This book is the culmination of twentyfive years of teaching geometrical optics. Geometrical optics in describing the propagation of light as a wave we need to understand. One sees the typical blow up of the go ansatz at the caustic. This is an envelope of rays check out clairauts equation for the idea and it is shown to be responsible for the apparent shift in position for an object under water. Geometrical optics is one of the oldest of the physical sciences, but still remains the most effective approach for explaining a good part of the most common optical phenomena. Analytical illuminance and caustic surface calculations in geometrical optics. The light source may be collimated rays, a point source, or an extended source.
In the module to follow, you will learn about the otherphysical wave optics. However, because the longitudinal direction has a physically different status from the transverse directions. Every point in the object is mapped to a unique point in the image. For technical reasons, its often easier to work with equations like f 0 instead of r something, especially if you are talking about the geometry of surfaces.
These rays are produced by incident rays which hit edges, corners, or vertices. Geometrical optics an overview sciencedirect topics. The analytical illuminance monitoring technique provides an exact expression within the geometrical optics limit for the illuminance over an image surface for light that has passed through a multiinterface optical system. Geometrical optics is the treatment of the passage of light through lenses, prisms, etc. Optics notes topics in these notes are wave properties polarization focal lengths geometrical optics i. Wavefronts and caustic associated with durnins beams. Light is an electromagnetic disturbance, and as such is described using maxwells equations, which expresses the relationship between the electric. In this module, we shift the emphasis from light rays to light wavesfrom geometrical optics to physical optics. In addition, the conditions for the formation of a caustic curve are derived and explained in detail. Diffraction near fake caustics m v berry and s klein h h wills physics laboratory, tyndall avenue, bristol bs8 1tl, uk. Geometrical optics article about geometrical optics by the. In spite of this geometrical optics is remarkably robust, remaining as a most practical tool in the solution of optical problems where at first glance it would seem to be totally inappropriate.
A diacaustic or caustic is actually derived in the first few pages. Light is an electromagnetic disturbance, and as such is described using maxwells equations, which. An optical image may be regarded as the apparent reproduction of an object by a lens or mirror system, employing light as a carrier. Opti 202l geometrical and instrumental optics lab 21 lab 2. However, because the longitudinal direction has a physically different status from the transverse directions, not all orientations and linear distortions are possible. Pdf geometric optics with caustic crossing for some. Ray paths are determined as paths orthogonal to the eikonal surfaces, along which the flow of electromagnetic energy occurs, and can be alternatively described in terms of fermats principle. It is well known that the geometrical optics approximation, generally valid for highfrequency fields, fails in the vicinity of a caustic. The caustic in the acoustics of historic interiors. Diffraction near fake caustics professor sir michael. 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 principal application of geometrical optics remains in the field of optical design. In optics, the term ray means the direction of light propagation, but it is also applied in other areas like the propagation of sound or electromagnetic waves. Shealy university of alabama at birmingham, department of physics, 1530 3rd ave.
A bright light for geometrical optics secondorder derivative matrices of a ray and its opl. Each point on the illuminated side x caustic is reached by two rays which are labeled. In geometrical optics, the focus is the point of convergence of rays originating from a definite point and subject to the concentration by optical instruments. The caustic is a curve or surface to which each of the light rays is tangent, defining a boundary of an envelope of rays as a curve of concentrated light. Osa analytical illuminance and caustic surface calculations.
Wills physics laboratory, tyndall avenue, bristol bs81tl, uk received may 21, 1986. Geometrical optics please remember to photocopy 4 pages onto one sheet by going a3a4 and using back to back on the photocopier. The caustics of geometrical optics appear in experiments as scaled and sheared versions of the canonical forms given by catastrophe theory. The volume is organised such that the single spherical refracting surface is the basic optical element. The orientations and distortions of caustics in geometrical optics, opt. Geometric optics practice problems center for teaching. Optics notes massachusetts institute of technology. Feb 05, 2015 what the author did is simply rewrite r r cos sec as rr cos sec 0. The methods of the algebraic topology allow us to introduce the homotopy classes of di. Maslovs method makes use of a representation of the geometrical optics.
Physical optics lecture notes pdf 44p this note covers the following topics. The exact equations are derived for caustics formed by the reflection of light from a general surface. In, we show that the rays of geometrical optics for this simplified toy problem produce a fold straight caustic curve xx c see fig. In geometric optics, the following statements are true for real and virtual images.
A selection of variables, principally angular with the center of the sphere as a common point, allows a global, straightforward, and geometrically transparent way to the rays, caustics, and wavefronts, internal as well as external, for. Geometrical optics convergence coefficient for whistler case. In principle, ray tracing can help us to analyze image formation in any given optical. In most introductory texts, geometrical optics appears after maxwells equations and theory of light. In this module, you will learn about one of the two main divisions of basic optics geometrical ray optics. In this module, you will learn about one of the two main divisions of basic opticsgeometrical ray optics. Geometric optics download ebook pdf, epub, tuebl, mobi.
Archimedes and other ancient greek thinkers made original contributions but we mention here heron of alexandria c. A geometric optics method for highfrequency electromagnetic. Remarks upon the equations of the caustic curves and surfaces. Osa caustic surfaces and the structure of the geometrical image. That is why these singulrities of geometrical optics are physically importantas recognised by the. A ray is a line that has an origin, but does not have an end. Geometricoptic methods for the estimation of fields in. The ray aspect of light list the ways by which light travels from a source to another location. They are highly applied in computer graphics when a realistic scene rendering is required mitchell and. Stavroudis, the kfunction in geometrical optics and its re lationship to the archetypical wave front and the caustic surface. It introduces diffracted rays in addition to the usual rays of geometrical optics.
