GENERAL PHYSICS II

Module MODULE II

The course aims at providing the student with a somewhat detailed understanding of the electromagnetic field, its interaction with matter, as well as physical and geometrical optics.

Knowledge and understanding:

Knowledge of the basic phenomenology of electromagnetism and (very basic) structure of matter, as well as the interaction between (electromagnetic) radiation and matter. Understanding of their physical implications and their mathematical description.

Applying knowledge and understanding:

bility to identify the main physical laws underlying an electromagnetic phenomenon, and to apply them to solve problems and exercises at a various level of complexity and approximation (both physical and numerical), using both analytical and numerical techniques, as appropriate.

Making judgements:

Estimating the order of magnitude of the main variables intervening in electromagnetism. Assessing the level of importance of a physical law (axiom, conservation law, universal law, theorem, global/integral vs local/differential version of a given law, and its degree of generality, properties of the materials, etc)

Communication skills:

Ability to describe scientific concepts with property of language, at various levels.

Learning skills:

Application of concepts and mathematical-theoretical techniques to physics.

Frontal lectures (in person).

Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course.

NOTE: Information for Students with disabilities/SLD

In order to guarantee equality and in compliance with applicable laws, any interested Student may request an individual meeting, so as to schedule any possible compensation/dispensation measure, depending on the teaching aims and specific requirements.

It is also possible to contact Professor Filippo Stanco, in his quality of contact professor at DMI for CInAP (Centro per l'integrazione Attiva e Partecipata - Servizi per le Disabilità e/o DSA).

Knowledge of General physics I (Mechanics and Thermodynamics), Calculus I and II (real functions of one and more than one real variables) is strongly recommended.

Lectures attendance is strongly advised.

Maxwell equations. Their derivation from the laws of electromagnetism. Scalar and vector potentials. Gauge invariance. Lorentz gauge. Coulomb gauge. Helmholtz theorem. Energy and momentum density of the electromagnetic field. Poyinting theorem and its vector. Maxwell tensor. Radiation pressure. Perfectly absorbing and perfectly reflecting surface.

Waves. D'Alembert equation. Its general integral and initial values problem. Superposition principle for linear PDEs. Derivation of the wave equation for elastic waves in a solid rod and in a tight rope. Longitudinal and transverse waves. Harmonic plane waves. Wave frequency and wave vector. Wave period and wavelength. Dispersion relation. Phase. Fourier series. Linear, elliptic, circular polarization. Wave intensity. Energy propagation in wave phenomena. Three-dimensional waves. Wave front. Wave radius. Spherical waves. Laplacian in polar coordinates. Wave packet. Phase and group velocities. Doppler effect.

Electromagnetic waves. Hertz experiment. Plane waves. Polarization and helicity of an electromagnetic wave. Huygens-Fresnel principle and Kirchhoff theorem (hints). Reflection and refraction of an electromagnetic wave. Laws of Snell-Descartes. Reminder: refraction of the lines of the electromagnetic field. Fresnel formulas for waves polarized in a perpendicular and in a parallel direction to the incidence plane. Reflected and refracted intensity. Limit angle. Wave guides. Optical fibers. Brewster angle. Polaroids. Malus experiment. Dispersion and absorption. Mechanical analogy. Reminder: elliptic polarization.

Electromagnetic waves in matter. Drude-Lorentz model. Constitutive relations: phase difference between P and E. Physical meaning of the imaginary part of the dielectric function ε(ω). Qualitative behaviour of ε(ω) within the Drude-Lorentz model. Group velocity in a dispersive mean. Static and high-frequency limits: (dielectric) insulators and metals. Plasmas and their oscillations.

Interference. Superposition principle. Coherent sources. Optical path. Young double-slit experiment. Fresnel mirrors. Interference among N sources. Thin films. Thin wedge. Newton rings. Michelson interferometre.

Diffraction. Fresnel and Fraunhofer formulation. Fresnel diffraction by an obstacle. Fraunhofer diffraction by a rectangular slit. Analogy with Fourier transforms. Fraunhofer diffraction by a circular slit. Bessel functions (hint). Resolutive power of an optical system: Rayleigh criterion. Diffraction lattice. Dispersion. Emission and absorption spectra (hints). X-ray diffraction by crystals and quasicrystals (hints).

Geometrical optics. Eikonal equation and its physical meaning. Ray equation. Optical path. Reflection and refraction laws (again). Lagrange integral invariant. Fermat principle. Laws od Snell and Descartes. Main optical systems: plane and spherical mirrors; prism; spherical and plane dioptre; thin and thick lenses.

Textbooks recommended for Modulo 1:

• Si veda la pagina: http://studium.unict.it/dokeos/2016/main/course_description.

Textbooks recommended for Modulo 2:

1. J. D. Jackson, Classical Electrodynamics (J. Wiley & Sons, Hoboken, NJ, 1998).

2. P. Mazzoldi, M. Nigro, and C. Voci, Fisica. Vol. 2: Elettromagnetismo, Onde, 3 ed. (EdiSES, Napoli, 2007).

3. L. D. Landau and E. M. Lifsits, Teoria dei campi (Ed. Riuniti – Ed. Mir, Roma – Mosca, 1985); also available in English.

4. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

5. H. D. Young, R. A. Freedman, A. Lewis Ford, Principi di fisica. Vol. 2: Elettromagnetismo e ottica (Pearson, Milano, 2016); also available in English.

6. F. Porto, G. Lanzalone, I. Lombardo, Problemi di fisica generale: Elettromagnetismo e ottica (EdiSES, Milano).

The exam includes a written and an oral examination. The allotted time for the written examination is of 2 hours. The written exam requires solving (with clear comments) (A) 2 problems on the topics of Module 1, and (B) 2 problems on the topics of Module 2. The candidate may stand each part (A and B) of the exam on different session dates, available and compatible with the her/his status ("in corso", "fuori corso" etc). In that case, the allotted time for each part is 1 hour. Each problem receives a score between 0/30 (min) and 7.5/30 (max).

Candidates who receive an overall evaluation of their written exam below 15/30 (or 7.5/30, for a single module) are not recommended to stand the oral exam. In any case, they are not admitted to any oral exam on a session date after the successive written exam.

The full oral exam includes the discussion of at least 3 different topics in the course contents, whereof the first one is chosen by the candidate. During the oral exam it may be required to prove theorems or important results in the course contents, also providing numerical estimates of the order of magnitude of physical quantities involved in a given phenomenon.

Evaluation may also take place online, should circumstances require, and current regulations allow that.

- Discuss Maxwell equations, and derive them from the global version of the laws of electromagnetism

- Describe the gauge transformations and the gauge invariance of Maxwell equations

- D'Alembert equation: general integral and initial values problem

- Electromagnetic waves

- Optical properties of matter: metals and insulators

- Laws of Snell-Descartes

- Mirrors, thin lenses