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Code: 100156 ECTS Credits: 9
Degree Type Year Semester
2500097 Physics OB 3 A


Angel Lizana Tutusaus

Teaching groups languages

You can check it through this link. To consult the language you will need to enter the CODE of the subject. Please note that this information is provisional until 30 November 2023.


Juan Ignacio Pedro Campos Coloma


There are no special requirements, but it would be convenient if the student has completed the subjects of Electromagnetisme, Ones i Òptica, and those related to mathematics fundamentals given at previous academic courses.  

Objectives and Contextualisation

The general goal of the Òptica subject is to present to students a general view of the classical optics field, which encompasses a wide range of knowledge areas, from optical instrumentation to interferential and diffraction phenomena. The quantum optics theory is addressed within another subject of the physics degree. The Òptica subject, in addition to provide basic knowledge in the optics field, it is also useful to illustrate how different phenomena can be described by using different theoretical models: electromagnetic model, wave model, geometrical model, etc. This approach meets a transversal competence of learning how to identify a problem, and considering the most suitable methodology to solve it.

The Òptica subject is highly interrelated with the Laboratori d’Òptica subject, which is taught in the same academic course and presents an experimental approach of the Optics phenomena, forming up a thematic cluster.

By means of the geometrical model, the knowledge required to understand the basic optical instruments is provided: Human eye, photographic camera, telescope, and the microscope. By means of the light electromagnetic theory, the interaction of light with different materials is studied, taking special attention to isotropic media and to anisotropic homogeneous and linear media. Regarding to dielectric materials, the classical Lorentz model is introduced to explain the dispersion phenomenon. Finally, by means of the wave model, interferential and diffraction phenomena are studied.


  • Develop strategies for analysis, synthesis and communication that allow the concepts of physics to be transmitted in educational and dissemination-based contexts
  • Formulate and address physical problems identifying the most relevant principles and using approximations, if necessary, to reach a solution that must be presented, specifying assumptions and approximations
  • Know the fundamentals of the main areas of physics and understand them
  • Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
  • Use mathematics to describe the physical world, selecting appropriate tools, building appropriate models, interpreting and comparing results critically with experimentation and observation

Learning Outcomes

  1. Apply the Fourier transform to describe and polychromatic waves and to describe the phenomenon of diffraction.
  2. Assess the resolution of optical systems taking size into consideration.
  3. Calculate the direction of propagation for waves transmitted in anisotropic media.
  4. Calculate the energy carried by a beam.
  5. Calculate the figure of diffraction produced by different apertures, applying the approaches necessary.
  6. Calculate the interference pattern produced in different interferometers and determine changes in the figure when varying certain system parameters.
  7. Calculate the refraction of a plane wave in anisotropic medium and the divergence produced.
  8. Calculate the waves transmitted and reflected in an interface between two isotropic media and assess their state of polarization.
  9. Describe induced polarization in a dielectric medium and the complex refractive index.
  10. Describe methods to evaluate the diffraction produced by different apertures.
  11. Describe the Maxwell equations and the obtention, from these, of the equation of electromagnetic waves.
  12. Describe the classical Lorentz model of light-matter interaction.
  13. Describe the conditions of propagation for a wave in an anisotropic medium (ordinary and extraordinary wave).
  14. Describe the conditions required for stable interference to occur.
  15. Describe the effects that modify the index ellipsoid of a material.
  16. Describe the functioning of retardant plates.
  17. Describe the main types of wave fronts and the harmonic solution of wave equation.
  18. Describe the phenomena of refraction and reflection in isotropic media.
  19. Describe the phenomenon of light diffraction.
  20. Describe the polarization states of light.
  21. Describe the various devices to produce interference.
  22. Determine the state of polarization of a beam before and after crossing a retarding plate.
  23. Identify optical phenomena observed in nature and explain them clearly in non-specialized settings.
  24. Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
  25. Use the complex representation of harmonic waves.
  26. Use wave equation and its general solutions.