This study relates to a refringent sphere illuminated by a point source placed at a distance h from its center. 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. All structured data from the file and property namespaces is available under the creative commons cc0 license. A new light on old geometrical optics raytracing equations of geometrical optics. The first research relating to the general properties of systems that are composed of light rays goes back to the year 1682, where caustic curves were.
This site is like a library, use search box in the widget to get ebook that you want. The caustic is the envelope of the family of rays corresponding to the beam. In the case m 0, the wavefronts are cones and the caustic degenerates into an in. We use the intensity law of geometrical optics to find the caustic surfaces and the irradiance everywhere in the. Maurolycus, 1575 was that the rays of a normal system are tangential to a surface, the socalled caustic surface, and that the general ray is tangential to the caustic surface in two points, ref. This may be approximately true if the depth of the mirror or the thickness of the lens is small compared with. In optics, a caustic or caustic network is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. Asymptotic evaluation of highfrequency fields near a caustic. Pdf caustic surfaces in a keplerian twolens beam shaper.
The envelope to a family of rays reflected from some surface is called a caustic, and the hilbert integral along an envelope degenerates. Flux density for ray propagation in geometrical optics. The geometrical theory of diffraction is an extension of geometrical optics which accounts for diffraction. Files are available under licenses specified on their description page. Exact and geometrical optics energy trajectories in. An equation for the caustic curve a d mcintosh aylesbury grammar school, buckinghamshire, uk in his book experiments in physics siddons 1988, colin siddons speaks fondly of the caustic curve and mentions that he has yet to discover an equation for the cusp. Chapter 3 geometrical optics university of illinois. Lastly, you are right that near caustics geometrical optics breaks down. Geometrical optics b c and focus f of a concave mirror, the image formed 7.
Caustics are focal singularities of geometrical optics. Aberrations in ideal imaging, rays originating from one object point converge to a single image point. Universal heuristic conditions for the application of geometric optics are formulated. Click download or read online button to get geometric optics book now. The geometrical energy distributions can be graphically displayed as a line or point spread. These conditions are based on the concept of the fresnel volume of a ray, which is defined as a part of space delimited by the first fresnel zones which are threaded onto the ray. Lenses and geometrical optics olympus life science. Analytical caustic surfaces introduction the study of caustic surfaces is rooted in antiquity. Pedrotti cord waco, texas in module, basic geometrical optics, we made use of light rays to demonstrate reflection and refraction of light and the imaging of light with mirrors and lenses.
Theory of systems of rays by william rowan hamilton emis. Pdf wavefront and caustics of a plane wave refracted by an. The most familiar example is the rainbow, where the. Pedrotti cord waco, texas optics is the cornerstone of photonics systems and applications. Nasa goddard photo and video, via flickr learning objectives 25. New framework for go that is free from caustic singularities. A upright, magnified and real b upright, the same size and virtual c inverted, demagnified and real d inverted, magnified and virtual. 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.
An entire image is generally produced simultaneously, as by the lens in a camera. Wave properties in general there are two types of waves. Geometrical optics approximation we are in the realm of geometrical optics when wavelength is considered b lbl d h 0 lim physical optics geometrical optics. The fake caustic diffraction pattern arises from averaging. We also acknowledge previous national science foundation support under grant numbers 1246120, 1525057. When an object is placed in front of a plane mirror the image is. The subject of ray optics, or geometrical optics, is defined by the eikonal approximation, briefly outlined in chapter 2. Optics is the cornerstone of photonics systems and applications. In the module to follow, you will learn about the other physical wave optics. S, birmingham, al 352941170 abstract geometrical optics is commonly associated with the raylike properties of. Again, see landau and lifshitz for a poignant explanation. The basic concepts explored in this discussion, which are derived from the science of geometrical optics, will lead to an understanding of the magnification process, the properties of real and virtual images, and lens aberrations or defects. Analytical illuminance and caustic surface calculations in. More recently the optical method of caustics, a technique based on geometrical optics, was the first one to be successfully applied to the study of deformation fields.
Pdf flux density for ray propagation in geometrical optics. Light is a form of energy which flows from a source to a receiver. Both wave front and caustic can be expressed as the sum of two vectors, the first being the direction vector of the ray and the second being the gradient of the arbitrary function. 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. A general solution of the eikonal equation is used to derive general expressions for both the wave fronts and the caustic surface associated with an orthotomic system of rays in a homogeneous optical medium. Geometrical optics go refers to the simple ray tracing techniques that have been used for centuries at optical frequencies. Note that only one geometrical optics computation is necessary to compute approximation for any frequency indeed the discretization of the go ansatzthe starsdoes not change. Longitudal waves are those in which the displacement of the mediumor eld is in the direction of the wave. Caustic surfaces in a keplerian twolens beam shaper. Osa geometric optics of a refringent sphere illuminated. In geometrical optics, we assume that the wavelike behaviour of light is. This criterion can also be used to evaluate the inapplicability of geometric optics to the study of foci and caustics. Complex geometrical optics solutions samulisiltanen the socalled complex geometric optics cgo solutions were introduced in the context of inverse problems and imaging by sylvester and uhlmann in 1987 9, reinventing and extending the quantum scattering results of faddeev 6. Natures optics and our understanding of light professor sir.
765 1450 646 1452 97 1593 1333 859 1399 431 286 388 714 862 412 76 899 1613 1247 1013 848 1409 1061 1540 683 830 984 599 1215 516 1365 697 406 171 700 61 1061 680 1101 571 665