# Geometrical optics and its applications

Huygens—Fresnel principle and geometrical optics Fourier optics is the study of classical optics using Fourier transforms FTsin which the waveform being considered is regarded as made up of a combination, or superpositionof plane waves. A key difference is that Fourier optics considers the plane waves to be natural modes of the propagation medium, as opposed to Huygens—Fresnel, where the spherical waves originate in the physical medium. A curved phasefront may be synthesized from an infinite number of these "natural modes" i.

This is a most Geometrical optics and its applications approximation in the practical design of many optical systems and instruments. Geometrical optics is either very simple or else it is very complicated. By that we mean that we can either study it only superficially, so that we can design instruments roughly, using rules that are so simple that we hardly need deal with them here at all, since they are practically of high school level, or else, if we want to know about the small errors in lenses and similar details, the subject gets so complicated that it is too advanced to discuss here!

If one has an actual, detailed problem in lens design, including analysis of aberrations, then he is advised to read about the subject or else simply to trace the rays through the various surfaces which is what the book tells how to dousing the law of refraction from one side to the other, and to find out where they come out and see if they form a satisfactory image.

People have said that this is too tedious, but today, with computing machines, it is the right way to do it. One can set up the problem and make the calculation for one ray after another very easily.

So the subject is really ultimately quite simple, and involves no new principles. Furthermore, it turns out that the rules of either elementary or advanced optics are seldom characteristic of other fields, so that there is no special reason to follow the subject very far, with one important exception.

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. So, appreciating that geometrical optics contributes very little, except for its own sake, we now go on to discuss the elementary properties of simple optical systems on the basis of the principles outlined in the last chapter.

Figure 27—1 In order to go on, we must have one geometrical formula, which is the following: One way is this. We leave the case of arbitrary indices of refraction to the student, because ideas are always the most important thing, not the specific situation, and the problem is easy enough to do in any case.

Focusing by a single refracting surface. This condition supplies us with an equation for determining the surface. The answer is that the surface is a very complicated fourth-degree curve, and the student may entertain himself by trying to calculate it by analytic geometry.

It is interesting to compare this curve with the parabolic curve we found for a focusing mirror when the light is coming from infinity. So the proper surface cannot easily be made—to focus the light from one point to another requires a rather complicated surface.

It turns out in practice that we do not try to make such complicated surfaces ordinarily, but instead we make a compromise. The farther ones may deviate if they want to, unfortunately, because the ideal surface is complicated, and we use instead a spherical surface with the right curvature at the axis.

It is so much easier to fabricate a sphere than other surfaces that it is profitable for us to find out what happens to rays striking a spherical surface, supposing that only the rays near the axis are going to be focused perfectly.

Those rays which are near the axis are sometimes called paraxial rays, and what we are analyzing are the conditions for the focusing of paraxial rays. We shall discuss later the errors that are introduced by the fact that all rays are not always close to the axis.

Likewise, we could imagine it the other way. Remember the reciprocity rule: Therefore, if we had a light source inside the glass, we might want to know where the focus is.

In particular, if the light in the glass were at infinity same problem where would it come to a focus outside? Of course, we can also put it the other way. This theorem, in fact, is general. It is true of any system of lenses, no matter how complicated, so it is interesting to remember.

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We did not prove here that it is general—we merely noted it for a single surface, but it happens to be true in general that the two focal lengths of a system are related in this way. It does mean something very interesting and very definite.

It is still a useful formula, in other words, even when the numbers are negative. What it means is shown in Fig. This is an apparent image, sometimes called a virtual image. If the light really comes to a point, it is a real image.

But if the light appears to be coming from a point, a fictitious point different from the original point, it is a virtual image. Likewise, we can use the same equation backwards, so that if we look into a plane surface at an object that is at a certain distance inside the dense medium, it will appear as though the light is coming from not as far back Fig.

We could go on, of course, to discuss the spherical mirror.Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves.

Wave Optics Chapter Ten WAVE OPTICS INTRODUCTION In Descartes gave the corpuscular model of light and derived Snell’s law. It explained the laws of reflection and refraction of light at an interface. The Fractional Fourier Transform: with Applications in Optics and Signal Processing [Haldun M.

Ozaktas, Zeev Zalevsky, M. Alper Kutay] on metin2sell.com *FREE* shipping on qualifying offers. The discovery of the Fractional Fourier Transform and its role in optics and data management provides an elegant mathematical framework within .

Optics is the cornerstone of photonics systems and applications. Geometrical optics, or ray optics, is to study the geometry of paths of lights and their imagery through optical systems. Light will be treated as a form of energy which travels in straight lines called rays. When light comes to be.

The Optical Society of America is a professional society dedicated to serving optics professionals and academics, in the U.S. and around the world.. Editor-in-Chief: Dr. Michael Bass is professor emeritus at the University of Central Florida's Center for Research and Education in Optics and Lasers (CREOL)..

Associate Editors: Dr. . Geometric Optics Applications Endoscopy A nonsurgical procedure which is used in examining a person's digestive tract Done when there is a belief of a digestive disease or other such problem.

Geometric Optics Applications by Morgan Soultz on Prezi