**Discipline -5**

**M.Sc. (PHYSICS)**

**(Fibre Optics & Communication)**

1. Mechanics:
Laws of motion, motion in a uniform field, components of velocity and acceleration in different coordinate systems. Uniformly rotating frame, centripetal acceleration, Coriolis force and its applications.
Motion under a central force, Kepler’s law. Gravitational law and field. Potential due to a spherical body, Gauss and Poisson equations for gravitational self-energy.
System of particles, center of mass, equation of motion, conservation of linear and angular momenta, conservation of energy, elastic and inelastic collisions.
2. Properties of matter:
Elasticity, small deformations, Hooke’s law, elastic constants for an isotropic solid, beams supported at both ends, cantilever, torsion of a cylinder, bending moments and shearing forces.
Kinematics of moving fluids, equations of continuity, Euler’s equation, Bernaulli’s theorem, viscous fluids, streamline and turbulent flow. Poiseulle’s law. Capillary tube flow, Reynold’s number, stokes law.
Surface tension and surface energy, molecular interpretations of surface tension, pressure on a curved liquids surface, wetting.
3. Kinetic Theory of Matter
Ideal Gas: kinetic model, deduction of Boyle’s law, interpretation of temperature, estimation of rms speeds of molecules. Brownian motion, estimate of the Avagadro number. Equipartition of energy, specific heat of monatomic gas, extension to di- and tri-atomic gases, behavior at low temperatures. Adiabatic expansion of an ideal gas, applications to atmospheric physics.
Real Gas: Van der Waal gas, equation of state, nature of Van der Waals forces, comparison with experimental P-V curves. The critical constants, gas and vapor. Joule expansion of ideal gas, and of a Van der Waals gas, Joule coefficient,
Liquification of gases: Boyle temperature and inversion temperature. Principle of regenerative cooling and of cascade cooling, liquification of hydrogen and helium. Refrigeration cycles, meaning of efficiency.
4. Thermodynamics
The laws of thermodynamics: The Zeroth law, various indicator diagrams, work done by and on the system, first law of thermodynamics, internal energy as a state function and other applications. Reversible and irreversible changes, Carnot cycle and its efficiency, Carnot theorem and the second law of thermodynamics. Different versions of the second law, practical cycles used in the internal combustion engines. Entropy, principle of increase of entropy. The thermodynamics scale of temperature; its identity with the perfect gas scale. Impossibility of attaining the absolute zero; third law of thermodynamics.
5. Oscillations:
Potential well and periodic oscillations, case of harmonic oscillations, differential equation and its solution, kinetic and potential energy, examples of simple harmonic oscillations, spring and mass system, simple and compound pendulum, torsional pendulum, bifilar oscillations. Helmholtz resonator, LC circuit Superposition of two simple harmonic motions of the same frequency along the same line, interference, superposition of two mutually perpendicular simple harmonic vibrations of the same frequency, Lissajous figures, case of different frequencies.
6. Waves
Waves in media: Speed of transverse waves on a uniform string, speed of longitudinal waves in a fluid, energy density and energy transmission in waves, typical measurements. Waves over liquid surface: gravity waves and ripples. Group velocity and phase velocity, their measurements.
Superposition of waves: Linear homogenous equations and the superposition principle, nonlinear superposition and consequences.
Standing waves: Standing waves as normal modes of bounded systems, examples, Harmonics and the quality of sound; examples Production and detection of ultrasonic and infrasonic waves and applications.
7. Geometrical Optics & Physical Optics
Geometrical Optics:
Fermet’s Principle: Principle of extreme path, the aplanatic points of a sphere and other applications.
General theory of image formation: Cardinal points of an optical system, general relationships, thick lens and lens combinations. Lagrange equation of magnification, telescopic combinations, telephoto lenses and eyepieces.
Aberration in images: Chromatic aberrations, achromatic combination of lenses in contact and separated lenses.
Optical instruments: Entrance and exit pupils, need for a multiple lens eyepiece, common types of eyepieces.
Physical Optics:
Interference of a light: The principle of superpositions, two-slit interference, coherence requirement for the sources, optical path retardations, lateral shift of fringes, Rayleigh refractometer and other applications. Localized fringes; thin films, applications for precision measurements for displacements.
Fresnel diffraction: Fresnel half-period zones, plates, straight edge, rectilinear propogation.
Fresnel diffraction: Diffraction at a slit, half –period zones, phasor diagram and integral calculus methods, the intensity distribution, diffraction at a circular aperture and a circular disc, resolution of images, Rayleigh criterion, resolving power of telescope and microscopic systems, outline of phase contract microscopy.
Diffraction gratings: Diffraction at N parallel slits, intensity distribution, plane diffraction grating, reflection grating and blazed grating.
Double refraction and optical rotation: refraction, in uniaxial crystals, its electromagnetic theory, phase retardation plates, double image prism. Rotation of plane of polarization, origin of optical rotation in liquids and in crystals.
