Mechanics and Waves
Dimensional analysis. Newton's laws of motion and applications, variable
mass systems, projectiles. Rotational dynamics-kinetic energy, angular
momentum, theorems of moment of intertia and calculations in simple cases.
Conservative forces, frictional forces. Gravitaional potential and intensity
due to spherical objects. Central forces, Kepler's problem, escape velocity
and artificial satellites (including GPS). Streamline motion, viscosity,
Poiseuille's equation. Applications of Bernoulli's equation and Stokes' law.
Special relativity and Lorentz transformation-length contraction, time
dilation, mass-energy relation.
Simple harmonic motion, Lissajous figures. Damped oscillation, forced
oscillation and resonance. Beats, Phase and group velocities. Stationary
waves, vibration of strings and air columns, longitudinal waves in solids.
Doppler effect. Ultrasonics and applications.
Geometrical and Physical 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. Simple optical
instruments-magnifier, eyepieces, telescopes and microscopes.
Huygens' principle-reflection and refraction of waves. Interference of
light-Young's experiment, Newton's rings, interference by thin films,
Michelson interferometer. Fraunhofer diffraction-single slit, double slit,
diffraction grating, resolving power. Fresnel diffraction-half-period zones
and zone plate. Production and detection of linearly, circularly and
elliptically polarised light. Double refraction, quarter-waves plates and
half-wave plates. Polarizing sheets. Optical activity and applications.
Rayleigh scattering and applications.
Elements of fibre optics-attenuation; pulse dispersion in step index and
parabolic index fibres; material dispersion. Lasers, characteristics of
laser light-spatial and temporal coherence. Focussing of laser beams and
Heat and Thermodynamics
Thermal equilibrium and temperature. The zeroth law of thermodynamics.
Heat and the first law of thermodynamics. Efficiency of Carnot engines.
Entropy and the second law of thermodynamics. Kinetic theory and the
equation of state of an ideal gas. Mean free path, distribution of molecular
speeds and energies. Trasport phenomena. Andrew's experiements-van der Waals
equation and applications. Joule-Kelvin effect and applications. Brownian
motion. Thermodynamic potentials-Maxwell relations. Phase transitions.
Kirchhoff's laws. Black-body radiation-Stefan-Boltzmann law, spectral
radiancy, Wien displacement law, application to the cosmic microwave
background radiation, Planck radiation law.
Electricity and Magnetism
Electric charge, Coulomb's law, electric field, Gauss' law. Electric
potential, van de Graff accelerator. Capacitors, dielectrics and
polarization. Ohm's law, Kirchhoff's first and second rules, resistors in
series and parallel, applications to two-loop circuits. Magnietic field-Gauss'law
for magnetism, atomic and nuclear magnetism, magnetic susceptibility,
classification of magnetic materials. Cirulating charges, cyclotron,
synchrotron. Hall effect. Biot-Savart law, Ampere's law, Faraday's law of
induction., Lenz's law. Inductance. Alternating current circuits-RC, LR,
single-loop LRC circuits, impedance, resonance, power in AC circuits.
Displacement current, Maxwell's equations (MKS units), electromagnetic
waves, energy transport and Poynting vector.
Atomic and Nuclear Physics
Photoelectric effect, Einstein's photon theory. Bohr's theory of hydrogen
atom. Stern-Gerlach experiment, quantisation of angular momentum, electron
spin. Pauli exclusion principle and applications. Zeeman effect. X-ray
spectrum, Bragg's law, Bohr's theory of the Mosley plot. Compton effect,
Compton wavelength. Wave nature of matter, de Broglie wavelength,
wave-particle duality. Heisenberg's uncertainty relationships.
Schroedinger's equation-eigenvalues and eigenfunctions of (i) particle in a
box, (ii) simple harmonic oscillator and (iii) hydrogen atom. Potential step
and barrier penetration. Natural and artificial radioactivity. Binding
energy of nuclei, nuclear fission and fusion. Classification of elementary
particles and their interactions.
Diodes in half-waves and full-wave rectification, qualitative ideas of
semiconductors, p type and n type semiconductors, junction diode, Zener
diode, transistors, binary numbers, Logic gates and truth tables, Elements
of microprocessors and computers.