  1. Waves:
    1. Wave motion equation. Plane waves, spherical waves.
    2. Harmonic solution of the wave equation. Fourier analysis.
    3. Superposition of waves with the same frequency.
    4. Superposition of waves with different frequency. Phase and group velocities.
    5. Superposition of waves with orthogonal electric fields.
  2. Light electromagnetic theory. Electromagnetic waves:
    1. Macroscopic Maxwell equations. Material response. Energy relations.
    2. Electromagnetic waves. Linear, homogeneous and isotropic media. Transverse characteristic of plane waves.  Energy transport.
  3. Isotropic media:
    1. Reflection and refraction at dielectric interface. Fresnel equations.
    2. Dielectric media. Induced polarization. Classical Lorentz model for the dipole description.
    3. Propagation and diffusion of a light beam.
  4. Geometrical Optics. Paraxial approximation:
    1. Fermat principle. Ray trajectory equation. Light propagation in non-uniform media.
    2. Imaging with geometrical optics.
    3. Paraxial optics. Abbe’s invariant. Magnification.
    4. Composed optical systems. Focal points and focal planes. Principal points and principal planes. Thick lenses. Coupled optical systems.
  5. Optical instrumentation:
    1. Human eye.  
    2. Photographic systems and projectors.
    3. Telescopes.
    4. Near vision instruments: Magnifying glass, optical microscope.
  6. Anisotropic media. Polarization:
    1. Electrical susceptibility. Indices ellipsoid.
    2. Wave equation in anisotropic media. Propagation conditions.
    3. Light refraction in an anisotropic media. Fresnel construction. Indices ellipsoid construction.
    4. Absorbing anisotropic media.
  7. Interferences:
    1. General principles. Conditions for interferences.
    2. Wave front division interferences: Young interference pattern, practical arrangements.
    3. Amplitude division interferences.  Michelson interferometer.
    4. Interference produced by multiple light beams obtained by amplitude division. Fabry-Perot interferometer.
  8. Diffraction:
    1. Huygens-Fresnel principle.
    2. Fresnel and Fraunhofer diffraction approaches.
    3. Fraunhofer diffraction produced by a single aperture: single slit, rectangular aperture, circular aperture. Instruments resolution power.
    4. Fraunhofer diffraction produced by diverse apertures: Double slit, diffraction grating.
    5. Introduction to the Kirchhoff scalar theory.




Within this type of activity the theoretical concepts of the course will be provided. Those slides used during the course will be uploaded to the virtual campus.

Students will be encouraged to participate and to ask questions related to doubts that may rise by using the subjects forum at the virtual campus. In addition, professors will ask questions to them in order to evaluate their comprehension of the knowledge taught.


These classes will be used to put into practice the concepts described at the theory classes, with the aim of identifying the type of problem to be solved, and the more suitable methodology to be applied to resolve it. The problems statements will be uploaded at the Campus Virtual well in advance, in order to students can try to solve them before the resolution is described at class, and thus, they can ask their doubts in the corresponding problem session.


This activity is performed with the aim of enhancing the observation capacity of students and to foster their capability to relate phenomena present in the nature with the concepts taught in the Òptica subject.  

Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.


Title Hours ECTS Learning Outcomes
Type: Directed      
Problems sessions 25 1 1, 2, 4, 3, 6, 5, 7, 8, 19, 16, 12, 21, 15, 20, 18, 10, 17, 9, 13, 14, 11, 22, 24, 25, 26
Theory sessions 50 2 1, 2, 4, 3, 6, 5, 7, 8, 19, 16, 12, 21, 15, 20, 18, 10, 17, 9, 13, 14, 11, 22, 24, 25, 26
Type: Supervised      
Photographs of optical phenomena in the nature 5 0.2 23, 24
tutorship 4.5 0.18 24
Type: Autonomous      
Problems solving 51 2.04 1, 2, 4, 3, 6, 5, 7, 8, 22, 24, 25, 26
Self-study 80 3.2 19, 16, 12, 21, 15, 20, 18, 10, 17, 9, 13, 14, 11, 24