8. Relativity
Reference systems, inertial frames, Galilean invariance and conservation laws, propagation of light, Michelson-Morley experiment; search for ether.
Postulates for the special theory of relativity, Lorentz transformations, length contraction, time dilation, velocity addition theorem, variation of mass with velocity, mass-energy equivalence, particle with a zero rest mass.
9. Quantum Mechanics
Origin of the quantum theory: Failure of classical physics to explain the phenomena such as black-body spectrum, photoelectric effect, Ritz combination principle in spectra, stability of an atom. Planck’s radiation law, Einstein’s explanations of photoelectric effect, Bohr’s quantization of angular momentum and its applications to hydrogen atom, limitations of Bohr’s theory.
Wave-particle duality and uncertainty principle: de Broglie’s hypothesis for matter waves; the concept of wave and group velocities, evidence for diffraction and interference of ‘particles’, experimental demonstration of matter waves.
Consequences of de Broglie’s concepts; quantization in hydrogen atom; energies of a particle in a box, wave packets, Heiesnberg’s uncertainity relation for p and x, its extension to energy and time.
Consequences of the uncertainty relation: gamma ray microscope, diffraction at a slit, particle in a box, position of electron in Bohr orbit.
Quantum Mechanics: Schrodinger’s equation. Postulatory basis of quantum mechanics; operators, expectation values, transition probabilities, applications to particle in a one and three dimensional boxes, harmonic oscillator, reflection at a step potential, transmission across a potential barrier.
10. Nuclear Physics
Interaction of charged particles and neutrons with matter, working of nuclear detectors, G-M counter, proportional counter and scintillation counter, cloud chambers, spark chamber, emulsions.
11. Solid State Devices
Semiconductors: Intrinsic semiconductors, electrons and holes, Fermi level. Temperature dependence of electron and hole concentrations. Doping; impurity states, n and p type semiconductors, conductivity, mobility, Hall effect, Hall coefficient.
12. Electronics
Power supply: Diode as a circuit element, load line concept, rectification, ripple factor, zener diode, voltage stabilization, IC voltage regulation, characteristics of a transistor in CB, CE and CC mode, graphical analysis of the CE configuration, low frequency equivalent circuits, h-parameters, bias stability, thermal runaway.
13.Electrostatics:
Coulombs law in vacuum expressedin vector forms, calculations of E for simple distributions of charged at rest, dipole and quadrupole fields.
Work done on a charge in a electrostatic field expressed as a line integral, conservative nature of the electrostatic field. Electric potential f, E= -Ñf, torque on a dipole in a uniform electric field and its energy, flux of the electric field, Gauss’s law and its application for finding E for symmetric charge distributions, Gaussian pillbox, fields at the surface of a conductor. Screening of E
field by a conductor, capacitors, electrostatic field energy, force per unit area of a surface of a conductor in an electric field, conducting sphere in a uniform electric field, point charge in front of a grounded infinite conductor.
Dielectrics, parallel plate capacitor with a dielectric, dielectric constant, polarization and polarization vector, displacement vector D, molecular interpretation of Claussius-Mossotti equation, boundary conditions satisfied by E and D at the interface between two homogenous dielectrics
14. Electric Currents (steady and alternating)
Steady current, current density J, non steady currents and continuity equation, Kirchoff’s law and analysis of multiloop circuits, rise and decay of current in LR and CR circuits, decay constants, transients in LCR circuits, AC circuits, complex numbers and their applications in solving
15. Magneto-statics
Force on a moving charge; Lorentz force equation and definition of B, force on a straight conductor carrying current in a uniform magnetic field, torque on a current loop, magnetic dipole moment, angular momentum and gyromagnetic ratio.
Biot and Savert’s law, calculation of H order in simple geometrical situations, Ampere’s Law Ñ.B=0, Ñ x B= m

_{0 }J, field due to a magnetic dipole, magnetization current, magnetization vector,
16. Time Varying Fields
Electromagnetic induction, Faraday’s law, electromotive force, e= ò E.dr, integral and differential forms of Faraday’s law, mutual and self inductance, transformers, energy in a static magnetic field. Maxwell’s displacement current, Maxwell’s equations, electromagnetic field energy density.
17. Electromagnetic Waves
The wave equation satisfied by E and B, plane electromagnetic waves in vacuum, Poynting’s vector, reflection at a plane boundary of dielectrics, polarization by reflection and total internal reflection, Faraday effect, waves in a conducting medium, reflection and refraction by the ionosphere.
18. Lasers
Laser system: Purity of a special line, coherence length and coherence time, spatial coherence of a source, Einstein’s A and B coefficients, Spontaneous and induced emissions, conditions for laser action, population inversion.
Application of lasers: Pulsed lasers and tunable lasers, spatial coherence and directionality, estimates of beam intensity, temporal coherence and spectral energy density.

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