Physics Optional

Paper 1 : 

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-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. 

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) Geometrial 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) Polarisation and Modern Optics:

Production and detection of linearly and circularly polarised 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, 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. 

(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 rms values in AC circuits; DC and AC circuits with R,  L and C  components; Series and parallel resonance; Quality factor; Principle of transformer. 

4. 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- Stefan-Boltzmann law, Wien’s  displacement law and Rayleigh-Jeans law.

5. 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-Boltzmann 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 application; 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 specific heat of gases and  blackbody radiation; Concept of negative temperatures.