Further on we shall see how important the prism has lately become as a method of analysis; in the meantime we see how a ray of light is bent in passing through a prism.

LESSON XXX.-LENSES AND OTHER OPTICAL

INSTRUMENTS.

277. Lenses.-These are formed of some transparent substance, and have generally such shapes as are given in the following figure :

A is bounded by two spherical surfaces, and is called a double convex lens; B has one spherical and one plane surface, and is called a plano-convex ; D is in like manner a double concave, while E is a plano-concave; and, finally, c is a converging meniscus, possessing on the whole the properties of a convex lens, while F is a diverging meniscus possessing on the whole the properties of a concave lens.

The first three lenses, A, B and C, are converging; that is to say, if a beam of parallel rays falls upon one of these lenses, the beam is made to converge to a focus on the other side. The other three are diverging lenses, inasmuch as they cause a beam of parallel rays to diverge.

The effects produced by lenses depend not only on their shape, but on the materials of which they are composed, and these effects will be most easily understood by referring to the action of a prism on a ray of light. From Fig. 82 it will be seen that the ray of light is bent towards, not from, the base or thickest part of a prism, and we should therefore expect that a ray of light should be bent towards the thickest part of a lens. Now it will be noticed that the lenses A, B, and C are thickest in the centre, while D, E, and F are thinnest

in the centre. Hence if a beam of parallel rays (Fig. 84) falls upon a convex lens such as A, the rays will be bent towards the centre, and made to converge to some focus, F, on the other side of the lens, and this focus will be a real and not a virtual focus.

On the other hand, if a beam of parallel rays (Fig. 85) falls upon a concave lens it will diverge, as if it proceeded from a focus not real but virtual at F.

We

278. The most important lens is the double convex. have already said that if a beam of parallel rays (Fig. 84) fall upon such a lens, it will be brought to a focus at some point F: this focus is called the principal focus of the lens, and we may denote its distance from the lens by f.

Now (Fig. 86) let a divergent beam of light strike upon a double convex lens, proceeding from a point at a distance from the lens which we shall call p; it will be bent into a

focus on the other side at some distance, p', and the relation between these two distances is obtained by the following

We see from this formula that if p

source of light is at an infinite distance from the lens, then

I

=

I

and hence pf; that is to say, the focus be

of

p f comes the principal focus. As, however, the distance the source of light from the lens is diminished, the distance of the focus on the other side is increased, until when the distance of the source becomes equal to that of the principal focus, or p f, we have in consequence

=

I

が

= 0;

that is to say, p' is infinite, or the rays emerge from the lens parallel, and are not brought to a focus at all.

Still diminishing the distance of the source of light, if

p is less than ƒ,

is negative. か

This denotes that the beam of light, after it has passed the lens, is not a convergent or even a parallel beam, but is divergent, as if it proceeded from a virtual focus on the same side of the lens as the source of light itself.

In fact the source of light is now so near the lens, and the pencil is in consequence so divergent, that the lens cannot even bend it into a parallel beam, but all it can do is to lessen its divergence. This peculiar action of a convex

It will be noticed that p' is greater than p, which means that although the lens has not been able to render the beam convergent, it has at any rate diminished its divergence.

279. Images formed by Lenses. We see by the following figure how to find the position and size of the image of a luminous body formed by a double convex lens :

For instance, let A B denote a luminous flame further from the lens than its principal focus. Through A draw a line, A CA', passing through C, the centre of the lens; and through B draw in like manner a line, B C B',' passing also through C. Again, let A denote the focus of the luminous point A as given by the lens, and B' the focus of B; hence A'B' will be the image of the luminous flame A B. It will readily appear from the figure that this image is real and inverted, and that its size may be found as follows:

Size of image is to size of object as A' C is to AC. If

however, the luminous flame be placed nearer the lens than its principal focus, the image, as in Fig. 89, will be a magnified, erect, and virtual image.

We thus encounter two sets of phenomena in looking through a lens. In the first place, if we use the lens in order to view an object placed behind it and nearer than its principal focus, we shall see a magnified and erect image of the object. This is the ordinary way of using a lens. If,

however, the object be much further away than the principal focus, and if the eye be placed further from the lens than the image of the object, then this image will be perceived as inverted, but small. We may see this action of a lens if we view a distant landscape through it, at the same time placing the eye at a sufficient distance from the lens. 280. The chief optical

LENS

FIG. 90.

B

C

instruments will now be very briefly described. Let us begin with the Camera Obscura. This consists of a small chamber or box blackened in the inside, and having a lens placed in front of it.

This lens receives the rays of light proceeding from the objects outside, and an image of these objects is produced in the chamber at BC. If now a piece of ground glass be placed at BC, this image will be pictured on the ground glass;