Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

290. As yet we have considered only a single medium. In order to extend the definitions of the fits from one medium to another, Newton established the following proposition.

If the luminous particles, of whatever species, pass perpendicularly into different media, the intervals of the fits of easy transmission and reflection, in any two of these media, are to each other, as the sine of incidence to the sine of refraction, when the particles under consideration pass from one to the other. This is the mathematical generalization of the ratios before observed between the thicknesses of water and air, which reflect or transmit the same tint under a perpendicular incidence. Hence it follows, that for each kind of luminous particles, the length of the fits, under a perpendicular incidence, is always the same in the same medium, whatever be the bodies traversed before coming to it.

According to this rule if we take for unity the thickness of air, which, when viewed perpendicularly, reflects a certain tint, the thickness of a vacuum which reflects this same tint would be greater in the proportion of the ratio of refraction of air, that is, as 3388 is to 3389; so that the nicest precision would hardly detect a difference. Accordingly, when we have formed coloured rings by compressing a plate of air between two objectglasses, the size and colour of these rings do not appear to un

employed; and if we reduce them to degrees, as in article 169, the lengths of the arcs thus obtained will be;

[blocks in formation]

These ares differ so little from those of Newton, that we might substitute them in their stead, without making any appreciable alteration in the estimates of the compound colours. Thus we see that this mode of distribution, so singular in appearance, is closely connected with the values of the fits. Whether Newton was aware of this connexion and followed it, or whether it is derived solely from the nature of the numerical results, which the experiment furnished him, is not known.

dergo any change, if we put the glasses into a vacuum, or heat them strongly in order to expel the air from between them. Mazéas, who first made these trials, was very much astonished to find no difference, and this circumstance did not fail to be urged as an objection to Newton's theory; whereas it is, as we perceive, a consequence of it.

291. By means of the two last propositions, the length of the fits, under a perpendicular incidence, will be determined generally for every species of refracting medium and of luminous particles, if their value for a single case be ascertained. This may be easily done from the observations of Newton upon the thicknesses of air, which reflect or transmit any colour whatever under a perpendicular incidence. Let us take for an example, the luminous particles which form, on the spectrum, the limit between the yellow and orange. We have found that the alternations of their transmission, and reflection expressed in parts of an inch, succeed each other at the mean thicknesses which follow; Transmission....0 17000 177000

Reflection...... 178000 17000 17000

2

Accordingly, the length of a fit for this species of light will be 175 of an inch; and double this quantity or T8000, which becomes, will be the interval of two fits of the same nature, whether of transmission or reflection. If we combine this result with one of the preceding propositions, we shall obtain the intervals of the fits for the different species of particles, which form the eight limits of the colours of the spectrum.

The following table contains their values in millionths of an inch.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small]

292. The numbers which express the fits in air, are deduced from the table of article 264, by doubling all the values of e', belonging to the limits of the different colours. The numbers of the other columns are obtained by multiplying these first results by for a vacuum, for water, and for the glass ៖៖៖៖ which Newton used.

We are now to connect together the reflections and transmissions which take place for the same ring under different obliquities. For this purpose Newton modified the intervals of the fits, according to the table of article 246, or rather according to the law which he deduced from it and which he found to be applicable to water and to all other substances, as explained in article

258.

Although these ratios were established by observations upon curved plates, the application which Newton here makes of them is not the less legitimate, because the thicknesses compared were all deduced from measurements taken upon the transverse diameter of the rings; so that the luminous rays which limited each diameter, traversed the thin plates at points where the tangents of its two surfaces were sensibly parallel; this rendered constant the thickness which separated them.

But the values of the oblique fits, obtained from these observations, could not be employed, if the two surfaces traversed by the ray, were so much inclined to each other that the lengths of the fits might be sensibly different at the entrance and emergence. The experiments of Newton do not decide how the fits would in that case change near the second surface, and it is a point yet to be inquired into.

