Geometrical Optics

Course Description

ETS 2215 – Geometrical Optics is a 3-credit-hour course in the Engineering Technologies taxonomy under Specialty Engineering Technology. The course introduces the fundamental principles governing the behavior of light treated as rays. Students study how light propagates through homogeneous media, interacts with planar and curved optical surfaces, and is redirected by reflection and refraction at interfaces such as lenses, mirrors, and prisms. Emphasis is placed on the mathematical modeling of optical systems, image formation theory, aperture and stop analysis, and the identification of optical aberrations. The course prepares students for advanced work in photonics, laser technology, optical instrumentation, and related engineering technology fields.

Learning Outcomes

Required Outcomes

Upon successful completion of this course, students will be able to:

• Apply Snell's Law and Fermat's Principle to analyze reflection and refraction at planar and curved optical surfaces.
• Perform ray tracing through single and multi-element optical systems using the paraxial approximation.
• Calculate image location, orientation, and magnification using the thin lens equation and Gaussian optics.
• Analyze the function of prisms, mirrors, and lenses as components in optical systems.
• Identify and describe aperture stops, field stops, F-number, and numerical aperture in optical systems.
• Distinguish between chromatic and monochromatic aberrations and explain their impact on image quality.
• Analyze the optical properties of common systems such as telescopes, cameras, and microscopes.
• Apply principles of radiometry and photometry to quantify light propagation in optical systems.

Optional Outcomes

Depending on institutional emphasis, students may also:

• Use optical design software (e.g., Zemax, OpticStudio) to model and simulate optical systems.
• Apply matrix (ABCD) methods for paraxial ray propagation through sequential optical elements.
• Analyze natural optical phenomena such as rainbows, mirages, and halos using ray optics principles.
• Characterize fiber optic light transmission and total internal reflection in waveguide applications.
• Use computational tools such as MATLAB to perform optical calculations and data analysis.
• Evaluate image quality metrics including the modulation transfer function (MTF) and point-spread function (PSF).

Major Topics

Required Topics

1. Introduction to Geometrical Optics – Nature of light as rays; wavefronts and rays; propagation in homogeneous media; limits of the geometrical optics approximation; radiometry fundamentals.
2. Planar Optical Surfaces – Refractive index; optical path length; Fermat's Principle; Snell's Law; reflection and refraction; plane-parallel plates; prisms; optical materials and dispersion.
3. Curved Optical Surfaces – Refraction at spherical surfaces; lensmaker's equation; optical spaces; shape of optical surfaces; paraxial approximation; ray tracing through curved surfaces.
4. Thin and Thick Lenses – Thin lens model; focal length; magnification; cardinal points; Gaussian optics; thick lenses; mirrors as equivalent optical elements.
5. Imaging Systems – Image formation theory; real and virtual images; lens design principles; ZZ′ (object–image) diagrams.
6. Apertures and Stops – Aperture stop; field stop; entrance and exit pupils; F-number; numerical aperture; depth of focus and depth of field.
7. Aberration Theory – Monochromatic aberrations (spherical, coma, astigmatism, field curvature, distortion); chromatic aberrations; diffraction limit.
8. Example Optical Systems – Telescopes (refracting and reflecting); cameras; microscopes; beam expanders; luminaires and concentrators.

Optional Topics

• Matrix (Ray Transfer) Methods – ABCD matrices for sequential ray propagation; system matrix analysis.
• Natural Optical Phenomena – Rainbows, mirages, halos, and total internal reflection in nature.
• Optical Design Software – Introduction to lens design using industry tools; tolerance analysis.
• Fiber Optics and Waveguides – Total internal reflection; acceptance angle; numerical aperture of fibers; fiber transmission basics.
• Radiometry and Photometry in Depth – Irradiance, radiance, luminous flux; detector coupling; étendue.
• Image Quality Metrics – Spot diagrams; ray fans; modulation transfer function (MTF); point-spread function (PSF).

Resources & Tools

• Textbook: Geometrical and Trigonometric Optics, E. L. Dereniak and T. D. Dereniak, Cambridge University Press – widely used at Florida optics programs including UCF CREOL.
• Optical Design Software: Zemax OpticStudio (student edition), Oslo (free EDU version), or open-source alternatives (e.g., ray-optics Python library).
• Computational Tools: MATLAB or Python for ray tracing calculations, data fitting, and graphical analysis.
• Laboratory Equipment (where applicable): Optical benches, light sources, lens and mirror sets, prisms, beam splitters, photodetectors, and optomechanical components.
• Online References: SPIE Digital Library; MIT OpenCourseWare Optics (2.71); UCF CREOL open syllabi; Florida SCNS profile at flscns.fldoe.org.

Career Pathways

Completion of ETS 2215 supports entry into the following career areas:

• Photonics / Laser Technician – Assembling, testing, and maintaining laser and electro-optical systems in manufacturing, defense, and research settings. (Aligns with Valencia College Laser and Photonics T.C. and HCC Laser and Photonics CCC.)
• Optical Systems Technician – Fabricating and aligning optical components for cameras, telescopes, sensors, and medical devices.
• Fiber Optics Technician – Installing and maintaining fiber optic communication systems in the telecommunications industry.
• Electro-Optical Systems Technician – Supporting the design, build, test, and troubleshoot of electro-optical systems in defense, aerospace, and industrial sectors.
• Engineering Technology (A.S. / B.S.) Pathway – This course articulates into the A.S. Engineering Technology degree and supports transfer toward a B.S. in Electrical and Computer Engineering Technology.

Special Information

Program Articulation

ETS 2215 is a specialty course in the Florida SCNS Engineering Technologies taxonomy (prefix ETS – Specialty Engineering Technology). It is commonly offered as part of Laser and Photonics College Credit Certificate (CCC) and Associate in Science (A.S.) programs at Florida colleges such as Hillsborough Community College (HCC) and Valencia College. Credits earned may apply toward the A.S. in Electrical and Computer Engineering Technology or Engineering Technology and, with articulation agreement, toward a B.S. in Engineering Technology.

Industry Certification Preparation

Coursework in geometrical optics provides foundational knowledge supporting industry-recognized credentials in photonics and optical systems, including preparation relevant to SPIE-aligned photonics technician competencies and OP-TEC (National Center for Optics and Photonics Education) curriculum standards. Students are encouraged to pursue SPIE student membership and to explore OP-TEC's national stackable credentials for photonics technicians.

ABET Alignment

Where the course is offered within an ABET-accredited Engineering Technology program, it addresses student outcomes related to the application of mathematics and science, the ability to design and conduct experiments, and the use of modern engineering tools — consistent with ABET Criterion 3 for Engineering Technology programs.