Basic Geometrical Optics

Basic Geometrical Optics
Leno S. Pedrotti
CORD
Waco, Texas
Optics is the cornerstone of photonics systems and applications. In this module, you will learn
about one of the two main divisions of basic optics—geometrical (ray) optics. In the module to
follow, you will learn about the other—physical (wave) optics. Geometrical optics will help you
understand the basics of light reflection and refraction and the use of simple optical elements such
as mirrors, prisms, lenses, and fibers. Physical optics will help you understand the phenomena of
light wave interference, diffraction, and polarization; the use of thin film coatings on mirrors to
enhance or suppress reflection; and the operation of such devices as gratings and quarter-wave
plates.
Prerequisites
Before you work through this module, you should have completed Module 1-1, Nature and
Properties of Light. In addition, you should be able to manipulate and use algebraic formulas,
deal with units, understand the geometry of circles and triangles, and use the basic trigonometric
functions (sin, cos, tan) as they apply to the relationships of sides and angles in right triangles.
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Objectives
When you finish this module you will be able to:
• Distinguish between light rays and light waves.
• State the law of reflection and show with appropriate drawings how it applies to light
rays at plane and spherical surfaces.
• State Snell’s law of refraction and show with appropriate drawings how it applies to
light rays at plane and spherical surfaces.
• Define index of refraction and give typical values for glass, water, and air.
• Calculate the critical angle of incidence for the interface between two optical media and
describe the process of total internal reflection.
• Describe how total internal reflection can be used to redirect light in prisms and trap
light in fibers.
• Describe dispersion of light and show how a prism disperses white light.
• Calculate the minimum angle of deviation for a prism and show how this angle can be
used to determine the refractive index of a prism material.
• Describe what is meant by Gaussian or paraxial optics.
• Describe the relationship between collimated light and the focal points of convex and
concave mirrors.
• Use ray-tracing techniques to locate the images formed by plane and spherical mirrors.
• Use the mirror equations to determine location, size, orientation, and nature of images
formed with spherical mirrors.
• Distinguish between a thin lens and a thick lens.
• Describe the shapes of three typical converging (positive) thin lenses and three typical
diverging (negative) thin lenses.
• Describe the f-number and numerical aperture for a lens and explain how they control
image brightness.
• Use ray-tracing techniques to locate images formed by thin lenses.
• Describe the relationship between collimated light and the focal points of a thin lens.
• Use the lensmaker’s equation to determine the focal length of a thin lens.
• Use the thin-lens equations to determine location, size, orientation, and nature of the
images formed by simple lenses.
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Scenario—Using Geometrical Optics in the Workplace
Manuel Martinez is a photonics technician hired recently to work for a large optical
company that manufactures optical components such as mirrors, lenses, prisms,
beam splitters, fibers, and Brewster windows—all to customer specifications. While
in school Manuel studied light imaging with mirrors and lenses, ray tracing, and
calculations with simple formulas. After two months on the job he has discovered
that he uses those same ideas day in and day out. To be sure, things are much
more “high tech” in his company, for now Manuel has access to powerful
computers and computer programs that trace rays through complicated optical
systems, often containing elements with nonspherical surfaces, something Manuel
never had a chance to do at school. He enjoys the challenge of using state-of-theart
lab equipment he’s never seen before, including autocollimators,
spectroreflectometers, and surface profilers. All in all, he’s really satisfied because
all of the optics he had in his “Geo” course back at school really prepared him well
for his laboratory work here. This month Manuel is learning how to “grind and polish
optical surfaces to spec,” and how to apply the principles of geometrical optics to
determine when the surfaces are “near tolerance.” Manuel finds his work
fascinating and can hardly wait to get to work each morning. “Geo” was never so
much fun.
Opening Demonstrations
Note: The hands-on exercises that follow are to be used as short introductory laboratory
demonstrations. They are intended to provide you with a glimpse of some of the phenomena
covered in this module and to stimulate your interest in the study of optics and photonics.
1. Comparing Ordinary Light with Laser Light. In an appropriately darkened room, and
with plenty of “chalked-up” erasers, examine the dramatic difference between ordinary
“flashlight” light and laser light. Use a focusable mini MAGLITE (MAG Instrument, Ontario,
Canada, 909-947-1006) and a well-collimated, ordinary low power (5.0 mW or less) diode laser
pointer (Edmund Scientific Company, Barrington, New Jersey, 609-573-6250). Shine each light
beam, in turn, from one side of the room to the other. Have participants “pat the erasers”
together over the entire path of the light beams. The light beams outline themselves dramatically
as they scatter their light energy off the settling chalk particles. Which beam remains well
defined along its path? Which beam more closely describes a “ray of light”?
2. Bending Light Rays in a Fish Tank. Fill an ordinary rectangular five-gallon