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different tightness. A string half the length of another, and of the same tension, vibrates twice as quickly, and the musical note produced by it has a fixed relation to that produced by the other. From this it will be understood why a fiddler places his fingers up and down on the strings as he plays. The string can only vibrate as far as the point on which he places his finger; by putting his finger on the string a good way up, he shortens the string, and a sharper sound is produced ; thus, besides having the range of the four strings, which give different notes from being stretched to a different tightness (the bass-string being also loaded with copper wire, to make it vibrate more slowly), he has a range of notes on each string, by means of shortening them to different lengths.
Different notes are also obtained from pipes, according to their length. The sound produced by a pipe is due to the vibrations of the air in the pipe, which are caused by the shock communicated by blowing into it, or partly by the construction of a mouth-piece. The shorter the pipe, the greater is the shrillness of the note produced. Everyone knows that the note of a large flute is soft and mellow, while that of a small one is shrill. In an organ, there is a pipe for every note, the different lengths being calculated with extreme care; while in a flute a similar effect is produced by opening and shutting holes along the length of the one pipe. Another system on which musical notes are produced is by placing a slender elastic plate over a slit or opening through which air is made to pass, by blowing, as in the musical toy of this description. The air causes the little pieces of steel to vibrate with great rapidity and thus produce a musical note. The human voice consists simply of musical notes produced by the vibration of two membranes at the top of the windpipe, with their free edges opposite each other, and a slit or opening left between them for the passage of the air by which they are vibrated. When a boy places a blade of grass
between his thumbs, and, by blowing on the edge, produces a note by no means musical in one sense, the note is produced exactly on the principle of the human voice as produced by the larynx, being caused by the extremely rapid vibrations of the edge of the blade of grass. The voices of children and women are shriller than those of men, because the membranes of the larynx are shorter in the former than in the latter, and thus produce sharper notes,
The subjects treated of in the science of OPTICS 1 are Light and Vision. We learned in the chapter on Acoustics, that the sensations of Sound are produced by vibrations in sounding bodies being communicated to the air, and by it transmitted to the nerves of the ears. It is now believed that both Light and Heat consist of a vibratory motion of the particles of light-giving and hot bodies, and that they are transmitted in a manner exactly similar to the transmission of sound. The medium, however, cannot be the air, since light and heat pass where there is no air ; philosophers have accordingly come to the conclusion that all space is occupied by an infinitely elastic substance or fluid called ether. The vibrations of the particles of a luminous body are communicated to the ether ; the pulses transmitted through it enter the eye, and strike upon the retina, and, being thence conveyed to the brain, produce the sensation of Sight. These vibrations pass from a luminous body in every direction, and for this reason Light is said to be composed of rays, from Latin radius, the spoke of a wheel, and these rays are said to be divergent. Light travels at the rate of about 194,000 miles in a second.
When light falls on the surfaces of bodies, some or all of the rays are reflected, or thrown back by the surface; or, some or all of the rays are transmitted, or pass through the body, according to the nature of the body, and the manner in which the light falls upon it. Rays which are transmitted from one substance into another, are bent out of the straight line, and are said to be refracted. The following lessons on Optics consist of a short statement of the Laws of Reflection and Refraction.
Reflection. Let AB (fig. 24) be a reflecting surface, as a mirror, with a ray of light falling on it in the direction of ed; and let cd be a line perpendicular to AB: then, by the first law of reflection, the rayed will be reflected from AB in the direction db, so that ed, dc, and db shall all be in the same plane ; and by the second, the angle cdb is equal to the ngle cde. A ray falling on a surface, as ed, is called the incident 2 ray, and d is called the point of incidence; cd, the perpendicular at the point of incidence, is called the normal; and db, the reflected ray. The first law of reflection may
1 From Greek optikos, relating to sight.
2 From Latin incido, to fall upon,
now be stated thus—The incident ray, the normal, and the reflected ray
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 Fig. 25.
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 divergent 1 rays, or rays that spread out from a point, fall
on a mirror, the point from which the R
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 Fig. 26.
of R and S; the point q, from which
they seem to proceed, is on the opposite side of the mirror, and the distance Nq is equal to the distance NQ.
Refraction. 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.
This is seen by a very simple
experiment. Let a coin be placed in the bottom of a basin so that it is just out of sight. If water be poured into the basin without moving the coin, it will gradually come into sight, the cause being, that the light from the coin is bent out of the straight line in passing from the water
into the air, so that the light Fig. 27.
that comes from a, along aDC, 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
B of light transmitted through a prism, of
R 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
VA the new medium, the ray will be refracted
Fig. 28. 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
regard to prisms be kept in mind, that rays of light transmitted through them
are always refracted to7 8
wards the thick part, beFig. 29.
cause 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
perpendicular, as IF, is therefore turned towards C, the centre of the curve of the surface. Now, if
ray fall on any other point of AV, since the normal must
always be the line from that Fig. 30.
point to C, and the ray must
be refracted towards the normal, it must also be turned towards C; and so for all rays that fall 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 Fig. 31.
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