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now be stated thus-The incident ray, the normal, and the reflected ray


Fig. 25.


are all in one plane. Again, edc is called the angle of incidence, and cdb the angle of reflection; and the second law of reflection is-The angle of reflection is equal to the angle of incidence. Two other facts will now be easily understood.

1. Rays of light that fall on a reflecting surface parallel to each, will be reflected parallel to each other. Rays being reflected from a surface at the same angle as they fall upon it, it is evident that after reflection they must remain parallel. If P and Q (fig. 25) are parallel when they fall on CD, R and S will also be parallel. 2. When divergent1 rays, or rays that spread out from a point, fall on a mirror, the point from which the reflected rays seem to proceed, is on the opposite side of the mirror, and at a distance equal to the distance of the point from which the rays actually proceed. Thus, let rays, diverging from the point Q (fig. 26), fall on a mirror at A and B, and be reflected in the direction of R and S; the point q, from which they seem to proceed, is on the opposite


Fig. 26.


side of the mirror, and the distance Ng is equal to the distance NQ.


The body or substance through which light passes is called a medium. When light passes from one medium into another, it is refracted or bent out of its straight course.


Fig. 27.

This is seen by a very simple

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seems to come straight from b, and the coin seems to be raised up.

1 From Latin dis, asunder, and vergo, to incline.

Another example of the same thing is the bent appearance of a stick when held partly in water, the explanation being, that the light from every part of the stick under water is refracted, so that it seems to be raised up, as was the case with the coin. So, too, objects at the bottom of a clear stream or pond appear to be raised up, and the water seems less deep than it really is. The principle on which these phenomena take place is, that light when passing from a rarer to a denser medium (for example, water and glass are denser than air, and air is said to be rarer than water or glass) is refracted towards the perpendicular; and on passing from a denser into a rarer, is refracted from the perpendicular; and this in proportion to the relative velocity with which light passes through the different media. Thus, suppose a ray of light to pass through a piece of glass: on entering the glass, it is turned towards the perpendicular to a certain extent; but on leaving the glass and entering the air again, it will be refracted from the perpendicular; and as this must be exactly to the same extent as it was turned towards it on entering the glass, it is clear that the ray, on emerging from the glass, will proceed in the same direction as it was doing before it entered.

Having hitherto treated of media with parallel surfaces, we will now consider the case of a medium the surfaces of which are not parallel but are supposed to meet. A medium of this form is called a prism, as BAC, and the angle at which the surfaces meet, as A, is called the vertex.1

A ray


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Fig. 28.

of light transmitted through a prism, of any substance denser than the surrounding medium, is always refracted from the vertex. Let a ray, SP, fall on the transparent prism BAC at P; let nn' and mn' be the perpendiculars to the two surfaces. On first entering the new medium, the ray will be refracted from its straight course, SD, towards the perpendicular, into the direction of PQ, say. Now, at first sight, it might be expected that, on emerging into the air again, it would proceed in a direction nearly the same as before entering the prism, that is, turn towards the vertex of the prism; but it is clear, from the construction of the figure, that the ray must emerge on the opposite side, that is, turn away from the vertex along QR. It would be the same, although the incident ray were on the side of the perpendicular next to the vertex ; because the refracted ray in the prism must always be on the side of the perpendicular next the vertex, and must therefore always emerge on the opposite side, away from the vertex.

All the effects produced on light by passing through different lenses

1 Latin vertex, the top or turning point, from verto, to turn.

will now be easily understood, especially if the general principle with


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Fig. 29.

regard to prisms be kept in mind, that rays of light transmitted through them are always refracted towards the thick part, because most lenses are simply

double prisms. Thus, take the double-convex and the double-concave lenses 1 and 4 in the figure: the first is as if two prisms were fixed together with their vertices turned outward, and the second the same, only with the vertices of the prisms meeting in the middle. When a ray of light, as RI, fig. 30, falls on a convex surface, as AVB, the perpendicular (or normal) at that point, NIC, is the perpendicular to the tangent-plane; and the ray being refracted towards the

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perpendicular, as IF, is therefore turned towards C, the centre of the curve of the

surface. Now, if a ray fall on any other point of AV, since the normal must always be the line from that point to C, and the ray must be refracted towards the norand so for all rays that fall

mal, it must also be turned towards C; on AV. In the same manner, all rays that fall on VB would be turned towards C, because they must all be refracted towards the normal at every point, and the normal must always point to C. The effect of the whole surface, AB, then, is to draw rays of light that fall on it together, to a point behind the surface. Rays which draw together in this way are said to converge. This is the effect produced by rays of light which fall on the transparent cornea of the eye; they are made to converge and pass through the pupil; at least, by means of it, more rays pass through it than if there had been no refracting medium in front of the iris. (HUMAN PHYSIOLOGY, page 73.) This being the effect of one convex surface, it is very much greater when there are two together, as in a double-convex lens, fig. 31, which will be at once clear from what was said of the prism. The effect of the prism was seen to be to cause a double refraction towards the thick side; now, one side of a double-convex lens, as PAB, is equivalent to a number of prisms all turned one way, because at every point of the curved

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Fig. 31.