293. The preceding definitions, obtained from actual experiment, characterise all the modifications which the fits experience in the act of refraction. Those which they receive from reflection yet remain to be determined; but the observations hitherto related, will not serve to solve this problem, because the thinness of the plates employed, prevents us from observing separately the influence to which the rays are subjected in them before and after being reflected at their second surface; or at least, the indications to be furnished by such experiments cannot be perceived till after we have separated, by some other method, the different actions thus produced. This Newton has effected by a new series of observations. He has rendered

the rings sensible upon thick plates, in which the two paths of the rays, before and after the interior reflection, could thus be distinguished. From these new phenomena he derived the following proposition.

When the luminous particles of any species whatever, having arrived at the second surface of the body in which they move, experience either the specular or radiant reflection, they take after reflection new fits, in departing from the reflecting surface; and the lengths of these fits are the same as they would have been, if the particles, coming from the exterior medium to the body where they are found, had entered this body with the obliquity derived from reflection. This proposition completes the characteristics of the fits.

Application of the preceding Theory to the Reflection of Rays of Light which have traversed thick Media.

294. THE fits of luminous particles being completely defined by the preceding considerations, we come now to develope the consequences which result from them with respect to the reflection and refraction of light at the second surface of thick bodies, in order to see whether these consequences are conformable to observation.

To begin with the sources of these phenomena, let us first consider a luminous body placed in an indefinite medium, like the air; and following in imagination the different luminous particles which emanate from it, let us see what must be their tendency to reflection or refraction, at every distance. For the solution of this problem, we must have given the nature of the medium, that of the luminous particles emitted, the direction of their introduction, and the initial state of each of them at the instant it escapes the action of the radiating body. With the two first data, we can calculate the length of the fits of each particle, and by adding this length continually to itself, beginning with the primitive position and state, we shall have all the successive returns of the same state or the opposite one. Then, if we place at any point whatever a surface whose reflecting force is given with respect to the medium which surrounds it, we can determine from the Opt.

36

state of each luminous particle, whether it will yield or not to reflection. These will be the modifications belonging to each particle. If afterwards, we wish to predict the phenomena as to colour that will arise from their mixture, we can do it by combining their colorific properties according to the method of Newton already employed for a similar purpose.

295. But this combination will not be necessary, except when the medium traversed by the light is extremely thin; for, if it has sufficient extent to allow the least refrangible of the particles to experience in it only 12 or 15 fits, the effect of reflection will become sensibly constant, at least with respect to our senses, and the reflected ray will always appear of the same colour as the incident light. This is the case with respect to reflection at the second surface of thick bodies.

To understand the cause, we must remember that in the general division of the spectrum a certain extent is occupied by the violet, another by the indigo, another by the blue, and so on for the seven principal colours; that is, the sensation of each of these colours does not strictly belong to one single class of rays whose refrangibility is mathematically fixed, but may be excited by rays whose refrangibility is in a slight degree different, yet so nearly alike as to make us confound them. Accordingly, in the phenomena of colour, we may consider together, the effects of any one of these different groups. Beginning, for example, with the violet, let us suppose that the light emitted contains only the varieties of particles which are capable of producing the sensation of this colour, and let us suppose that all these escape from the luminous body at the same time, and in the same stage of a fit of the same nature. Then their unequal refrangibility will give to their fits unequal lengths; and, according to the table of article 291, if the length of the most refrangible is 3,99698, that of the least refrangible will be 4,32308, which gives for each fit a difference of extent equal to 0,3261. Consequently, at the same distance from the luminous body the most refrangible of the violet particles will have experienced more alternations than the others; and it is easy to perceive that after 13 fits and about a quarter, the difference 0,3261, continually repeated, will have become equal to 4,32308, that is, to an entire alternation; so that when the rays of one description are in a fit of easy transmission, the other will be in a fit of easy reflection.

« ΠροηγούμενηΣυνέχεια »