GENERAL PHYSICS IIModule MODULE II
Academic Year 2023/2024  Teacher: Giuseppe Gioacchino Neil ANGILELLAExpected Learning Outcomes
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 mathematicaltheoretical techniques to physics.
Course Structure
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).
Required Prerequisites
Attendance of Lessons
Detailed Course Content
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. Threedimensional 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. HuygensFresnel principle and Kirchhoff theorem (hints). Reflection and refraction of an electromagnetic wave. Laws of SnellDescartes. 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. DrudeLorentz 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 DrudeLorentz model. Group velocity in a dispersive mean. Static and highfrequency limits: (dielectric) insulators and metals. Plasmas and their oscillations.
Interference. Superposition principle. Coherent sources. Optical path. Young doubleslit 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). Xray 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.
Textbook Information
Textbooks recommended for Modulo 1:

Si veda la pagina: http://studium.unict.it/dokeos/2016/main/course_description.
Textbooks recommended for Modulo 2:

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

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

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

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

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

F. Porto, G. Lanzalone, I. Lombardo, Problemi di fisica generale: Elettromagnetismo e ottica (EdiSES, Milano).
Course Planning
Subjects  Text References  

1  Equazioni di Maxwell  Jackson, Mazzoldi 
2  Trasformazioni di gauge ed invarianza delle equazioni di Maxwell  Jackson 
3  Teorema e vettore di Poynting. Tensore di Maxwell. Pressione di raziazione.  Jackson, Mazzoldi 
4  Fenomeni ondulatori  Mazzoldi, Jackson 
5  Onde elettromagnetiche  Jackson, Mazzoldi 
6  Riflessione, rifrazione: leggi di SnellCartesio  Mazzoldi 
7  Formule di Fresnel, polarizzazione  Mazzoldi 
8  Dispersione, assorbimento. Onde elettromagnetiche nella materia. Funzione dielettrica. Modello di DrudeLorentz. Isolanti e metalli. Plasmi  Mazzoldi, Jackson 
9  Interferenza e diffrazione.  Mazzoldi, Jackson, (Born per approfondimenti) 
10  Ottica geometrica  Mazzoldi (Born e Landau per approfondimenti) 
Learning Assessment
Learning Assessment Procedures
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.
Examples of frequently asked questions and / or exercises
 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 SnellDescartes
 Mirrors, thin lenses