PDF ISBN: | Print ISBN: DESCRIPTION. This Field Guide derives from the treatment of geometrical optics that has evolved. Download Now: #PDF~ Field Guide to Geometrical Optics site #ebook #full #read. Library of Congress Cataloging-in-Publication Data. Greivenkamp, John E. Field guide to geometrical optics / John E. Greivenkamp p. cm (SPIE field guides).

Field Guide To Geometrical Optics Pdf

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Sample Pages pdf-favicon This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate. This Field guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences. Fiel Guide to Geometrical Optics - JJhon Greivenkamp - Download as PDF File iel Guide Gu d to o. Geometrical Optics. John E. Greivenkamp. Field Guide to.

You all had a good laugh at Mr. Student: Vary the distance between them. Professor Ramamurti Shankar: You vary the distance. It looks very natural. Even the distance equal to the circumference of the earth is not enough, because it takes one seventh of a second for a light signal to go around the earth, if it could be made to go in a circle.

So the idea of finding the velocity of light, the first correct way, came from Roemer, I think in And the moon goes round and round Jupiter, and we know from Newtonian physics that it will go in an orbit with a certain time period. If the earth was stationary, this would go round and round with some period. So what you do is you record the pulse. Pick any one key event in its orbit, then wait for the next pulse, and wait for the next pulse, and wait for the next pulse.

You understand what I mean by pulse?

You can see it all the time, but wait till it comes to a particular location in its orbit, then repeat, then time them. So that should be one hour and something. But you notice that as the earth begins its journey around the sun, it takes longer and longer and longer, the pulses get spaced apart a little more.

Namely, this pulse, with respect to the anticipated time, is 22 minutes delayed. Do you understand? The delay is continuous, but take the case now and take the case six months later, and the pulse should have come right there if it was not moving, but it comes 22 minutes later. And he attributed that to the fact that it takes light time to travel, and it takes an extra time of traveling the whole diameter of the orbit around the sun.

And how do you know you are right? Well, you know you are right, because as you start going back now, the remaining six months, the pulses get closer and closer. So this delay is clearly due to the motion. Student: How could they still see it [inaudible]? That was quite an achievement.

But it was quite an achievement, take a number that could have been infinity and to nail it to within 50 percent accuracy. Then after that, people started doing laboratory experiments to measure the velocity of light.

Everybody has something to say about velocity of light. The main thesis is to tell you that what people had figured out by the seventeenth century is that it travels, and it travels at a certain speed. Now you guys have learned geometrical optics in high school, right?

Fiel Guide to Geometrical Optics - JJhon Greivenkamp

Who has not seen geometrical optics, lenses and mirrors? First thing they teach you is if light hits a mirror, it bounces off in such a way that the angle of incidence is the angle of reflection. Second thing they will teach you is that if light travels from one medium to another medium, say this is air and say this is glass, then the first thing to note is that the velocity of light, c, is the velocity in vacuum. The velocity is altered by a factor called n, which is bigger than 1 or equal to 1, and n is called the refractive index of that medium.

I think glass is like 1. Every medium has a refractive index and the effective velocity of light is slowed by this factor, n. So when light goes from a rare medium to a dense medium, it will go even closer to the perpendicular, or to the normal. And if you run the ray backwards, from the dense medium to the rare medium at some angle, it will go away from the normal even more. That was done and that was measured and all that stuff.

Then you can look at more things. Every parallel ray goes through the focal point, so you can use it to focus the light ray. Then you learn other stuff. Well, you have to do other constructions. If you have an object here, for example, you want to know what image will be formed. You draw a parallel line and that goes through the focal point.

You draw a line through the focal point. That comes out parallel, and where they meet is your image. And this is called h1, this is called h2. By the way, there is no universal agreement on what to call these distances. Some people call it i and o for image and object. When I was growing up, they called it u and v. This is a piece of glass and it has the property that when you shine parallel light from one side, it all focuses on the other side.

And if you have an object here, it will go and form an image on the other side, which will be upside down and that also obeys the same equation, except u is the distance of the object and v is the distance of the image and f is the focal length. This parallel ray of light, you can sort of imagine, will go off like that.

