UPSC Syllabus: Physics Optional
Paper - 1
Mechanics
1. 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.
2. Mechanics of Rigid Body
- 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.
3. 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.
4. 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.
Waves and Optics
1. 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.
2. Geometrical 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
3. Interference
- Interference of light -Young’s experiment
- Newton’s rings, interference by thin films
- Michelson interferometer
- Multiple beam interference and Fabry Perot interferometer
4. 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.
5. 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.
Electricity and Magnetism
1. Electrostatics and Magnostatics
- 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.
2. 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.
Electromagnetic Waves and Black Body radiations
- 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.
Thermal and Statistical Physics
1. 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, n, 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.
2. 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 - 2
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.
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
- 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.
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.
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.
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Notes to boost your Preparation
Optional Notes
Note - This is my Vision IAS Notes (Vision IAS Class Notes) and Ashutosh Pandey Sir's Public Administration Class notes. I've also added some of the information on my own.
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