**UPSC Mains Physics Syllabus**

### Paper - I: Physics Syllabus

**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, the 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, the 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 a 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, the 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 microstates, statistical distributions, Maxwell-Boltzmann, Bose-Einstein
and Fermi-Dirac distributions, applications to the specific heat of gases and
blackbody radiation; Concept of negative temperatures.

### PAPER-II: Physics Syllabus

**1. Quantum Mechanics:** Wave-particle
duality; 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, the 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, the 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, 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 the 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; on- p and np-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.`

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