that are parallel, as through a plate of glass, they will continue still parallel to one another, and to their original direction, after refraction. For this reason, therefore, we see through such plates of glass objects in their natural positions and relation.

The optical prism is a transparent medium, having plane surfaces inclined to one another. It is usually a wedge-shaped piece of glass, a a, Fig. 229, which can be turned into any suitable position, on a ball and socket-joint, c, and is supported on a stand, b. As this instrument is of great use in optical researches, we shall describe the path of a ray of light through it more minutely. Let, therefore, A B C, Fig. 230, be such a glass Fig. 229. prism seen endwise, and let a b be a ray of light inci

dent at b. As this ray is passing from a rarer to a denser medium it is refracted toward the perpendicular to

Fig. 230.

an extent dependent on the refractive power of the glass of which the prism is composed, and therefore pursues a new path, bc, through the glass; at c it again undergoes refraction, and now passing from a denser to a rarer medium, takes a new course, c d. To an eye placed at d, and looking through the prism, an object, a, seems though it were at a', in the straight line, de continued. Through this instrument, therefore, the position of objects is changed, the refracted ray, c d, proceeding towards the back, A B, of the prism.

But the prism in actual practice gives rise to far more complicated and interesting effects, to be described hereafter, when we come to speak of the colours of light.

The multiplying-glass is a transparent body, having several inclined faces. Its construction and action are represented at Fig. 231. Let A B be a plane face, C D also plane and parallel to it, but A C and D B inclined. Now let rays come from any object, a, those, a b, which fall perpendicularly on the two faces will pass without suffering refraction; but those, a c, a d, which fall on the inclined faces, will be refracted into new paths, cf, df, these portions acting like the prism heretofore described. Consequently an eye placed at ƒ will see three images of the object in the direction of the lines along which the have comerays —that is, at a', a, a". Hence the term multiplying-glass, because it gives as many figures of an object as it has inclined surfaces.

Fig. 231.

CHAPTER XXXVIII.

THE ACTION OF LENSES.

Different Forms of Lenses-General Properties of Convex Lenses-General Properties of Convave Lenses—Analogy between Mirrors and Lenses— Production of Images by Lenses--Size and Distance of Images-Visual Angle-Magnifying Effects—Burning Lenses.

TRANSPARENT media having curved surfaces are called lenses. They are of seven different kinds, as represented in Fig. 232. The plano-convex lens, 3, has one surface plane and the other convex; the plano-concave, 5, has one surface plane and the other concave; 2 is the double convex; 4 the double concave; 7 the meniscus ; 1 the sphere, or globe; and 6 the concavo-convex.

Sphere or Globe.

Fig. 232.

For optical uses lenses are commonly made of glass, but for certain purposes other substances are employed. For example, rock crystal is often used for making spectacle lenses; it is a hard substance, and is not, therefore, so liable to be scratched or

injured as glass.

In a lens the point c is called

Fig. 233.

the geometrical centre, for all lenses are ground to spherical surfaces, and c is the centre of their curvature; the aperture of the lens is a b, and d is its optical centre; fe is the axis, and any ray, m n, which passes through the optical centre, is called a principal ray.

The general action of lenses of all kinds may be understood after what has been said in relation to the prism, of which it was remarked that the refracted ray is bent toward the back. Thus, if we have two prisms, a c e, bce,

912

C

placed back to back, and allow parallel rays of light, m n, to fall upon them, these rays, after refraction, being bent from their parallel path toward the back of each prism, will intersect each other in some point, as f. Now, there is obviously a strong analogy between the figure of the double convex lens, and that of these two prisms; indeed, the former might be regarded as a series of prisms with curved surfaces, and from such consideration it is clear, that when parallel rays fall on a convex lens, they will converge to a focal point.

Fig. 234.

Again, let us suppose that a pair of prisms be placed edge to edge, as shown in Fig. 235, and that parallel rays, mn, are incident upon them. These rays undergo refraction, as before, toward the back of their respective prisms, 6 c, d e, and therefore emerge divergent, as at ƒ and g.

b

Now, there

is an analogy between such a combination of prisms and a concave lens, and we therefore see that the general action of such a lens upon parallel rays is to make them divergent.

By the aid of the law of refraction it may be proved that lenses possess the following properties:

Every principal ray which falls upon á convex lens of limited thickness is transmitted without change of direction.

Rays parallel to the axis of a double equi-convex glass lens are brought to a focus at a distance from the optical centre equal to the radius of curvature of the lens. glass, the focal distance is twice as great. called the principal focus.

Fig.235:

But if it be a plano-convex The focus for parallel rays is

Rays diverging from the principal focus of a convex lens after refraction become parallel.

Rays diverging from a point in the axis more distant than the principal focus converge after refraction, their point of convergence being nearer the lens as the point from which they radiated was more distant.

Rays coming from a point in the axis nearer than the principal focus diverge after refraction.

With respect to concave lenses, the chief properties may be described as follow :

Every principal ray passes without change of direction.

Rays parallel to the axis are made divergent. Thus m n, Fig. 236, being parallel rays falling on the double con

cave, a b, diverge after refraction in the directions g d; and if they be produced, give rise to a virtual or imaginary focus at f.

