**OPTIONAL: PHYSICS**

**Syllabus **

**Physics Syllabus Paper – I**

#### (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:

The 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, the 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.

**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.

**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.

**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, StefanBoltzmann law, Wien’s displacement law and Rayleigh-Jeans’ law.

**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 the specific heat of gases and blackbody radiation; Concept of negative temperatures.

** Physics Syllabus Paper – II**

**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.

**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; FrankCondon 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.

**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.

**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 microscopes; 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; 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.

**Reference Books:**

Classical Mechanics

- Gupta, Kumar & Sharma H.Goldstein
- Takewale & Puranik

Mechanics

- D.S. Mathur
- Kleppner & Kolenkov

Wave

- D.S. Mathur
- Kleppner & Kolenkov

Special Relativity

- Gupta & Goyal
- R.Resnic

Optics

- Ajay Ghatak
- B S Agarwal

Electrodynamics

- David Griffiths

EM Theory

- Chopra & Agarwal
- Satya Prakash

Thermal Physics

- P.K Chakraborty
- Satya Prakash, Singhal & Agarawal

Quantum Physics

- Resnick & Eisberg

Concept of Modern Physics

- Arthut Bevser

Quantum Mechanics

- Chatwal & Anand
- Ghatak & Loknathan
- Satya Prakash

Atomic & Molecular Spectra

- Nuclear Physics
- Rajkumar
- S.B Patel

Solid State Physics

- Allon Mottershead
- Electronics
- Kittel

Objective Physics

- H.C. Verma
- TMH

Statistical Physics

- B.B Laud

**Optional notes: available under mentorship rogram.**

**Strategy:**

**Merits:**

- You can score through numerical problems if you practice well enough.
- You can score well by drawing diagrams.
- This can be your scoring point subject if you have a solid base in it.
- Candidates with a science particularly Physics major in their graduation.and Candidates with engineering backgrounds at university can opt for this subject.

**Demerits:**

- Being a science subject, there is no scope for interpretation. If you know the answer and can write it satisfactorily, you will get marks. Nothing is subjective here.

**How to prepare:**

- Memorise the Syllabus.
- Stick to limited reference books
- Before starting preparation, go through previous year qps

- Theory building and problem solving ability are very important to score good marks in the Physics optional paper.
- Derivations are important in your answers. Assess the number of marks allocated to a question and decide if you would derive the whole equation or just give the equation.
- If it is a 20-marks question, you should derive the relevant equation. Analyse the space and time constraints and decide. So, practice derivations diligently since you cannot mug up all of them.

- Practice numerical problems sincerely, especially for paper I. Paper II is more theory-based.
- In every topic in Physics, you must know the basic definitions in words and in equations.
- In a question where a particular phenomenon is asked, you must explain the underlying physics as well rather than just write the mathematical solution.
- It is a good practice to make summary notes for every chapter. This will come handy while you revise.
- Practice many problems before the exam.
- When you give a formula, explain the units and terms used in it.
- Solve at least 10 previous year question papers.

**Previous Year Question Papers:**

2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 |

Paper – 1 | Paper – 1 | Paper – 1 | Paper – 1 | Paper – 1 | Paper – 1 | Paper – 1 | Paper – 1 |