In this section, the observation capacity of the student will be evaluated and the concepts studied will be related to natural phenomena.
Each student must present 6 original photographs (made by themselves) of natural phenomena related to the concepts studied in the subject. No photos obtained in the laboratory, nor downloads from the internet (in this case the note corresponding to the photos will be 0). In addition, you must give a brief explanation (about a sheet) of the phenomenon analyzed.
Each of the 6 photographs must be dedicated to a different phenomenon. 3 pictures will be presented online at the end of each semester (before the corresponding partial exam) in pdf or word format.
The name of the files will be: Name_Surname_n ...
n will be equal to 1 or 2 depending on the delivery of the first semester or the second semester.
Students who are evaluated through the single assessment modality must take a final test that will consist of a theory exam in which they must answer a series of questions related to the course syllabus. Next, they will have to do a problem based test in which they will have to solve a series of exercises similar to those previously studied in the Classroom Practice sessions. Finally, they will submit a report with six photographs of optical phenomena taken by themselves (and their corresponding description), with a maximum length of 6 pages, and must make a brief oral presentation to comment the described phenomena. These tests will be carried out on the same day, time and place as the tests of the second part of the continuous assessment modality.

The student's grade will be the weighted average of the three previous activities, where the theory exam will account for 30% of the grade, the problems exam for 40% and the presentation/defense of optical phenomena for 10%.

If the final score does not reach the minimum value of 5, the student will have another opportunity to pass the course by taking the remedial exam that will be held on the date stated by the Degree Coordination. In this situation, the final mark of the subject will be that obtained at the remedial exam


Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
1er Partial examination 45 2.5 0.1 1, 2, 4, 8, 12, 20, 18, 17, 9, 11, 24, 25, 26
2n Partial examination 45 2.5 0.1 3, 6, 5, 7, 19, 16, 21, 15, 10, 13, 14, 22, 24
Partials remedial exam 90 3.5 0.14 1, 2, 4, 3, 6, 5, 7, 8, 19, 16, 12, 21, 15, 20, 18, 10, 17, 9, 13, 14, 11, 22, 24, 25, 26
Photographs delivery 10 1 0.04 23, 24



  • J. Casas. Óptica. Universidad de Zaragoza
  • E. Hecht. Optics. Addison-Wesley Publishing Company.
  • M.V. Klein, T. E. Furtak. Optics. John Wiley & Sons
  • Keigo Iizuka, Elements of Photonics Volume 1. John Wiley & Sons, Inc. ISBNs: 0-471-83938-8 (Hardback); 0-471-22107-4 (Electronic)
  • R. Guenter. Modern Optics. John Wiley & Sons
  • B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics, second edition. John Wiley & Sons. ISBN: 978-0-471-35832-9 
  • F.G. Smith, J.H. Thomson, Optics, John Wiley & Sons Ltd. ISBN 0 471 91534 3


  • E. Hecht. Teoría y Problemas de Óptica. MacGraw-Hill
  • M. López, J.L. Díaz, J.M. Jiménez. Problemas de Física volumen V. Óptica. Editorial Romo.
  • M. Fogiel, THE OPTICS PROBLEM SOLVER, Research and Education Association. ISBN: 0-87891-526-5 
  • Lim Yung-kuo,  Problems and Solutions on Opticsm. World Scientific. ISBN: 981-02-0438-8



Optic's Applets in Matlab: http://sedoptica.es/appletsmatlab

Optic’s Applets in java:  http://www.ub.es/javaoptics/index-en.html

Physics’ Applets in java: http://www.walter-fendt.de/ph14s/

Virtual Campus: Applets in LabView and videos related to some optics phenomena


Applets of optical phenomena in Matlab