UPSC Mains Syllabus for Physics Optional – A Comprehensive Guide

The Physics Optional in the UPSC Civil Services Mains Examination is highly conceptual and analytical, ideal for candidates with a science background, particularly in physics or engineering. The syllabus is divided into two papers – Paper I and Paper II, each carrying 250 marks, making the total 500 marks.

This blog provides a detailed breakdown of the Physics Optional syllabus as per the latest UPSC notification, with clear categorization, bullet points, and in-depth descriptions to help aspirants grasp the scope of the subject.

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Paper I – Classical and Modern Physics

Paper I primarily focuses on classical mechanics, electromagnetism, thermodynamics, optics, and quantum mechanics. Here's the detailed syllabus:

1. Mechanics of Particles

• Laws of Motion: Newton's laws, inertial frames, constraints, and degrees of freedom.
• Conservation Laws: Energy, linear momentum, and angular momentum.
• Dynamics of Rigid Bodies: Rotational motion, torque, moment of inertia, Euler's equations.
• Motion in Non-inertial Frames: Coriolis and centrifugal forces, pseudo forces.
• Central Force Motion:
• Motion under central forces, orbits, and their classification.
• Kepler's laws of planetary motion.
• Rutherford scattering and impact parameter.

2. Mechanics of Systems of Particles

• Two-body Problems: Reduction to one-body problem.
• Collisions: Elastic and inelastic collisions, laboratory and center-of-mass frames.
• Small Oscillations:
• Linear and nonlinear oscillations.
• Damped and driven harmonic oscillator.
• Resonance phenomena.

3. Special Relativity

• Michelson-Morley Experiment: Failure of ether theory.
• Postulates of Special Relativity.
• Lorentz Transformations: Time dilation, length contraction, and simultaneity.
• Relativistic Mechanics: Energy-momentum relations, relativistic dynamics.

4. Waves and Optics

• Wave Motion: Superposition principle, group and phase velocity.
• Interference:
• Young's double slit experiment.
• Interference in thin films and Newton’s rings.
• Diffraction:
• Fresnel and Fraunhofer diffraction.
• Diffraction at single slit, double slit, and grating.
• Polarization:
• Methods of producing polarized light.
• Brewster’s law, Malus law.
• Double refraction and optical activity.

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5. Electricity and Magnetism

• Electrostatics:
• Gauss’s Law and applications.
• Laplace and Poisson equations.
• Magnetostatics:
• Biot-Savart law, Ampere’s law, and applications.
• Magnetic vector potential.
• Time-varying Fields:
• Faraday’s law of induction.
• Displacement current.
• Maxwell’s Equations:
• Derivation and physical interpretation.
• Electromagnetic waves in vacuum and media.
• Poynting theorem and electromagnetic energy flow.

6. Thermodynamics and Statistical Physics

• Laws of Thermodynamics:
• Zeroth, First, Second, and Third Laws.
• Concepts of entropy and reversible/irreversible processes.
• Maxwell’s Relations and Thermodynamic Potentials.
• Kinetic Theory of Gases:
• Distribution of velocities.
• Specific heats and equipartition of energy.
• Statistical Distributions:
• Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann distributions.
• Applications to blackbody radiation and electron gas.

7. Modern Physics

• Blackbody Radiation: Planck’s law, Wien’s law, Stefan-Boltzmann law.
• Photoelectric Effect: Einstein’s explanation.
• Compton Effect and de Broglie Hypothesis.
• Wave-Particle Duality: Matter waves and Davisson-Germer experiment.
• Uncertainty Principle and Applications.

8. Quantum Mechanics

• Schrödinger Equation: Time-dependent and time-independent forms.
• Applications:
• Particle in a box.
• Harmonic oscillator.
• Hydrogen atom.
• Operators and Eigenvalues.
• Commutation Relations and Expectation Values.
• Angular Momentum and Spin.

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Paper II – Advanced and Applied Physics

Paper II focuses on atomic physics, nuclear physics, solid-state physics, electronics, and other advanced topics. Here's a detailed structure:

1. Atomic and Molecular Physics

• Bohr’s Theory: Hydrogen spectrum and energy levels.
• Sommerfeld’s Extension.
• Vector Atom Model:
• Quantum numbers, LS and JJ coupling.
• Zeeman effect and Stark effect.
• Molecular Spectra:
• Rotational, vibrational, and electronic spectra.
• Raman effect and its applications.
• Laser Physics:
• Principles of laser action.
• Population inversion and optical pumping.
• Types of lasers and applications.

2. Nuclear and Particle Physics

• Nuclear Properties:
• Mass, binding energy, nuclear radius, and charge.
• Semi-empirical mass formula.
• Radioactivity:
• Alpha, beta, and gamma decay.
• Decay constants and half-life.
• Nuclear Models:
• Liquid drop model, shell model, and collective model.
• Nuclear Reactions:
• Fission, fusion, and chain reactions.
• Nuclear reactors and applications.
• Elementary Particles:
• Classification: baryons, mesons, leptons.
• Conservation laws: baryon number, lepton number, charge, etc.
• Fundamental interactions (strong, weak, electromagnetic, gravitational).

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3. Solid State Physics

• Crystal Structure:
• Bravais lattices and crystal systems.
• Miller indices and X-ray diffraction.
• Bonding in Solids:
• Ionic, covalent, metallic, and van der Waals bonds.
• Electronic Properties:
• Energy bands, conductors, semiconductors, and insulators.
• Fermi energy and density of states.
• Semiconductors:
• Intrinsic and extrinsic types.
• P-N junctions, diodes, and transistors.
• Magnetic and Dielectric Properties:
• Diamagnetism, paramagnetism, ferromagnetism.
• Polarization and dielectric constant.

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4. Electronics and Devices

• Semiconductor Devices:
• P-N junctions, Zener diodes, LED, photodiodes.
• Transistors and Amplifiers:
• Bipolar junction transistors, FETs.
• Amplifier circuits and feedback.
• Operational Amplifiers:
• Characteristics and applications.
• Adder, subtractor, integrator, differentiator.
• Digital Electronics:
• Logic gates, flip-flops, counters.
• Boolean algebra and simplification.
• Communication Electronics:
• Modulation and demodulation.
• AM, FM, and basic concepts of digital communication.

5. Experimental Physics

• Error Analysis:
• Types of errors and propagation.
• Least squares fitting.
• Basic Experiments and Instruments:
• CRO, Galvanometer, Multimeter, Spectrometer.
• Interference and diffraction experiments.
• Measurement Techniques:
• Hall effect, conductivity measurement, e/m determination.
• X-ray diffraction and electron microscopy.

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Conclusion

Physics as an optional subject can be highly rewarding for candidates who have a good grasp of the subject at the undergraduate level. The key to success lies in:

• Understanding the conceptual foundation.
• Solving numerical problems regularly.
• Practicing previous year UPSC questions.
• Keeping diagrams, formulas, and derivations crisp and accurate in the exam.

If you're comfortable with the technical depth and ready to commit to disciplined study, Physics can be a scoring optional in UPSC Mains.