Physical Optics: Concepts, Optical Elements, and Techniques

UNITEXT for Physics

Giovanni Giusfredi

Physical Optics Concepts, Optical Elements, and Techniques

UNITEXT for Physics Series Editors Michele Cini, University of Rome Tor Vergata, Roma, Italy Attilio Ferrari, University of Turin, Turin, Italy Stefano Forte, University of Milan, Milan, Italy Guido Montagna, University of Pavia, Pavia, Italy Oreste Nicrosini, University of Pavia, Pavia, Italy Luca Peliti, University of Napoli, Naples, Italy Alberto Rotondi, Pavia, Italy Paolo Biscari, Politecnico di Milano, Milan, Italy Nicola Manini, University of Milan, Milan, Italy Morten Hjorth-Jensen, University of Oslo, Oslo, Norway

UNITEXT for Physics series, formerly UNITEXT Collana di Fisica e Astronomia, publishes textbooks and monographs in Physics and Astronomy, mainly in English language, characterized of a didactic style and comprehensiveness. The books published in UNITEXT for Physics series are addressed to graduate and advanced graduate students, but also to scientists and researchers as important resources for their education, knowledge and teaching.

More information about this series at http://www.springer.com/series/13351

Giovanni Giusfredi

Physical Optics Concepts, Optical Elements, and Techniques

123

Giovanni Giusfredi European Laboratory for Non-Linear Spectroscopy (LENS) Istituto Nazionale di Ottica—Consiglio Nazionale delle Ricerche (INO-CNR) Sesto Fiorentino, Italy

ISSN 2198-7882 ISSN 2198-7890 (electronic) UNITEXT for Physics ISBN 978-3-030-25278-6 ISBN 978-3-030-25279-3 (eBook) https://doi.org/10.1007/978-3-030-25279-3 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland



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Chapter 2 Geometrical Optics All what we see, it is seen in a rectilinear direction. Pseudo-Eukleidēs, Catoptrics, 2nd postulate

Introduction Geometrical Optics is one of the oldest of the physical sciences, but still remains the most effective approach for explaining a good part of the most common optical phenomena. It is particularly useful for tracing the propagation of light in inhomogeneous media and for describing or designing optical instruments. The emphasis of this discipline is to find the path of light rays, imagined as geometric lines along which energy flows. It is based on a few simple observations: a) light propagates in a straight line in homogeneous media and, in particular, it is possible to produce thin beams of light, similar to geometrical rays within the physically unattainable limit of an infinite subtlety; b) the laws of reflection and refraction; c) different light beams propagate without disturbing each other; d) “natural” sources are generally uncorrelated between them, for which their light beams overlap without showing interference. On the other hand, the electromagnetic field associated with visible light is characterized by very small wavelengths, on the order of 106  107 m. Therefore, the phenomena that violate the first and the last of the above observations can be observed only with accurate experiments. Indeed, the effects of diffraction or interference are almost hidden using natural sources, for which the visibility of the fringes is reduced. The diffraction phenomena appear when there are rapid changes in the amplitude of the field, such as that produced by a sharp obstacle, particularly when some dimension of the optical system, such as the diameter of an aperture, is comparable to the wavelength; or in the neighborhood of a focal point; or over long distances compared to the transverse dimension of a wave, particularly when there is a delimitation imposed upon it. Lastly, point (c) follows from the linearity of the media at the ordinary beams’ intensity. In this chapter, we will explore the consequences of such observations taken as empirical data. However, we will derive the laws of Geometrical Optics by Maxwell’s equations within the limit at which the wavelength  tends to zero. We will also see that, within such a limit, the intensity can be deduced from the transverse dimension of a thin pencil of rays and that the polarization state can be associated with each ray. Therefore, in Geometrical Optics, the rays are associated with the Electronic supplementary material The online version of this chapter (https://doi.org/10.1007/ 978-3-030-25279-3_2) contains supplementary material, which is available to authorized users.

© Springer Nature Switzerland AG 2019 G. Giusfredi, Physical Optics, UNITEXT for Physics, https://doi.org/10.1007/978-3-030-25279-3_2

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