most cases, the colours of transparent, and also of opaque bodies, are far from being monochromatic. They consist, in reality, of a great number of different rays. Thus the common blue-stained glass transmits almost all the blue light that falls upon it, and, in addition, a little yellow and red.

CHAPTER XLI.

UNDULATORY THEORY OF LIGHT.

Two Theories of Light-Applications of the Corpuscular Theory-Undulatory Theory-Length of Waves is the cause of Colour-Determination of the Periods of Vibration Interference of Light-Explanations of Newton's Rings, and Colours of thin Plates-Diffraction of Light.

IT has been stated that there are two different theories respecting the nature of light-the corpuscular and the undulatory. In accounting for the facts in relation to the production of colours, it is assumed that, in the former, there are various particles of luminous matter answering to the various colours of the rays, and which, either alone or by their admixture, give rise to the different tints we see. In white light they all exist, and are separated from one another by the prism, because of an attractive force which such a transparent body exerts; and that attractive force being unequal for the different colour-giving particles, difference of refrangibility results. The colours of natural objects on this theory are explained by supposing that some of the colour-giving particles are reflected or transmitted, and others stifled or stopped by the body on which they fall. The phenomena of reflection by polished surfaces are therefore reduced to the impact of elastic bodies; and in the same way that a ball is repelled from a wall against which it is thrown, so these little particles are repelled, making their angle of reflection equal to their angle of incidence. But while there are many of the phenomena of light, such as reflection, refraction, dispersion, and coloration, which can be accounted for on these principles, there are others which the emanation or corpuscular theory cannot meet. are, however, explained in a simple and beautiful manner by the other theory.

These

The undulatory theory rests upon the fact that there exists throughout the universe an elastic medium called THE ETHER, in which vibratory movements can be established very much after the manner that sounds arise in the air. Whatever, therefore, has been said in Chapter XXXI., &c., respecting the mechanism and general principles of undulatory movements, applies here. Waves in the ether are reflected, and made to converge or diverge on the same principles that analogous results take place for waves upon water, or sounds in the air. It will have been observed already that the reflections of undulations from plane, spherical, elliptic, or parabolic surfaces, as given in Chapter XXXI., are identically the same as those which we have described for light in Chapter XXXVI.

From the phenomena of sound we can draw analogies which illustrate,

L

in a beautiful manner, the phenomena of light; for, as the different notes of the gamut arise from undulations of greater or less frequency, so do the colours of light arise from similar modifications in the vibrations of the ether. Those vibrations that are most rapid impress our eyes with the sensation of violet, and those that are slower with the sensation of red. The different colours of light are, therefore, analogous to the different notes of sound.

In Chapter XXXII. it was shown how the frequency of vibration, which could give rise to any musical note, might be determined, and it appeared that the ear could detect vibrations, as sound through a range commencing with 15, and reaching as far as 48,000 in a second. The frequency of vibration in the ether required for the production of any colour has also been determined, and the lengths of the waves corresponding. The following table gives these results. The inch being supposed to be divided into ten millions of equal parts, of those parts the wave lengths are:

More recent investigations have proved the remarkable fact, that the length of the most refrangible violet wave being taken as one, that of the least refrangible red will be equal to two, and the most brilliant part of the yellow one and a half.

Knowing the length of a wave in the ether required for the production of any particular colour of light, and the rate of propagation through the ether, which is 195,000 miles in a second, we obtain the number of vibrations executed in one second, by dividing the latter by the former.

From this it appears that if a single second of time be divided into one million of equal parts, a wave of red light vibrates 458 millions of times in that short interval, and a wave of violet light 727 millions of times.

Further, whatever has been said in Chapter XXXI. in reference to the interference of waves, must necessarily, on this theory, apply to light. Indeed, it was the beautiful manner in which some of the most incomprehensible facts in optics were thus explained that has led to its almost universal adoption in modern times. That light added to light should produce darkness seems to be entirely beyond explanation on the corpuscular theory; but it is as direct a consequence of the undulatory as that sound added to sound may produce silence.

Between these

From a lucid point, p, Fig. 250, let rays of light fall upon a double prism, m n, the angle of which, at C, is very obtuse. From what has been said respecting the multiplying-glass (Chapter XXXVII.), it appears that an eye applied at a would see the point p double, as at p and p". images there is also perceived a number of bright and dark lines perpendicular to a line joining p' and p". On covering one-half the prism the lines disappear, and only one image is seen.

This alternation of light and darkness is caused by ethereal waves from the points p and p" crossing one another, and giving rise to interference. If, therefore, with those points as centres, we draw circular arcs, 0, 1,

2, 3, 4, &c., these may them being half waves.

Fig. 250.

represent waves, the alternate lines between It will be perceived that wherever two whole waves or two half waves encounter, they mutually increase each other's effect; but if the intersection takes place at points where the vibrations are in opposite directions, interference, and therefore a total absence of light, results, as is marked in the figure by the large dots.

Wherever, therefore rays of light are arranged so as to encounter one another in opposite phases of vibration, interference takes place. Thus, if we take a convex lens of very long focus, and press it upon a flat glass by means of screws, Fig. 251, at the point of contact, when we inspect the instrument by reflected light, a black spot will be seen, surrounded alternately by light and dark rings. These pass under the name of Newton's coloured rings. When the light is homogeneous the dark rings are black, and the coloured ones of the tint which is employed; but when it is common white light the central black spot is surrounded by a series of colours. When the instrument is inspected by transmitted light, the colours are all complementary, and the central spot is of course white. These rings arise from the interference of the rays reflected from the anterior and posterior The colours of

Fig. 251.

boundaries between the two glasses.
soap-bubbles and thin plates of
gypsum are referable to the same

cause.

