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THE REFRACTION AND ACCOMMODATION
OF THE EYE.
LUMINOUS POINT AND RAYS.
If a stone be thrown into water, the surface of which was hitherto quiet and smooth, a series of circles, concentric about the point where the stone strikes, will be seen to form upon this surface. These circles remain concentric, because the disturbance communicated by the shock at one point to the aqueous molecules is propagated in the form of ripples, in the plane of the surface and with equal rapidity in every direction.
A luminous point produces analogous phenomena in space. It causes, everywhere around it, an undulatory movement of the ether. These undulations, however, are not limited solely to the horizontal plane, as appears to be the case in the water; they are not merely circles. They are propagated in every plane and in every direction, and thus form around the luminous point, as a centre, larger and larger spheres.
Light is therefore propagated from the luminous point in all directions in straight lines, that is to say, following the radii of these spheres of undulation of the ether. These lines of direction are commonly called luminous rays. Thus it may be said that a luminous point gives off rays, which are propagated in all directions, in straight lines and with equal rapidity as long as they remain in the same medium
REFRACTION BY A PLANE SURFACE.
When one of such rays meets another transparent medium, separated from the first by a plane surface, its course is modified
according to the nature of the medium and the angle at which the ray falls upon this separating surface. If the ray strike the surface perpendicularly, it continues its course in the same direction; the rapidity of propagation of the light is, however, increased or diminished according to the nature of the second medium.
When the ray falls upon the surface at any other than a right angle, it is deviated from its primitive direction, though remaining in the same plane—the nlane of incidence. This is called the refraction of light.
We give the name incident ray to the ray before its passage into the second medium, and that of emergent ray to the ray after it has penetrated the second medium.
INDEX OF REFRACTION.
Not all transparent media refract light equally. We distinguish, from an optical point of view, between denser and rarer media. In the former the light is propagated less rapidly, in the latter more rapidly.
When a luminous ray passes from a rarer into a denser medium, it is deviated toward a perpendicular let fall at the point where it strikes the surface; and it will approach nearer to this perpendicular in proportion as the difference of refractive power (density) between the two media is greater.
Conversely, when a ray passes from a refractive medium into one of less refractive power, it is deviated in the opposite direction; i.e., it deviates from the perpendicular in pursuing its course, and that, too, proportionately to the difference, as to density, between the two media. This follows directly, moreover, from what we have just said. have only to invert the case, and consider the emergent ray as the incident. The incident ray will then become the emergent, according to the well-known law that the course followed by a luminous ray, emanating from a point A of one medium, and passing through any number of other media to reach a point C, is exactly the same as that taken by a ray passing from C to A. This is a law with which we shall very frequently have to deal further on.
1 In strict exactness it should be said that a portion of the light is reflected in the plane of incidence, at an angle equal to the angle of incidence, whenever the luminous ray strikes the surface at a certain angle. Only a part of the light, then, penetrates the second medium.
In relation to the portion refracted, the reflected part is greater in proportion as the angle of incidence is greater. As this angle increases, there comes a time when all the light is reflected, and when none of it penetrates the second medium. This is the total reflection of which we shall have occasion to speak again, later on.
The refraction to which a luminous ray is subjected, in passing from one medium to another, is evidently as much greater as the ray is more deviated from its primitive direction.
To express the relation of the refractive powers of two media, we employ, therefore, the relation of the angle of incidence with the angle of refraction.
Let M' (Fig. 1) be the first, M” the second medium, and SS the plane surface which separates them. From the luminous point A is given off a ray which strikes the surface at B. This is the incident ray. Erect at the point B a perpendicular P P'. The plane of the paper will be the plane of incidence, and the angle A B P the angle of incidence (i).
Instead of continuing its course in the same direction, the ray A B is deflected toward the point C. C B P' is the angle of refraction (,).
In order to deal more clearly with the fundamental laws of refraction, let us take, instead of a single ray, a pencil of luminous rays a a' bW (Fig. 2).
They have come sufficiently far from the luminous source, that the surface of the wave, of which cV represents a section, may be regarded as plane, and the rays as parallel to each other. The light of this pencil has been propagated in the medium M' with a rapidity (u), up to the time when it meets the plane surface SS, which separates the two media M' and M". The latter medium is the denser ; that is to say, that light is propagated in it with less rapidity. The surface cb' of the last wave, which is entirely in the medium M', forms, with the surface, the angle cb'a'. We designate this angle by i. While the portion of the wave corresponding to the point b enters the medium M", and is there propagated with lessened speed only to the point d, the portion c of the same wave still remains in the medium M', and takes a longer course to a'. Hence a'd is the first wave-surface which contains all the light of the pencil. It forms, in the second
medium, with the surface SS, the angle b' a'd. This we call r. Now, Vc being perpendicular to a a', and a' d perpendicular to Bb", it will be seen that
Now the angle i is equal to the angle p bb; that is, to the angle of incidence, since their sides are perpendicular to each other. For the same reason, the angle r is equal to the angle 6" b' p ; that is, to the angle of refraction.
The length of a' c is evidently proportional to the rapidity of propagation of the light in the medium M' = v. The length of b'd is proportional to the rapidity of propagation of the light in the medium M" = v". Hence we have
sin i v'