ratio, called the index of refraction, varies in different substances. For instance, it is

2'9 for chromate of lead.

2'0 for flint glass.

15 for crown glass.

13 for water.

454. If we receive a beam after its passage through the prism on a piece of smooth white paper, we shall see that this is not all. Not only has the ray been bent out of its original course bodily, so to speak, but instead of a spot of white light the size of the hole which admitted the beam, we have a lengthened figure of various colours, called a spectrum.

455. This spectrum will be of the same breadth as the spot which would have been formed by the admitted light, had it not been intercepted by the prism. The lengthened figure shows us, therefore, that the beam of light in its passage through the prism must have been opened out, the various rays of which it is composed having undergone different degrees of deviation, which are exhibited to us by various colours-from a fiery brownish red where the refraction is least, to a faint reddish violet at the point of greatest divergence. This is called dispersion.

456. If we pass the light through prisms of different materials, we shall find that although the colours always maintain the same order, they will vary in breadth or in degree. Thus, if we employ a hollow prism, filled with oil of cassia, we shall obtain a spectrum two or three times longer than if we used one made of common glass. This fact is expressed by saying that different media have different dispersive powers-that is, disperse or open out the light to a greater or less extent.

457. Every species of light preserves its own relative place in the general scale of the spectrum, whatever be the media between which the light passes, but only in

order, not in degree; that is, not only do the different media vary as to their general dispersive effect on the different kinds of light, but they affect them in different proportions. If, for instance, the green, in one case, holds a certain definite position between the red and the violet, in another case, using a different medium, this position will be altered.

This is what is termed by opticians the irrationality of the dispersions of the different media-or shortly, the irrationality of the spectrum.

Stat

458. What has been stated will enable us to understand the action of a common magnifying-glass or lens. Thus as a prism acts upon a ray of light as shown in the above Fig. 53, two prisms arranged as in Fig. 54 would cause two

beams coming from points at a and b to converge to one point at c. A lens, we know, is a round piece of glass, generally thickest in the middle, and we may look upon it as composed of an infinite number of prisms. Fig. 55 shows a section of such a lens, which section, of course, may be taken in any direction through its centre, and a little thought will show that the light which falls on

its whole surface will be bent to c, which point is called the focus. If we hold a common burning-glass up to the sun, and let the light fall on a piece of paper, we shall find that when held at a certain distance from the lens a hole will be burned through it; this distance marks the focal

distance of the lens. If we place an arrow, ab (Fig. 56), in front of the lens mn, we shall have an image of an arrow behind at a' b', every point of the arrow sending a ray to every point in the surface of the lens; each point of the arrow,

FIG. 56.-Showing how a Convex Lens, mn, with an arrow, a b, in front of it, throws an inverted image, a' b', behind it.

in fact, is the apex of a cone of rays resting on the lens, and a similar cone of rays, after refraction, paints every point of the image. At a, for instance, we have the apex of a cone of rays, man, which rays are refracted so as to form the cone of rays, m a' n, painting the point a' in

the image. So with b, and so with every other point. We see that the action of a lens, like the one in the figure, thickest in the middle, called a convex lens, is to invert the image. The line ry is called the axis of the lens.

459. Such, then, is a lens, and such a lens we have in our eye; and behind it, where the image is cast, as in the diagram, we have a membrane which receives the image as the photographer's ground glass or prepared paper does; and when the image falls on this membrane, which is called the retina, the optic nerves telegraph as it were an account of the impression to the brain, and we see.

LESSON XXXVII.-Achromatic Lenses. The Telescope. Illuminating Power. Magnifying Power.

460. Now in order that we see, it is essential that the rays should enter the eye parallel or nearly so, and the nearer anything is to us the larger it looks; but if we attempt to see anything quite close to the eye, we fail, because the rays are no longer parallel-they are divergent. Here the common magnifying-glass comes into use; we place the glass close to the eye, and place the object to be magnified in its focus, that is, at c in Fig. 55: the rays which diverge from the object are rendered parallel by the lens, and we are enabled to see the object, which appears large because it is so close to us.

461. Similarly if we place a shilling twenty feet off, and employ a convex lens, the focal length of which is five feet, half way between our eye and the shilling, we shall have formed in front of the eye an image of the shilling, which being within six inches of the eye, while the real shilling is twenty feet off, will appear forty times larger, although in this case the image is of exactly the same

size as the shilling. So much for the action of a single convex lens.

462. Now, if instead of arranging the prisms as shown in Fig. 54, with their bases together, we place them point to point, it is evident that the rays falling upon them will no longer converge, or come together to a point. They will in fact separate, or diverge. We may therefore suppose a lens formed of an infinite number of prisms, joined together in this way; such a lens is called a concave lens, and the shape of any section of such a lens and its action are shown in Fig. 57.

463. In some lenses one surface is flat, the other being either concave or convex; so besides the bi-convex and

parallel rays.

bi-concave, already described, we have plano-convex and plano-concave lenses.

464. Now we have already seen (Art. 458) that a lens is but a combination of prisms; we may therefore expect that the image thrown by a lens will be coloured. This is the case; and unless we could get rid of such effects, it would be impossible to make a large telescope worth using. It has been found possible however to get rid of them, by using two lenses of different shapes, and made of different kinds of glass, and combining them together, so making a combination called an achromatic, or colourless, lens.