By concave lenses diverging rays are made still more divergent.

m

n

When the effects of lenses are compared with those of mirrors, it will be found that there is an analogy in the action of concave mirrors and convex lenses, and of convex mirrors and concave lenses.

M

It has already been remarked that concave mirrors give images of external objects in their focus. The same holds good for convex lenses. Thus, if we take a convex lens, and place behind it, at the proper distance, a paper screen, we shall find upon that screen beautiful images of all the objects in front of the lens in an inverted position. The manner in which they form may be understood from Fig. 237. Where L L is a double convex lens, M N any object, as an arrow, in front of it, the lens will give an inverted image, n m, of the object at a proper distance behind. From the point M all the rays, as

Fig. 237.

M L, M C, M L', after refraction, will converge to a focus, m; and from the point N all rays, as N L, N C, N L', will likewise converge to a focus, n; and so, for every intermediate point between M and N, intermediate foci will form between m and n, and therefore conjointly give rise to an inverted image.

The images thus given by lenses or mirrors may be made visible by being received on white screens, or on smoke rising from a combustible body, or directly by the eye placed in a proper position to receive the rays. They then appear as if suspended in the air, and are spoken of as aërial images. The distance of such images from a lens, and also their magnitude, vary with circumstances.

If the object be very remote, it gives a minute image in the focus of the lens; as it is brought nearer, the image recedes further, and becomes larger; when it is at a distance equal to twice the focal distance, the image is equidistant from the lens on the opposite side, and is of the same size as the object. As the object approaches still nearer, the image recedes, and now becomes larger than the object. When it reaches the focus, the image is at an infinite distance, the refracted rays being parallel to one another. And, lastly, when the object comes between the focus and the surface of the lens, an erect and magnified image of the object will appear on the same side of the lens as the object itself. Hence convex glasses are called magnifying-glasses.

From these considerations it therefore appears that the magnifying power of lenses is not, as is often popularly supposed, due to the peculiar nature of the glass of which they are made, but to the figure of their surfaces. The dimensions of all objects depend on the angles under which they are seen. A coin at a distance of 100 yards appears of a very small size; but as it is brought nearer the eye, its size increases, and when only a few inches

B

Fig 238.

off, it can obstruct the view of large objects. Thus, if A represents its size at a remote distance, the angle D E F, or the visual angle, is the angle under which it is seen; when brought nearer, at B, the angle is GE H; and at C

increases to I E K. In all cases the apparent size of an object increases as the visual angle increases, and all objects become smaller as their distances increase; and any optical contrivances, either of lenses or mirrors, which can alter the angle at which rays enter the eye, and make it larger than it would otherwise be, magnify the objects seen through them.

On these principles concave mirrors and convex lenses magnify, and convex mirrors and concave lenses minify.

*The recent researches of Mr. Layard, at Nineveh, tend to prove the antiquity of magnifying-glasses. He discovered one possessing this property in one of the temples; and Sir David Brewster, who has inspected it, pronounces that it-is a decided and designed magnifying-glass. The opinion of the philosopher confirms the previous supposition of Mr. Layard and various students, that the cuneiform and many other inscriptions, and also the smaller sculptures, which are so minute as to be almost unintelligible without a magnifying-glass, could only have been executed by the aid of powerful magnifying-glasses.

From their property of converging parallel rays to a focus, convex lenses and concave mirrors have an interesting application, being used for the production of high temperatures,

by converging the rays of the sun. Our illustration represents such a burning-glass. The parallel rays of the sun falling on it are made to converge, and this convergence may be increased by a second smaller lens. At the focal point any small object being exposed, its temperature is instantly raised. In such a focus there are few substances that can withstand the heat-brick, slate, and other such earthy matters instantly boil; metals melt, and

Fig. 239.

even volatilize away. During the last century some French chemists, using one of these instruments, found that when a piece of silver was held over gold fused at the focus, it became gilded over by the vapour that rose from the melted mass; and in the same way gold could be whitened by the vapours of melted silver. The heat attained in this way far exceeds that of the best constructed furnace.

CHAPTER XXXIX.

OF COLOURED LIGHT.

Action of the Prism-Refraction and Dispersion-The Solar SpectrumIts Constituent Rays-They pre-exist in White Light-Theory of the Different Refrangibility of the Rays of Light-Different Dispersive Powers-Irrationality of Dispersion-Illuminating Effects-The Fixed Lines-Calorific Effects-Chemical Effects.

IN speaking of the action of a prism in Chapter XXXVII., it was observed that it gives rise to many interesting results connected with coloured lights. These, which constitute one of the most splendid discoveries of Newton, I next proceed to explain. Through an aperture, a, Fig. 240, in the shutter of a dark room let a beam of light, a e, enter, and let it be intercepted at some part of its course by a glass prism, seen endwise, bc. The light will undergo refraction, and in consequence of what has been already stated, will pass in a direction, d, toward the back of the prism. Now, for anything that has yet been said, it might appear that this refracted ray, on reaching the screen, de, would form upon it a white spot similar to that which it would have given at e, had not the prism intervened. But when the experiment is made, instead of the light going as a single pencil of uniform width, it spreads

Fig. 240.