In this theory, propagation of light in various optical media can be described by simple geometrical rules. Matrix methods in paraxial optics mit opencourseware. In this module, you will learn about one of the two main divisions of basic optics geometrical ray optics. String theory explained what is the true nature of reality. Fermat s principle is the basis of geometrical optics which ignores the wave nature of light. Using matrices to understand geometrical optics spie.
The principle has a theoretical basis in the quantum theory of light that avoids the. We start with a notation for specifying optics systems. This is for example relevant for the design of antireflective coatings and dielectric mirrors the reflection of light from a single interface between two media is described by the fresnel equations. The principles of gaussian optics and firstorder layout and design are emphasized, based on the tracing of two paraxial rays and the associated. Location of principal planes for an optical system a ray matrix of the optical system composite lenses and other elements can give us a complete description of the rays passing through the overall optical train. When an object is placed in front of a plane mirror the image is. The volume is organised such that the single spherical refracting surface is the basic optical element. Assumes that light is a stream of particles called photon. Geometric optics intuition with mirrors and lenses concave convex diverging converging.
General physics 2 geometric optics 16 sign conventions focal length positive for converging lenses negative for diverging lenses object distance positive if the object is on the side of the lens from which the light is coming this is usually the case otherwise, it is negative virtual object. Concept questions for physics using phet inquiry based algebrabased physics semester one lessons, clicker questions, and schedule in pdf inquiry based. In the module to follow, you will learn about the otherphysical wave optics. In the early 17th century, johannes kepler expanded on geometric optics in his writings, covering lenses, reflection by flat and curved mirrors, the principles of pinhole cameras, inversesquare law governing the intensity of light, and the optical explanations of astronomical phenomena such as lunar and solar eclipses and astronomical parallax. Lens design uses a calculation of the lens surfaces that permits us to obtain an image from a given object. In geometric optics, the following statements are true for real and virtual images. Lab 3 geometrical optics theory this laboratory is an exercise in geometrical optics, the reflection and refraction of light when it strikes the surface between air and glass, or air and water.
Location of principal planes for an optical system a ray matrix of the optical system composite lenses and other elements can give us a complete description of the rays passing through the overall optical. Explain how an image is formed by a converging lens using ray diagrams. The transfer matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium. A new hybrid snow light scattering model based on geometric. Archimedes and other ancient greek thinkers made original contributions but we mention here heron of alexandria c. A ray is a line that has an origin, but does not have an end. Beyond this boundary may be another medium which is distinguished by having a speed of light di. Part iii recent researches on the foundations of geometric optics and related investigations in electromagnetic theory. Pdf notes on matrix method of geometrical optics basic ideas of. It corresponds to a basis described by the direction. Introduction history of geometric optics let us first consider the law of rectilinear propagation.
Ideal spherical wave with radius of curvature r can be seen as collection of rays diverging from common point c. A upright, magnified and real b upright, the same size and virtual c inverted, demagnified and real d inverted, magnified and virtual. Physical optics lecture notes pdf 44p this note covers the following topics. Light can behave in many ways like a wave or a packet of photons which travel in a straight line exhibiting the property of rectilinear propagation. If you capture sunlight in a mirror or lens you can feel the heat where the sunlight is reflectedrefracted as a real image but you cannot feel the heat where the sunlight is. Basics of optics, laws of reflection and refraction, reflection from spherical mirrors, velocity of image, refraction at plane surfaces, prism theory, defects of images, refraction from.
On geometric optics and surface waves for light scattering by. Geometric optics on phase space develops both geometric optics and group theory from first principles in their hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional fourier transform currently used for image. The distance between successive wave fronts is the wavelength. Consider a circularly symmetric optical system formed by a. Geometrical optics deals with the propagation of light in a straight line and phenomena such as reflection, refraction, polarization, etc. There is a certain logic to this, first introducing a basic theory for light and then treating geometrical optics as a practical application of the theory.
This book is the culmination of twentyfive years of teaching geometrical optics. The most advanced and abstract theory of geometrical optics was worked out by hamilton, and it turns out that this has very important applications in mechanics. The wave direction is specified by the normal to the equiphase planes rays 3. Geometric optics of thick lenses and matrix methods mathematical. Light waves can be bent and reflected to form new and sometimes altered images. How changing the lens radius, index and diameter effects where the image appears and how it looks magnification, brightness and inversion. Ray optics or geometrical optics is the simplest theory for doing optics. But this is clearly not an historical approach since geometrical optics.
In the geometrical optics approximation, the behavior of a nonimaging optical system can be formulated and studied as a mapping g. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus. Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. When you look at this page, too, you are seeing light reflected from it.