By the diffraction of light is meant its deviation from the rectilinear path, as it passes by the f edges of bodies or through aper

tures. It arises from the circumstance that when ethereal, or, indeed, any kind of waves, impinge on a solid body, they give rise to new undulations, originating at the place of impact, and often producing interference. Thus, if a diverging beam of light

Fig. 252.

α

passes through an aperture, a b, Fig. 252, in a plate of metal, an eye placed beyond will discover a series of light and dark fringes. The cause of these has already been explained in Chapter XXXI., in which it was shown that from the points a and b new systems of undulations arise, which interfere with one another, and also with the original waves.

CHAPTER XLII.

OF POLARIZED LIGHT.

Peculiarity of Polarized Light-Illustrated by the Tourmaline-Polarization by Reflection-General Law of Polarization-Positions of no Reflection— Plane of Polarization.

WHEN a ray of common light is allowed to fall on the surface of a piece of glass, it can be equally reflected by the glass upward, downward, or laterally.

If such a ray falls upon a glass plate at an angle of 56°, and is received upon a second similar plate at a similar angle, it will be found to have obtained new properties. In some positions it can be reflected as before; in others it cannot. On examination it is discovered that these positions are at right angles to one another.

Again, if a ray of light be caused to pass through a plate of tourmaline, c d, Fig. 253, in the direction a b, and be received upon a second plate, placed symmetrically with the first, it passes through both without difficulty. But if the second plate be turned a quarter round, as at g h, the light is totally cut off.

Fig. 253. Considering these results, it therefore appears that we can impress upon a ray of light new properties by certain processes, and that the peculiarity

consists in giving it different properties on different sides. Such a ray, therefore, is spoken of as a ray of polarized light.*

When light is polarized by reflection, the effect is only completely produced at a certain angle of incidence, which therefore passes under the name of the angle of maximum polarization. It takes place when the reflected ray makes,

* Dr. Pareira, in his "Lectures on the Polarization of Light," delivered before the Pharmaceutical Society of London, contrasts some of the distinguishing characteristics of common and polarized light as follows:

A RAY OF COMMON LIGHT 1. Is capable of reflection at oblique angles of incidence in every position of the reflector.

2. Penetrates a plate of tourmaline (cut parallel to the axis of the crystal) in every position of the plate.

3. Penetrates a bundle of parallel glass plates in every position of the bundle.

4. Suffers double refraction by Iceland spar, in every direction, except that of the axis of the crystal.

A RAY OF POLARIZED LIGHT 1. Is capable of reflection at oblique angles of incidence in certain positions only of the reflector.

2. Penetrates a plate of tourmaline (cut parallel to the axis of the crystal) in certain positions of the plate, but in others is wholly intercepted.

3. Penetrates a bundle of parallel glass plates in certain positions of the bundle.

4. Does not suffer double refraction by Iceland spar in every direction, except that of the axis of the crystal. In certain positions it suffers single refraction only. A reference to the second column will at once explain the question, "What is polarized light?"-ED.

with the refracted ray, an angle of 90. Thus, let A B, Fig. 254, be a plate of glass, a b an incident ray, which, at b, is partly reflected along bc, and partly refracted along be, emerging therefrom at e d. Now maximum polarization ensues when e be is a right angle, from which it follows that the polarizing power is connected with the refractive, the law being that the index of refraction is the tangent of the angle of polarization Let A B, Fig. 255, be a plate of glass, on which a ray of light, a b, falls, and after polarization is reflected along bc; at c let it be received on a second plate, C D, similar to the former, and capable of revolving on c b, as it were on an axis. Let us now examine in what positions of this plate the polarized ray, bc, can be reflected, and in what it cannot.

Fig. 255.

C

Experiment at once shows that when the plane of reflection of the first mirror coincides with the plane of reflection of the second, the polarized ray

undergoes reflection; but if they are at right angles to one another, it is no longer reflected. To make this clear, let a b, Fig. 256, be the first mirror, and cd the second, so arranged as to present their edges, as seen depicted on this page. Again, let e f be the first, and g h the second, now turned half-way round, but still presenting its edge; in both those positions, the planes of incidence and reflection of both the mirrors coinciding, the ray polarized by a b or e f will be reflected. But if, as in i k, the second mirror, l, is turned so as to present its face, or, as in m n, it is turned at o, so as to present its back, in these cases, the planes of incidence and reflection of the two mirrors being at right angles, the polarized ray can no longer be reflected. We have, therefore, two positions in which reflection is possible, and two in which it is impossible, and these are at right angles to one another. By the plane of polarization we mean the plane in which the ray can be completely reflected from the second mirror.

Fig. 256.

0

When a ray of light falls on the surface of a transparent medium, it is divided into two portions, as has already been said, one of these being reflected, and the other refracted. On examination, both these rays are found to be polarized but they are polarized in opposite ways, or, rather, the plane of polarization of the refracted is at right angles to the plane of polarization of the reflected: ray.

Polarization by Refraction-Application of the Undulatory Theory-The Polariscope.

When it is required to polarize light by refraction, a pile of several plates