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surface we might suppose the plane face of a prism. Also the other half, as P'AB, is equivalent to a number of prisms all turned the other way ; so that the whole effect of a double-convex lens, as PP', is to cause a double refraction of all rays that are transmitted through it inwards. Thus, suppose a number of parallel rays to fall on the lens PP'; let one fall at P; then at the first surface it is refracted into the direction Pq, and if not further interfered with, it would meet the axis at q (corresponding to F in fig. 30), but at the second surface it is again refracted, and thrown more towards the thick part of the lens, so that it meets the axis at F. Again, of those that fall on the other side, let one fall at P'; it is refracted at the first surface into the direction P'q, and then at the second it is also turned to F. This is what takes place in the eye, when the light that enters by the pupil is transmitted through the crystalline lens. (HUMAN PHYSIOLOGY, page 74.) The point, F, at which the rays of light meet the axis or middle line O'q (for they all meet it at one point), is called the focus. In the eye this focus falls on the retina, and the cause of defective eyesight is simply that the rays of light are brought to a focus, not on the retina, but either in front of or behind it. In the former case, the individual is said to be short-sighted or near-sighted, and in the latter, far-sighted. The principle on which spectacles help to remedy those defects will be explained presently. After what has been said of a convex surface and the convex lens, it needs no proof to shew that the effect of a concave surface and of a double-concave lens (fig. 29) is exactly the reverse. As the normals to a concave surface all meet in the centre of the curve outside the body, inside they all diverge; and therefore parallel rays of light transmitted through a medium with a concave surface meeting them, being all refracted towards the normals, must all be made to diverge also. Then as to a double-concave lens, if we suppose it to be the same as two prisms with their thick part outwards, it is at once clear that all rays transmitted through it must suffer a double refraction outwards, that is, be made to diverge.

A very few words will now make the principle of spectacles perfectly intelligible. In the case of a near-sighted person, the defect in his sight is that rays of light are brought to a focus in front of the retina, the cornea and crystalline lens making the rays converge too much. To remedy this, it is necessary to make the rays diverge a little before entering the eye. This we saw to be done by a double-concave lens; therefore, near-sighted persons often wear spectacles with double-concave lenses. The defect in the case of far-sighted persons is that light is brought to a focus behind the retina: the refracting power of the cornea and crystalline lens is not strong enough, and it is necessary to make the rays converge. This, as we saw, is the effect of a convex lens; therefore, far-sighted people wear spectacles with double-convex lenses.


ELECTRICITY received its name from the Greek word elektron, amber, in which substance it was first detected. It was found, from the earliest times, that when a piece of amber was rubbed with a dry cloth, it had the power of attracting small light bodies lying near it. In later times, it was observed by scientific men that sulphur, glass, sealing-wax, and many other substances had the same property; and now-a-days electric experiments are all made with these common substances, instead of the comparatively rare and costly amber, especially since they exhibit the phenomena of electricity in as great perfection as the substance in which it was first discovered.

Fig. 32.

In order to observe better what takes place, let us suspend something very light a little ball of pith of the elder-tree is generally usedby a silk thread from a glass tube, as in the figure (the reason why glass and silk are used will be explained afterwards). If a glass tube be rubbed with a piece of dry silk, and then held near the pith-ball, the latter will at first be drawn to the glass, and then be driven away, as indicated in the figure. If a stick of sealing-wax be taken next, rubbed with a piece of flannel, and held to the ball, which has just been repelled by the glass, the same thing will take place-the ball will first be attracted, and then repelled. If the glass be rubbed again, the same thing may be repeated of course; so with the wax; and the pith-ball might thus be kept playing between the two for any length of time. There are thus two kinds of electricity, one produced in glass when rubbed with a piece of silk; and the other in sealing-wax when rubbed with a woollen cloth. When the electrified glass attracts the pith-ball, electricity is communicated to the ball, and then it is repelled; in other words, two bodies charged with the same kind of electricity repel each other. Then the ball is attracted by the wax, and is only repelled again when the electricity received from the glass has been replaced by the kind produced in the wax ; and we infer from this that two bodies charged with the different kinds of electricity attract each other. Special names have been given to these two kinds of electricity: the kind produced in glass and a number of other substances is called vitreous, from Latin vitrum, glass; while that produced in sealing-wax and a number of other substances of a resinous nature is called resinous.

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