications; 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.

## IAS Mains General Studies Study Kit

## PAPER - II:

**1. Quantum Mechanics:** Wave-particle dualitiy;
Schroedinger equation and expectation values; Uncertainty principle; Solutions
of the one-dimensional Schroedinger equation for a 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 hydrogen atom; L-S coupling, J-J
coupling; Spectroscopic notation of atomic states; Zeeman effect; Frank- Condon
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
properties-size, binding energy, angular momentum, parity, magnetic moment;
Semi-empirical mass formula and applications, mass parabolas; Ground state of
deuteron, magnetic moment and non-central 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;
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 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; pn- 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.`