Unit GEOMETRIC OPTICS LABORATORY
- Course
- Optics and optometry
- Study-unit Code
- A002458
- Curriculum
- In all curricula
- Teacher
- Maurizio Mattarelli
- Teachers
-
- Maurizio Mattarelli
- Marco Madami (Codocenza)
- Hours
- 55 ore - Maurizio Mattarelli
- 48 ore (Codocenza) - Marco Madami
- CFU
- 9
- Course Regulation
- Coorte 2026
- Offered
- 2026/27
- Learning activities
- Caratterizzante
- Area
- Microfisico della materia e delle interazioni fondamentali
- Sector
- PHYS-03/A
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
The laboratory consists of 7 geometric optics experiments:
• Reflection – experimental verification of the law of reflection on flat, concave, and convex mirrors
• Refraction – measurement of the index of refraction of a D-shaped acrylic lens using Snell's Law
• Object and image distances for a thin lens – verification of the thin lens equation and magnification measurement
• Telescope – construction of the Keplerian and Galilean telescope; magnification measurement
• Focimeter – construction of an automatic focimeter; measurement of the dioptric power of unknown lenses
• Dispersion – observation of chromatic dispersion through an acrylic prism; calculation of indices of refraction for red and blue light
• Magnifying lens, compound microscope, and infinity-corrected microscope – progressive construction of three optical systems; measurement of theoretical and experimental magnification
In all experiments, particular attention is devoted to experimental data acquisition methodologies and statistical methods for data analysis, including the preparation of structured laboratory reports.- Reference texts
Notes and materials provided by the instructor, available on Unistudium.- Educational objectives
The Geometric Optics Laboratory complements the Geometric Optics theory course, applying its principles and formulas in an experimental context. It is the first intensive laboratory course in the Optics and Optometry degree programme.
The course contributes to the degree programme's objectives by:
• translating into experimental practice the theoretical concepts acquired in the Geometric Optics course;
• developing practical skills in the use of optical instrumentation relevant to optometry (focimeter, microscope);
• introducing quantitative measurement methods and statistical data analysis as transversal competences.
Knowledge acquired:
• methods for experimental data acquisition and statistical analysis in optics;
• constructive and operating principles of complex optical systems (Keplerian and Galilean telescope, compound microscope, infinity-corrected microscope, focimeter);
• structure and writing of a scientific laboratory report.
Skills acquired:
• set up and conduct geometric optics experiments independently, applying known laws and formulas, identify sources of error and discuss their limits;
• measure optical quantities (indices of refraction, focal lengths, magnifications, dioptric power) and compare results with theoretical predictions;
• operate basic optical instrumentation in research laboratories and optometric settings, in particular the focimeter and the microscope;
• communicate results in written form through a structured report.- Prerequisites
There are no formal prerequisites. However, in order to engage profitably with the laboratory activities, students are expected to have acquired the knowledge of geometric optics provided by the Geometric Optics course, in particular:
• the laws of reflection and refraction (Snell's Law) and the concept of index of refraction;
• the thin lens equation and geometrical image construction;
• the operating principles of flat and curved mirrors;
• the concepts of focal length and linear magnification.
A basic knowledge of algebra and trigonometry is also recommended.- Teaching methods
The course is organized as follows:
• Introductory lectures, aimed at presenting the experimental context of each activity, recalling relevant theoretical principles, and illustrating measurement and data analysis procedures;
• Laboratory experiments carried out in small groups, in which students independently set up the optical bench, acquire data, and perform data analysis;
• Classroom discussions on the results obtained, sources of error, and comparison between experimental values and theoretical predictions.
At the end of each experiment, students write a structured laboratory report following a template provided by the instructor. For data processing and report writing, students use Microsoft Office 365 (in particular Excel), provided free of charge by the University to all students.
Teaching materials (experiment guides, report template) are available on Unistudium.- Other information
For information on office hours, contact the instructor by email or via Unistudium.