Understanding how light rays can be manipulated allows us to create better contact lenses, fiber optic cables, and high powered telescopes. Geometrical optics please remember to photocopy 4 pages onto one sheet by going a3a4 and using back to back on the photocopier. In geometric optics, we neglect the diffraction effects. The principle may be used to derive snells laws of reflection and refraction. Analysis of the stability for periodic optical focusing systems evaluate the effects of misalignment of individual elements on the overall ray matrix performances. Consider a ray tracing analysis using the paraxial approximation, sin. There is a certain logic to this, first introducing a basic theory for light and then treating geometrical optics as a practical application of the. It consists of three parts which can, and for practical purposes probably should, be done in any order. Geometrical optics and maxwells equations mathematical. Phase matrix for light scattering by concentrically stratified spheres. Firstorder optics a thirdorder optics, aberrations b higherorder approximations 3. The size of the matrices and the complexity of the expressions imposes some care on the choice of elements to display.
Geometrical optics is the treatment of the passage of light through lenses, prisms, etc. An introduction by allen nussbaum and a great selection of related books, art and collectibles available now at. The earliest surviving optical treatise, euclids catoptrics 1 280bc, recognized that light travels in straightlines in homogeneous media. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. The ray tracing technique is based on two reference planes, called the input and output planes, each perpendicular to the optical axis of the system.
After an analytical treatment1 of refraction for a thick lens geometry. Fermats principle is the basis of geometrical optics which ignores the wave nature of light. Using seventhorder matrix modeling, we can calculate the optical path. Geometric optics download ebook pdf, epub, tuebl, mobi. Models for light propagation a ray model geometric optics b wave model physical optics c photon model quantum optics 2. Thin lens equation and problem solving geometric optics. However, following the teachings of plato, euclid and all other ancient greeks thought that. Watch how the image changes when you adjust the focal length of the lens, move the object, move the lens, or move the screen.
Slyusarev, aberration and optical design theory, adam huger ltd. Geometrical optics please remember to photocopy 4 pages onto one sheet by going a3a4 and using back to back on the photocopier contents. Pdf notes on matrix method of geometrical optics basic. Geometric optics the part of optics dealing with the ray aspect of light is called geometric optics. Phase matrix for light scattering by concentrically. This text, now in its second edition, presents the mathematical background needed to design many optical combinations that are. The matrix methods in geometrical optics gaussian can be developed in terms of three basic op erators matrices for reflection, refrac tion and translation a nd also can be applied with ease in.
Jan 19, 2017 geometric optics intuition with mirrors and lenses concave convex diverging converging. For our purposes, in understanding how optical instruments work, the wave theory of light is entirely adequate. It is actually even more important in mechanics than it is in optics, and so we leave hamiltons theory for the subject of advanced analytical mechanics, which is studied in the. Introduction to geometrical optics world scientific. Geometrical optics 1 geometrical optics go refers to the simple ray tracing techniques that have been used for centuries at optical frequencies. S 2n s 2n from input phase space to output phase space, where s is an evendimensional piecewise differentiable manifold and n. We only consider the propagation of rays through optical. Pinhole camera wave optics geometric 12 fermats principle light propagating between two points follows a path, or paths, for which the time taken is an extremum minimum ignoring the wave nature of light basic theory for optical instruments geometrical optics revision geometric. Geometrical optics and optical design is an uptodate introductory treatment of geometrical optics which is intended to lead students toward the modern practices of computeraided optical design. Light is an electromagnetic disturbance, and as such is described using maxwells equations, which.
Optics is an exciting area of study, but as with most areas of physics it requires a variety of mathematical tools to be fully appreciated. Find the equivalent power of the lens and locate it principal planes. Optics physical optics wave optics quantum optics geometrical optics. Geometrical optics in describing the propagation of light as a wave we need to understand. The matrix methods in geometrical optics can be developed in terms of three basic operators matrices for reflection. Geometric optics post university of california, berkeley. A ray of light gives the direction of propagation of light.
The laws of geometric optics have been extensively. In most introductory texts, geometrical optics appears after maxwells equations and theory of light. This is because we observe the processes emission, reflection, scattering at a distance 10cms with bare eyes that are much longer than the wavelength of light 107. The ray in geometric optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. Now, the theory on which classical lens design is based has changed radically, as our theoretical foundations do.
Geometrical optics and optical design oxford series in. A set of general rules and laws permits us to calculate the essential points of the optical system, such as distances, thickness, pupils, and focal distances, among others. Jul 06, 2014 some examples of using the thin lens equation. Thus, we can define 2 x 2 ray matrices for any element. A light ray from a source goes in a straight line through the air, but when it encounters a lens, prism, or mirror it bends or changes direction. Spherical mirrors are treated as special cases of refraction, with. Pedrotti cord waco, texas optics is the cornerstone of photonics systems and applications. The ray in geometric optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances the simplifying assumptions of geometrical optics include that light rays. Geometrical optics 4 for an arbitrary angle of incidence and polarization, the field is decomposed into parallel and perpendicular components.
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