Centre of mass and laboratory
coordinates, conservation of linear and angular momentum. The rocket equation.
Rutherford scattering, Galilean transformation, intertial and non-inertial
frames, rotating frames, centrifugal and Coriolis forces, Foucault pendulum.
(more content follows the advertisement below)
A D V E R T I S E M E N T
System of particles
Constraints, degrees of freedom,
generalised coordinates and momenta. Lagrange's equation and applications to
linear harmonic oscillator, simple pendulum and central force problems. Cyclic
coordinates, Hamilitonian Lagrange's equation from Hamilton's principle.
Rigid body dynamics
Eulerian angles, inertia tensor,
principal moments of inertia. Euler's equation of motion of a rigid body,
force-free motion of a rigid body. Gyroscope.
Special Relativity, Waves & Geometrical Optics
Michelson-Morley experiment and its
implications. Lorentz transformations-length contraction, time dilation,
addition of velocities, aberration and Doppler effect, mass-energy relation,
simple applications to a decay process. Minkowski diagram, four dimensional
momentum vector. Covariance of equations of physics.
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.
Laws of relfection 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.
Interference of light-Young's
experiment, Newton's rings, interference by thin films, Michelson
interferometer. Multiple beam interference and Fabry-Perot interferometer.
Holography and simple applications.
Fraunhofer diffraction-single slit,
double slit, diffraction grating, resolving power. Fresnel diffraction: -
half-period zones and zones plates. 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.
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. Focussing of laser beams.
Three-level scheme for laser operation.
Electricity and Magnetism
Electrostatics and Magnetostatics
Laplace ad 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 bounary-value problems-conducting and
dielectric spheres in a uniform electric field. Magentic shell, uniformly
magnetised sphere. Ferromagnetic materials, hysteresis, energy loss.
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. LR CR and LCR circuits-
series and parallel resonance. Quality factor. Principal of transformer.
Electromagnetic Theory & Black Body Radiation
Displacement current and Maxwell's
equatons. Wave equations in vacuum, Poynting theorem. Vector and scalar
potentials. Gauge invariance, Lorentz and Coulomb gauges. 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. Normal and anomalous dispersion. Rayleigh scattering.
Balckbody radiation ad Planck
radiation law- Stefan-Boltzmann law, Wien displacement law and Rayleigh-Jeans
law. Planck mass, Planck length, Planck time,. Planck temperature and Planck
Thermal and Statistical Physics
Laws of thermodynamics, reversible
and irreversible processes, entropy. Isothermal, adiabatic, isobaric, isochoric
processes and entropy change. 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 lllrelations and
applications. Clausius- Clapeyron equation. Adiabatic demagnetisation,
Joule-Kelvin effect and liquefaction of gases.
Saha ionization formula.
Bose-Einstein condenssation. Thermodynamic behaviour of an ideal Fermi gas,
Chandrasekhar limit, elementary ideas about neutron stars and pulsars. Brownian
motion as a random walk, diffusion process. Concept of negative temperatures.