SEMESTER IV
PHYSICS-C VIII: OPTICS
(Credits: Theory-04) Theory: 60 Lectures
Mid Semester: 15 End Semester: 60 Full Marks: 75
Short Answer Type:
4 Marks (3 out of 5) & Long Answer Type: 12 Marks (4 out of 6)
Wave Optics:
Electromagnetic nature of light. Definition and properties of wave front. Huygens Principle.
Interference:
Division of amplitude and wavefront. Young’s double slit experiment. Fresnel’s Biprism. Phase change on reflection: Stokes’ treatment. Interference in Thin Films: parallel and wedge-shaped films. Fringes of equal inclination; Fringes of equal thickness. Newton’s Rings: Measurement of wavelength and refractive index.
Interferometer:
Michelson Interferometer, Idea of formation of fringes, Determination of Wavelength, Wavelength Difference. Fabry-Perot interferometer – theory and applications.
Fraunhofer diffraction:
Single slit. Circular aperture, Resolving Power of a telescope.. N slits. Diffraction grating. Resolving power of grating.
Fresnel Diffraction:
Fresnel’s Assumptions. Fresnel’s Half-Period Zones for Plane Wave. Explanation of Rectilinear Propagation of Light. Theory of a Zone Plate: Multiple Foci of a Zone Plate, Fresnel diffraction pattern of a straight edge, a slit and a wire.
Polarization:
Description of Linear, Circular and Elliptical Polarization. Double Refraction. Nicol Prism. Ordinary & extraordinary refractive indices. Production & detection of Plane, Circularly and Elliptically Polarized Light. Phase Retardation Plates: Quarter-Wave and HalfWave Plates.
Rotatory Polarization:
Optical Rotation. Biot’s Laws for Rotatory Polarization. Calculation of angle of rotation. Specific rotation. Laurent’s half-shade polarimeter.
Reference Books
• Introduction to Geometrical and Physical Optics, B. K. Mathur.
• Geometrical and Physical Optics, P. K. Chakraborty.
• Fundamentals of Optics, F.A. Jenkins and H.E. White, 1981, McGraw-Hill
• Principles of Optics, Max Born and Emil Wolf, 7th Edn., 1999, Pergamon Press.
• Optics, Ajoy Ghatak, 2008, Tata McGraw Hill
PHYSICS LAB- LAB C VIII (2 Credits) FM: 25
1. Familiarization with: Schuster`s focusing; determination of angle of prism.
2. To determine refractive index of the Material of a prism using sodium source.
3. To determine the dispersive power and Cauchy constants of the material of a prism using mercury source.
4. To determine wavelength of sodium light using Fresnel Biprism.
5. To determine wavelength of sodium light using Newton’s Rings.
6. To determine the thickness of a thin paper by measuring the width of the interference fringes produced by a wedge-shaped Film.
7. To determine wavelength of (1) Na source and (2) spectral lines of Hg source using plane diffraction grating.
8. To determine dispersive power and resolving power of a plane diffraction grating
PHYSICS-C IX: QUANTUM MECHANICS AND APPLICATIONS
(Credits: Theory-04) Theory: 60 Lectures
Mid Semester: 15 End Semester: 60 Full Marks: 75
Short Answer Type:
4 Marks (3 out of 5) & Long Answer Type: 12 Marks (4 out of 6)
Schrodinger theory:
Inadequcy of classical mechanics, Origin of old Quantum theory, Discretness of energy: Franck and Hertz experiment, Wave – particle duality of matter and radiation ( Photoelectric effect, Compton effect, Davisson and Germer experiment), Wave function and its physical meaning, Wave packets, Schrodinger time – independent and time – dependent equations, Concept of stationary states, Probabilty density and probability current density.
Operators:
Eigenvalues and eigenfunction; linear operators, product of two operators, commuting and noncommuting operators, simulataneous eigenfunctions, orthogonal functions. Hermitian operators, their eigenvalues, Hermitian adjoint operators, expectation values of an operator.
One-dimensional problems:
Rectangular potential barrier, Square well potential of finite and infinite depth, Particle in a rectangular box.
Heisenberg’s uncertainity principle:
Derivation of uncertainity relation using Schawrtz inequality and simple applications of uncertainity principle, expectation value of Time derivative of operators, Ehrenfest theorem.
Application to 1-D Problem:
Simple harmonic oscillator, eigenfunctions and eigenvalues of the ground state and excited states; zero-point energy. Orthogonality of wave functions. Rigid rotator.
Reference Books:
• Introduction to Quantum mechanics, Nikhil Ranjan Roy, 2016, Vikash Publishing House Pvt. Ltd. • A Text book of Quantum Mechanics, P.M.Mathews and K.Venkatesan, 2nd Ed., 2010, McGraw Hill • Quantum Mechanics, Robert Eisberg and Robert Resnick, 2nd Edn., 2002, Wiley.
• Quantum Mechanics, Leonard I. Schiff, 3rd Edn. 2010, Tata McGraw Hill.
• Quantum Mechanics, G. Aruldhas, 2nd Edn. 2002, PHI Learning of India.
• Quantum Mechanics, Bruce Cameron Reed, 2008, Jones and Bartlett Learning.
• Quantum Mechanics: Foundations & Applications, Arno Bohm, 3rd Edn., 1993, Springer
PHYSICS LAB- LAB C IX (2 Credits) FM: 25
Use C/C++/Scilab for solving the following problems based on Quantum Mechanics like
1. Solve the s-wave Schrodinger equation for the ground state and the first excited state of the hydrogen atom:
d^2 y/dr^2 = 𝐴 (𝑟ሻ𝑢(𝑟), 𝐴(𝑟ሻ = 2m/h^2 x [V(r) - E] where 𝑉 (𝑟ሻ = −e^2 /r
Here, m is the reduced mass of the electron. Obtain the energy eigenvalues and plot the corresponding wavefunctions. Remember that the ground state energy of the hydrogen atom is ≈ -13.6 eV. Take e = 3.795 (eVÅ)1/2, ħc = 1973 (eVÅ) and m = 0.511x106 eV/c2 .