In fact, the way it will go off is as if it came from some point called the focal point. In other words, these rays of light in this mirror, instead of really focusing at some point, seem to come from the focal point. That ray of light when seen by person here will seem to come from there, and if you join them, you get an image here. And if forms a reduced image of the object. Okay, so this is the scene from Jurassic Park. Here, if you put a screen, if you put a candle here and put a screen here, you will see a bright image of the candle.

The way you do these calculations, you use the same formula, except f will be a negative number. Instead of really focusing, it anti-focuses, so the focal point, if you want, is on the wrong side of the mirror.

So your textbook will have many examples of how to solve these problems, very simple algebra. But what I want to do, since many of you have seen this, and to make it interesting for you, is to show you there is a single unifying principle, just one principle, from which I can derive all these laws. Anybody know what that principle might be?

Have you heard of anything? Student: Yes. This is the famous Fermat, who had this theorem with prime numbers. His principle says light will go from start to finish in a path that takes the least amount of time.

You can derive everything. Where is the path of least time? No point going any other way. You are here. Whoever gets there first wins. Now there are different attitudes you can have. First is, you can start wandering like this. There are other reasonable people who may have a different view.

Now I already said, when you look at paths, the path to the mirror has got to be a straight line. You gain nothing by wiggling around. And the path back from the mirror to the receiving point should also be a straight line, because the winner lies somewhere there. This is at some height h1, this is at some height h2.

So what I will do, is I will simply calculate the time, then find the x for which the time is minimum. You understand? Therefore the point x has to satisfy this condition, but what is x over d1? So here is x and here is L - x. So x over d1 is cosine of this angle and that is cosine of that angle, right? So this is the first victory for the Principle of Least Time.

It reproduces this result. So here it is. Now the challenge is different. So here is h1 in a medium with a refractive index n1, and you want to go there in a medium, refractive index n2, and the distance between these points is L.

So imagine you are the light ray and this is the beach and this is the ocean. You are the lifeguard and here is the person asking for help.

Now how do you get there in the least amount of time? Or you can draw all kinds of possibilities.


And let this be at a distance x from the left. Now what do you want to minimize? Again, you want to minimize the travel time, T. You want to divide by the velocity in the medium. Velocity is c divided by n1.

And this will tell you what to do. You should calculate the gradient and go along the gradient. So this is one more thing. So I suggest we calculate it and keep the answer ready, because if you really want to be a lifeguard, what you should do is swim and measure your speed, run and measure your speed.

So what is x over this? This is the x. It also comes from the principle of least time. Each one of them has got interesting consequences. That means you can see stuff right up to the horizon by taking an angle, so that this comes exactly here. And if your angle x is a certain critical angle, your flashlight will go to the surface, and beyond that, it will just get fully reflected.

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What angle should you send it? These are all useful lessons from The third thing is very interesting, which is the following: we say, take the path of least time, right?

Take an elliptical room, Oval Office. You stand here, at one of the focal points, and you want to send a signal to the person in the other focal point, a light signal. You know what you have to do. That portion of the mirror is like horizontal mirror, right? Are you will me?

This is the angle at which you should send it. If you send it to this midpoint, by symmetry, it will come to the other focal point. Okay, so now imagine that this is not a mirror, but some steel walls and you have a gun. You are here and your enemy is here. Now what direction will you fire in? Pardon me? Student: At him. Professor Ramamurti Shankar: Right. So you can fire — very good.

See, this is why I forgot. Now what will you do? Now which direction should you aim? You know the answer.

Field guide to geometrical optics

I gave it, right? Give me an answer then. Student: At that point in the wall. Professor Ramamurti Shankar: At that point in the wall. But it turns out, you can aim anywhere you like. You will thank me when you use that rule. In other words, you can shoot any direction.

This is the guy who took only Physics This person took Physics You know that bullets are like light. You can see by symmetry. How about this one I shot at some random angle? The way to think of that is to draw a tangential plane mirror there. As far as this beam is concerned, the mirror could be flat. That angle better be equal to that angle. You shoot anywhere you like, you go crazy, shoot in any direction, they will all end up on this person. So why is that?

