UPSC PHYSICS OPTIONAL SYLLABUS

For a UPSC CSE aspirant, the optional subject is also an important subject. In the UPSC mains exam, optional marks have two papers, Paper 1 and Paper 2. Each paper is of 250 marks which makes a total of 500 marks. The UPSC optional subject list contains 48 subjects in total, one of which is Physics.

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SYLLABUS FOR PAPER I

UPSC Physics Syllabus 2020 - IAS Mains Optional Subjects

SECTION A:

  1. Classical Mechanics:

1.1. Particle dynamics: 

  • Conservation of linear and angular momentum
  • Centre of mass and laboratory coordinates
  • Galilean transformation
  • Foucault pendulum
  • Rutherford scattering, inertial and non-inertial frames, rotating frames, centrifugal and Coriolis forces
  • The rocket equation 

1.2. System of particles: 

  • Constraints, generalized coordinates, degrees of freedom, and momenta 
  • Lagrange’s equation and applications to the linear harmonic oscillator
  • Central force problems, and simple pendulum
  • Hamiltonian Lagrange’s equation from Hamilton’s principle
  • Cyclic coordinates

1.3. Rigid body dynamics: 

  • Inertia tensor, principal moments of inertia
  • The force-free motion of a rigid body
  • Euler’s equation of motion of a rigid body
  • Eulerian angles
  • Gyroscope
  1. Special Relativity, Waves & Geometrical Optics:

2.1. Special Relativity: 

  • Michelson-Morley experiment and its implications
  • Lorentz transformations- length contraction, the addition of velocities, time dilation, aberration and Doppler effect, simple applications to a decay process, mass-energy relation
  • Minkowski diagram
  • The covariance of equations of physics
  • The four-dimensional momentum vector

2.2.Waves: 

  • Simple harmonic motion, damped oscillation, forced oscillation, and resonance
  • Stationary waves in a string
  • Beats
  • Phase and group velocities 
  • Pulses and wave packets
  • Reflection and Refraction from Huygens’ principle

2.3. Geometrical Optics: 

  • Laws of reflection and refraction from Fermat’s principle
  • Matrix method in paraxial optic-thin lens formula, nodal planes, a system of two thin lenses, spherical and chromatic aberrations
  1. Physical Optics:
  • 3.1. Interference: 
  • Interference of light-Young’s experiment, interference by thin films, Michelson interferometer, Newton’s rings
  • Fabry-Perot interferometer
  • Multiple beam interference
  • Holography and simple applications

3.2. Diffraction: 

  • Fresnel diffraction: – half-period zones and zones plates
  • Fraunhofer diffraction-single slit, double slit, diffraction grating, resolving power
  • Fresnel integrals. 
  • Application of Cornu’s spiral to the analysis of diffraction at a straight edge and by a long narrow slit
  • Diffraction by a circular aperture and the Airy pattern

3.3. Polarisation and Modern Optics: 

  • Production and detection of linearly and circularly polarised light
  • Double refraction, a quarter-wave plate
  • Principles of fibre optics attenuation
  • Optical activity
  • Pulse dispersion in step-index and parabolic index fibres
  • Lasers- Einstein A and B coefficients
  • Material dispersion, single-mode fibres
  • Ruby and He-Ne lasers
  • Characteristics of laser light-spatial and temporal coherence
  • Three-level scheme for laser operation
  • Focussing of laser beams
UPSC Physics Syllabus | UPSC Syllabus Optional Physics for IAS , IPS -  YouTube

Section B

  1. Quantum Mechanics I:
  • Wave-particle duality
  • Uncertainty principle
  • Schroedinger equation and expectation values
  • Solutions of the one-dimensional Schroedinger equation-free particle (Gaussian wave-packet), particle in a box, linear harmonic oscillator particle in a finite well
  • Use of WKB formula for the life-time calculation in the alpha-decay problem
  • Reflection and transmission by a potential step and by a rectangular barrier
  1. Quantum Mechanics II & Atomic Physics:

2.1. Quantum Mechanics II: 

  • Particle in a three-dimensional box, the density of states, free electron theory of metals
  • The hydrogen atom
  • Properties of Pauli spin matrices
  • Problems on angular momentum, spin half problem

2.2. Atomic Physics: 

  • Stern-Gerlack experiment, electron spin, the fine structure of hydrogen atom
  • Spectroscopic notation of atomic states
  • L-S coupling, J-J coupling
  • Zeeman effect
  • Frank-Condon principle and applications
  1. Molecular Physics:
  • 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
  • Elementary ideas about Lamb shift and its significance

SYLLABUS FOR PAPER II

  1. Quantum Mechanics:
  • Wave-particle duality
  • Uncertainty principle
  • Schroedinger equation and expectation values
  • 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
  • Hydrogen atom
  • Properties of Pauli spin matrices
  • Angular momentum
  • Spin half particles
  1. 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
  • FrankCondon principle and applications
  • Elementary theory of rotational, vibrational, and electronic spectra of diatomic molecules
  • Zeeman effect
  • Raman effect and molecular structure
  • Laser Raman spectroscopy
  • Importance of neutral hydrogen atom, molecular hydrogen, and molecular hydrogen ion in astronomy
  • Elementary theory and applications of NMR and EPR
  • Fluorescence and Phosphorescence
  • Elementary ideas about Lamb shift and its significance
  1. Nuclear and Particle Physics:
  • Basic nuclear properties-size, binding energy, angular momentum, parity, magnetic moment
  • The ground state of deuteron, magnetic moment, and non-central forces
  • Semi-empirical mass formula and applications, mass parabolas
  • Meson theory of nuclear forces
  • Salient features of nuclear forces
  • Shell model of the nucleus – successes, and limitations
  • Gamma decay and internal conversion
  • Violation of parity in beta decay
  • 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
  • Quark structure of hadrons
  • Conservation laws
  • Field quanta of electroweak and strong interactions
  • Physics of neutrinos
  • Elementary ideas about unification of forces
  1. Solid State Physics, Devices and Electronics:
  • The crystalline and amorphous structure of matter
  • Methods of determination of crystal structure
  • Different crystal systems, space groups
  • X-ray diffraction, scanning, and transmission electron microscope
  • Thermal properties of solids, specific heat, Debye theory
  • Band theory of solids – conductors, insulators, and semiconductors
  • Magnetism: dia, para, and ferromagnetism
  • Elements of superconductivity, Meissner effect, Josephson junctions, and applications
  • Elementary ideas about high-temperature superconductivity
  • p-n-p and n-p-n transistors
  • Intrinsic and extrinsic semiconductors
  • 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
  • Fundamentals of microprocessors and digital computers
  • Thermistors, solar cells

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