2. Solve the s-wave radial Schrodinger equation for an atom:
d^2 y/dr^2 = 𝐴 (𝑟ሻ𝑢(𝑟), 𝐴(𝑟ሻ = 2m/h^2 * [V(r) - E]
where m is the reduced mass of the system (which can be chosen to be the mass of an electron), for the screened coulomb potential 𝑉 (𝑟ሻ = −e^2 /r x {e^(-r/a}
Find the energy (in eV) of the ground state of the atom to an accuracy of three significant digits. Also, plot the corresponding wavefunction. Take e = 3.795 (eVÅ)^1/2, m = 0.511x106 eV/c^2 , and a = 3 Å, 5 Å, 7 Å. In these units ħc = 1973 (eVÅ). The ground state energy is expected to be above -12 eV in all three cases.
3. Solve the s-wave radial Schrodinger equation for a particle of mass m:
d^2 y/dr^2 = 𝐴 (𝑟ሻ𝑢(𝑟), 𝐴(𝑟ሻ = 2m/h^2 x [V(r) - E]
For the anharmonic oscillator potential V(r) = ½ kr2 + 1/3br^3 for the ground state energy (in MeV) of particle to an accuracy of three significant digits. Also, plot the corresponding wave function. Choose m = 940 MeV/c^2 , k = 100 MeV fm^-2, b = 0, 10, 30 MeV fm^-3. In these units, cħ = 197.3 MeV fm. The ground state energy I expected to lie between 90 and 110 MeV for all three cases.
4. Solve the s-wave radial Schrodinger equation for the vibrations of hydrogen molecule:
d^2 y/dr^2 = 𝐴 (𝑟ሻ𝑢(𝑟), 𝐴(𝑟ሻ = 2μ/h^2 x [V(r) - E]
Where μ is the reduced mass of the two-atom system for the Morse potential ሺ𝑟ሻ = 𝐷 (e-2αr’ – e-αr’), r’ = (r-r0)/r Find the lowest vibrational energy (in MeV) of the molecule to an accuracy of three significant digits. Also plot the corresponding wave function. Take: m = 940x106eV/C^2 , D = 0.755501 eV, α = 1.44, ro = 0.131349 Å.
Laboratory based experiments:
5. Study of Electron spin resonance- determine magnetic field as a function of the resonance frequency
6. Study of Zeeman effect: with external magnetic field; Hyperfine splitting
7. To show the tunneling effect in tunnel diode using I-V characteristics.
8. Quantum efficiency of CCDs
9. Verification of plcank’s uncertainly principle
10. Determination of wavelength of an electron in ground state of hydrogen and establish deBroglie relation.
PHYSICS-C X: ELECTROMAGNETIC THEORY
(Credits: Theory-04) Theory: 60 Lectures
Mid Semester: 15 End Semester: 60 Full Marks: 75
Short Answer Type:
4 Marks (3 out of 5) & Long Answer Type: 12 Marks (4 out of 6)
Maxwell Equations:
Review of Maxwell’s equations. Displacement Current. Boundary Conditions at Interface between Different Media. Wave Equations. Plane Waves in Dielectric Media. Poynting vector and Poynting Theorem. Electromagnetic (EM) Energy Density.
EM Wave Propagation in dielectric Media:
Plane EM waves through vacuum and isotropic dielectric medium, transverse nature of plane EM waves, refractive index and dielectric constant, Boundary conditions at a plane interface between two media. Reflection & Refraction of plane waves at plane interface between two dielectric media-Laws of Reflection & Refraction. Fresnel's Formulae for perpendicular & parallel polarization cases, Brewster's law. Reflection & Transmission coefficients. Total internal reflection, evanescent waves.
EM Wave in conducting Media:
Propagation through conducting media, relaxation time, skin depth. reflection at and transmission through a conducting surface Wave propagation through dilute plasma, electrical conductivity of ionized gases, plasma frequency, refractive index, skin depth. Electromagnetic theory of dispersion.
Electromagnetic potentials:
Magnetic vector potential A and scalar potential φ. Lorentz gauge, Coulomb's gauge. Maxwell's equation in terms of potentials. Gauge invariance,
Radiation from accelerated charge:
Retarded potential, Lenard- Weichart potential, electric dipole radiation, magnetic dipole radiation, Radiation from an accelerated charged particle along and perpendicular to the direction of motion.
Reference Books:
1. Electromagnetic Theory, Chopra and Agarwal.
2. Electromagnetics, B. B. Laud.
3. Electromagnetic Theory,, Satya Prakash
4. Electromagnetic Theory, Gupta and Kumar
5. Introduction to Electrodynamics, D.J. Griffiths, 3rd Ed., 1998, Benjamin Cummings.
6. Introduction to Electromagnetic Theory, T.L. Chow, 2006, Jones & Bartlett Learning
PHYSICS LAB- LAB C X (2 Credits) FM: 25
1. To verify the law of Malus for plane polarized light.
2. To determine the specific rotation of sugar solution using Polarimeter.
3. To analyze elliptically polarized Light by using a Babinet’s compensator.
4. To determine the refractive Index of (1) glass and (2) a liquid by total internal reflection using a Gaussian eyepiece.
5. To study the polarization of light by reflection and determine the polarizing angle for airglass interface.
6. To determine the Boltzmann constant using V-I characteristics of PN junction diode.
NEXT :: SEMESTER 5