For information on support services for students with disabilities and/or DSA visit the page http://www.unipg.it/disabilita-e-dsa- Learning verification modality
The assessment of the course's learning outcomes consists of three integrated components:
1. Laboratory reports (7 reports, one per experiment)
During the course, working groups of typically 3 students submit a written report at the end of each of the 7 experiments, following the structured template provided by the instructor. Each report is assessed in terms of correctness of data processing, consistency with theoretical predictions, analysis of sources of error, and clarity of presentation. The average grade of the reports constitutes the starting point for the determination of the final grade.
2. Discussion of the reports
During the exam, the commission discusses the submitted reports with the student, with particular attention to critical points in the analysis. This component aims to verify the student's individual contribution to group activities, understanding of theoretical content, and ability to independently interpret results.
3. Practical test
The student replicates in the laboratory one of the experiments carried out during the course, chosen by the commission. The discussion of the reports and the practical test have a combined indicative duration of 30 minutes and aim to verify the ability to independently set up the optical bench, carry out measurements correctly, and operate the instrumentation with confidence.
The final grade out of thirty is determined by the commission taking into account the average of the reports, the outcome of the discussion, and the practical test. The discussion and practical test can significantly modify the grade relative to the report average, either upward or downward.
For information on support services for students with disabilities and/or DSA visit the page http://www.unipg.it/disabilita-e-dsa- Extended program
Course introduction (1 lecture)
Introduction to the course, laboratory procedures, and group work. Introduction to measurement methods, error estimation and propagation, use of Microsoft Excel for experimental data processing, and structure of the laboratory report.
Experiment 1 — Reflection
Experimental verification of the law of reflection on flat, concave, and convex mirrors. Measurement of angles of incidence and reflection with a protractor. Analysis of sources of angular error.
Experiment 2 — Refraction
Measurement of the index of refraction of a D-shaped acrylic lens using Snell's Law. Construction of the sin ¿1 vs sin ¿2 graph and determination of the index by linear regression. Calculation of the percentage error with respect to the theoretical value.
Experiment 3 — Object and image distances for a thin lens
Measurement of image distance as a function of object distance for a converging lens. Verification of the thin lens equation. Measurement of linear magnification and its relationship to object and image distances. Graphical representation and data linearisation.
Experiment 4 — Telescope
Construction of the Keplerian astronomical telescope (finite and infinite object distance) and the Galilean telescope with a diverging eyepiece. Measurement and comparison of theoretical and experimental magnifications. Parallax elimination. Ray diagram tracing.
Experiment 5 — Focimeter
An introductory lecture presents the operating principle of the focimeter and the relationship between reticle displacement and dioptric power of an unknown lens. In the laboratory, students construct an automatic focimeter using kit lenses (collimator objective f = 100 mm) and measure the dioptric power of unknown converging and diverging lenses. Comparison with theoretical predictions.
Experiment 6 — Dispersion
Observation of chromatic dispersion through an acrylic prism. Measurement of refraction angles for red and blue light. Calculation of the indices of refraction for both colours using Snell's Law and of the respective propagation speeds in the medium.
Experiment 7 — From the magnifying lens to the microscope
An introductory lecture presents the principles of microscopic systems and the differences between the compound microscope and the infinity-corrected microscope. In the laboratory, students progressively construct three optical systems: magnifying lens, compound microscope, and infinity-corrected microscope. For each system: determination of image position, calculation of theoretical magnification, experimental measurement of magnification, comparison and error analysis.- Obiettivi Agenda 2030 per lo sviluppo sostenibile
The course contributes to the following Sustainable Development Goals of the 2030 Agenda:
• Goal 4 – Quality Education: the course promotes quality scientific education based on active learning and the acquisition of practical and methodological skills applicable in both academic and professional contexts.
• Goal 9 – Industry, Innovation and Infrastructure: understanding the physical principles underlying optical instruments relevant to research and professional practice (focimeter, microscope, telescope), combined with quantitative data analysis skills, contributes to training professionals capable of operating in and contributing to the development of solutions in industrial and research settings in the optical and optometric sector.