You agree? Student: [inaudible] Professor Ramamurti Shankar: That is correct. But an ellipse is a figure that is drawn keeping the sum of that distance to that distance constant. Take two thumbtacks and put them in the paper and you take a string of some length, and you stretch it out, grab your pencil and move it, and you will draw the ellipse. So if you were to design a surface so that if you shot something one point, it will all end up here, all the light from here will focus here, you should build an ellipse, and send the light from one focal point.

Likewise, if you talk, also the sound will come to that other point. At sufficiently high frequency, the dog will hear it here.

But you are supposed to follow the Principle of Least Time. That means all those paths take the same time. There is more than one way to go from start to finish. Okay, so now let us ask how you build a focusing mirror.

So this is not very practical.

You want to put some mirror of some shape so that every one of these guys will come to the same focal point. Is it possible? If so, what do I have to do? It goes here. It goes to that mirror, hits the mirror, then it comes back a distance f.

So in the time it takes to go from here to here, had it continued going, it would have gone to this wall here, also at a distance f. Do you agree?

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The time it takes for it to hit the mirror and come to the focal point is the same as the time it would have taken, but for the mirror, to go the other side the same distance f.

But you want it to instead come here. So how will that happen? What will ensure that that happens? Can you guys think of what condition you have? Student: The two distances need to be the same. The distance from the mirror to the — Professor Ramamurti Shankar: Do you understand that?

That distance and that distance have to be equal. See, these guys came from infinity. Start with some plane here, so that everybody is counted from now on and see how much time you take. It is a surface with a property that its distance, any point on that curve, has the same distance from a fixed point as from a fixed line. A parabola is a curve which is equidistant from a point and from a line.

Distance to the point is very clear. Distance to the line is obtained by drawing a perpendicular and measuring that distance, the shortest distance. That will give me the equation for this curve.

So what is that distance it has to travel? You can see, x is the coordinate of this point.

Bacon was able to use parts of glass spheres as magnifying glasses to demonstrate that light reflects from objects rather than being released from them.

The first wearable eyeglasses were invented in Italy around He was also able to correctly deduce the role of the retina as the actual organ that recorded images, finally being able to scientifically quantify the effects of different types of lenses that spectacle makers had been observing over the previous years. In the late s and early s, Isaac Newton expanded Descartes' ideas into a corpuscle theory of light , famously determining that white light was a mix of colours which can be separated into its component parts with a prism.

In , Christiaan Huygens proposed a wave theory for light based on suggestions that had been made by Robert Hooke in Hooke himself publicly criticised Newton's theories of light and the feud between the two lasted until Hooke's death. In , Newton published Opticks and, at the time, partly because of his success in other areas of physics , he was generally considered to be the victor in the debate over the nature of light. Young's famous double slit experiment showed that light followed the law of superposition , which is a wave-like property not predicted by Newton's corpuscle theory.

This work led to a theory of diffraction for light and opened an entire area of study in physical optics. The ultimate culmination, the theory of quantum electrodynamics , explains all optics and electromagnetic processes in general as the result of the exchange of real and virtual photons. Glauber , and Leonard Mandel applied quantum theory to the electromagnetic field in the s and s to gain a more detailed understanding of photodetection and the statistics of light.

Classical optics[ edit ] Classical optics is divided into two main branches: geometrical or ray optics and physical or wave optics. In geometrical optics, light is considered to travel in straight lines, while in physical optics, light is considered as an electromagnetic wave. Geometrical optics can be viewed as an approximation of physical optics that applies when the wavelength of the light used is much smaller than the size of the optical elements in the system being modelled.Spectral dependence can also be added to these results.

Now there are different attitudes you can have. Under bright illumination. In a similar fashion, the sagittal wave fan must be symmetric, and the sagittal ray fan is anti-symmetric. Examples include periscopes, endoscopes and borescopes.

SPIE Press. Some people call it i and o for image and object. A tunnel diagram unfolds the optical path through the prism and shows the total length of the path through the prism.

So if you were to design a surface so that if you shot something one point, it will all end up here, all the light from here will focus here, you should build an ellipse, and send the light from one focal point. Gaussian Optics.

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