The Origin of the Refraction Index文献及翻译.docx

1、The Origin of the Refraction Index文献及翻译外文文献：The Origin of the Refraction IndexWe have said before that light goes slower in water than in air, and slower, slightly, in air than in vacuum. This effect is described by the index of refraction n. Now we would like to understand how such a slower velocit

2、y could come about. In particular, we should try to see what the relation is to some physical assumptions, or statements, we made earlier, which were the following:(a) That the total electric field in any physical circumstance can always be represented by the sum of the fields from all the charges i

3、n the universe.(b) That the field from a single charge is given by its acceleration evaluated with a retardation at the speed c, always (for the radiation field).But, for a piece of glass, you might think: Oh, no, you should modify all this. You should say it is retarded at the speed c/n.That, howev

4、er, is not right, and we have to understand why it is not.It is approximately true that light or any electrical wave does appear to travel at the speed c/n through a material whose index of refraction is n, but the fields are still produced by the motions of all the charges-including the charges mov

5、ing in the material-and with these basic contributions of the field travelling at the ultimate velocity c. Our problem is to understand how the apparently slower velocity comes about.We shall try to understand the effect in a very simple case. A source which we shall call the external source is plac

6、ed a large distance away from a thin plate of transparent material, say glass. We inquire about the field at a large distance on the opposite side of the plate. The situation is illustrated by the diagram of Fig. 31-1, where S and P are imagined to be very far away from the plate. According to the p

7、rinciples we have stated earlier, an electric field anywhere that is far from all moving charges is the (vector) sum of the fields produced by the external source (at S) and the fields produced by each of the charges in the plate of glass, everyone with its proper retardation at the velocity c. Reme

8、mber that the contribution of each charge is not changed by the presence of the other charges. These are our basic principles. The field at P can be written thus:（31.1）or，（31.2）where Es is the field due to the source alone and would be precisely the field at P if there were no material present. We e

9、xpect the field at P to be different from Es if there are any other moving charges.Why should there be charges moving in the glass? We know that all material consists of atoms which contain electrons. When the electric field of the source acts on these atoms it drives the electrons up and down, beca

10、use it exerts a force on the electrons. And moving electrons generate a field-they constitute new radiators. These new radiators are related to the source S, because they are driven by the field of the source. The total field is not just the field of the source S, but it is modified by the additiona

11、l contribution from the other moving charges. This means that the field is not the same as the one which was there before the glass was there, but is modified, and it turns out that it is modified in such a way that the field inside the glass appears to be moving at a different speed. That is the id

12、ea which we would like to work out quantitatively.Now this is, in the exact case, pretty complicated, because although we have said that all the other moving charges are driven by the source field, that is not quite true. If we think of a particular charge, it feels not only the source, but like any

13、thing else in the world, it feels all of the charges that are moving. It feels, in particular, the charges that are moving somewhere else in the glass. So the total field which is acting on a particular charge is a combination of the fields from the other charges, whose motions depend on what this p

14、articular charge is doing! You can see that it would take a complicated set of equations to get the complete and exact formula. It is so complicated that we postpone this problem until next year.Instead we shall work out a very simple case in order to understand all the physical principles very clea

15、rly. We take a circumstance in which the effects from the other atoms is very small relative to the effects from the source. In other words, we take a material in which the total field is not modified very much by the motion of the other charges. That corresponds to a material which the index of ref

16、raction is very close to 1, which will happen, for example, if the density of the atoms is very low. Our calculation will be valid for any case in which the index is for any reason very close to 1. In this way we shall avoid the complications of the most general, complete solution.Incidentally, you

17、should notice that there is another effect caused by the motion of the charges in the plate. These charges will also radiate waves back toward the source S. This backward-going field is the light we see reflected from the surfaces of transparent materials. It does not come from just the surface. The

18、 backward radiation comes from everywhere in the interior, but it turns out that the total effect is equivalent to a reflection from the surfaces. These reflection effects are beyond our approximation at the moment because we shall be limited to a calculation for a material with an index so close to

19、 1 that very little light is reflected.Before we proceed with our study of how the index of refraction comes about, we should understand that all that is required to understand refraction is to understand why the apparent wave velocity is different in different materials. The bending of light rays c

20、omes about just because the effective speed of the waves is different in the materials. To remind you how that comes about we have drawn in Fig. 31-2 several successive crests of an electric wave which arrives from a vacuum onto the surface of a block of glass. The arrow perpendicular to the wave cr

21、ests indicates the direction of travel of the wave. Now all oscillations in the wave must have the same frequency. (We have seen that driven oscillations have the same frequency as the driving source.) This means, also, that the wave crests for the waves on both sides of the surface must have the sa

22、me spacing along the surface because they must travel together, so that a charge sitting at the boundary will feel only one frequency. The shortest distance between crests of the wave, however, is the wavelength which is the velocity divided by the frequency. From the figure we can see that the only

23、 way for the waves to fit properly at the boundary is for the waves in the material to be travelling at a different angle with respect to the surface, from the geometry of the figure you can see that for a fit we must have, or, which is Snells law. We shall, for the rest of our discussion, consider

24、only why light has an effective speed of c/n in material of index n, and no longer worry, in this chapter, about the bending of the light direction.We go back now to the situation shown in Fig. 31-1. We see that what we have to do is to calculate the field produced at P by all the oscillating charge

25、s in the glass plate. We shall call this part of the field Ea, and it is just the sum written as the second term in Eq. (31.2). When we add it to the term Es, due to the source, we will have the total field at P.31-2 This is probably the most complicated thing that we are going to do this year, but

26、it is complicated only in that there are many pieces that have to be put together; each piece, however, is very simple. Unlike other derivations where we say, Forget the derivation, just look at the answer!, in this case we do notneed the answer so much as the derivation. In other words, the thing t

27、o understand now is the physical machinery for the production of the index.To see where we are going, let us first find out what the correction field Ea would have to be if the total field at P is going to look like radiation from the source that is slowed down while passing through the thin plate.

28、If the plate had no effect on it, the field of a wave travelling to the right (along the z-axis) would beor, using the exponential notation, Now what would happen if the wave travelled more slowly in going through the plate? Let us call the thickness of the plate. If the plate were not there the wav

29、e would travel the distance in the time But if it appears to travel at the speed c/n then it should take the longer time or the additional time. After that it would continue to travel at the speed c again. We can take into account the extra delay in getting through the plate by replacing in Eq. (31.

30、4) by or by. So the wave after insertion of the plate should be written（31.5）We can also write this equation as,(31.6)31-3 DispersionNotice that in the above process we have obtained something very interesting. For we have not only a number for the index of refraction which can be computed from the

31、basic atomic quantities, but we have also learned how the index of refraction should vary with the frequency c of the light. This is something we would never understand from the simple statement that light travels slower in a transparent material. We still have the problem, of course, of knowing how

32、 many atoms per unit volume there are, and what is their natural frequency w0. We do not know this just yet, because it is different for every different material, and we cannot get a general theory of that now. Formulation of a general theory of the properties of different substances-their natural frequencies, and so on-is possible only with quantum atomic mechanics. Also, different materials have different properties and different indexes, so we cannot expect, anyway, to get a general formula for the index which will apply to all substances.However, we shall discuss the formula we have o