164

MECHANISM OF UNDULATION.

[93.

air the particles of the medium undergo alternate condensation and rarefaction in the same direction as that in which the motion is communicated, and in which the wave is travelling, as occurs in the passage of sound through air; 2, in other cases the motion. is at right angles to that in which the wave is advancing.

A movement of the second kind takes place in water when a stone is dropped into it, or when its surface is ruffled by a breeze. Though the motion is propagated from the point struck, towards the edges, in circles continually widening, the particles of the liquid do not themselves travel onwards from the centre towards the circumference, but are alternately elevated and depressed, as may be seen by watching the movements of a cork or other light floating object; each vertical line in succession receiving and transmitting the motion produced by the first impulse, which gradually diminishes in intensity as the squares of the distance increase, and as the circle becomes more extended.

The mode in which the undulations of light are believed to be transmitted may be illustrated by loosely stretching a long cord, and striking it from above downwards near one end: the motion will be propagated in a vertical plane in successive waves from one extremity to the other, each portion of the cord becoming alternately first higher and then lower than the position which it assumes when at rest. If the cord be struck laterally, the waves will occur from side to side in a horizontal plane. In the passage of a ray of light, the motions of the particles of ether interposed between the eye and the luminous object will, like those of the cord, be at right angles to the track of the ray, or to that line in which the wave is advancing, and in the same plane as

FIG. 67.

that in which the impulse was given. Let R S (fig. 67) be the direction of the ray, the motion of the particles of the ether will be in the direction a b, at right angles to the course of the ray. The length of the line ab is called the amplitude of the vibration; and the distance from one crest of a wave to the next the wave-length.

That the undulations which produce light are occasioned by motions of the particles of the ether at right angles to the track of the ray may be inferred from the phenomena of polarization:In polarized light, as will be seen more fully hereafter, the results are such as can be explained only by admitting that ordinary light is resolved into two sets of rays, the undulations of which

94]

TRANSPARENCY AND OPACITY.

165

occur in planes at right angles to each other, although the two sets of rays travel onwards in the same direction.

If light were propagated by waves of alternate condensation and refraction, such waves from their nature could not be referred to any particular plane, and the phenomena of polarization consequently could not exist.

(94) Transparency and Opacity.-Bodies through which light passes freely, such as glass or air, are termed transparent, or diaphanous (from dia, through, paivo, to appear); they allow objects to be seen distinctly through them, whilst the majority of substances which, like wood, metals, &c., do not allow its passage, are said to be opaque. No substance, however, is perfectly transparent. The purest air arrests a portion of light: Young adopts the estimate that the horizontal sunbeams, which pass through about 200 miles of atmospheric air before they reach the eye, possess only one two-thousandth of their original intensity; and he states that a column of water 7 feet in depth, has been found to arrest one-half of the light which enters it. On the other hand, there is no such thing as perfect opacity. the densest of the metals, may be hammered out into very thin leaves, which transmit a green light if the metal be pure, and a purplish light if it be alloyed with silver. Between the extremes of opacity and transparency are innumerable gradations. Bodies vary greatly in translucency, that is, in their power of transmitting light. Porcelain is a translucent body; it breaks up the rays, but transmits a softened light, though it does not allow the form of an object to be seen if the porcelain be interposed between that object and the eye.

Gold, one of

Light proceeds through all homogeneous transparent media in straight lines from the object; these lines diverge or radiate in all directions from a luminous point, and a ray of light is an indefinitely narrow portion of a stream of light. The path of the rays in a direct line may often be traced across a darkened room into which a sunbeam is admitted, by the floating particles of dust, which reflect a small portion of the light in different parts of its course into the eye of the observer. The mere passage light through a transparent object does not excite the sense of vision, neither can the eye track the direction of the ray, unless the vibrations be carried towards the observer by reflection from the surface of some material object.

of

The impression of light upon the retina lasts for a brief interval, varying in different persons from a tenth to an eighth of

166

DIMINUTION OF LIGHT BY DISTANCE.

[94.

a second, after the light itself has ceased, and gives rise to many curious effects: for instance, the act of blinking produces no impediment to correct vision; a bright point made to revolve rapidly in the dark is seen as a luminous circle, and the jets of flame which in fireworks are whirled round before the eyes of the spectators, assume the form of wheels or stars of fire.

I

(95) Law of Diminution of Light by Distance.-When light diverges from a luminous centre, its intensity diminishes, like that of all radiations, not inversely as the distance, but inversely as the square of the distance. A little consideration will render the reason for this obvious:-Suppose the flame of a candle, or any luminous point, to be placed in the centre of a hollow sphere 2 metres in diameter, its light will fall upon the whole internal surface of the sphere, and the candle will be 1 metre distant from each point: a square centimetre of that surface will receive a given amount of light. The same candle, if placed in the middle of a globe 4 metres in diameter, will be at 2 metres distance from each point of the surface, or at double the distance that it was in the first globe, but its light will still illuminate the whole of the interior. The surface of the second globe, however, is four times greater than that of the first, because the surfaces of spheres are to each other as the squares of their radii; in this case as 12:22, or as I to 4; consequently each point, or each square centimetre, of the surface of the larger sphere, will receive only one-fourth of the light that fell on an equal space in the smaller globe, and yet the candle is only twice as far from it: so, if the globe were 8 metres across, the distance of the candle being now 4 times as great as in the first globe, the surface to be illuminated is 16 times as large, and consequently, a square centimetre of the 8-metre globe would receive only of the light that fell on a square centimetre of the 2-metre globe. A board at I metre from a candle receives a certain amount of light, at 2 metres it receives of that amount, at 3 metres , at 4 metres and experiment shows that a board, 1 decimetre square, at I metre distance, would cast a shadow that would cover a board exposing 4 times the surface, or 2 decimetres

FIG. 68.

in the side, if placed at a distance of 2 metres, as shown in fig. 68.

(96) Photometry-An application of this law affords a ready means of approximately determining the relative intensities of two lights which do not

97.]

PHOTOMETRY-REFLECTION OF LIGHT.

167

differ greatly in colour. Suppose, for instance, it were necessary to ascertain the illuminating power of a gas-light burning 5 cubic feet (or 142 litres) of gas per hour, as compared with that of a sperm candle burning 120 grs. (or 7°775 grms.) of spermaceti per hour:-Place at the distance, say of 100 inches from the gaslight, a vertical screen of white paper, and in front of this, at an inch distance, a narrow strip of wood or of metal, so as to cast a definite shadow. Between the gas-light and the screen place the candle, at such a distance that the shadow of the same object cast by the candle upon the screen shall have as nearly as possible the same intensity as that produced by the gas. Say that the distance of the candle from the screen is 27.75 inches. The shadow from each light is illuminated by the rays proceeding from the other light. If the shadows be sensibly equal, the amount of light falling upon the screen from each source must at that distance be equal also: the relative intensities of the two lights are then found by squaring the distances of each light from the screen; the gas-light will consequently cast a light which bears the same ratio to that of the candle as 100: 2775; or as 12'986 to 1.

When light falls upon any object it may be disposed of in three different ways. Ist, it may either be bent back or reflected; 2nd, it may be allowed to pass on in an altered direction, that is, it may be transmitted and refracted; or 3rd, it may disappear altogether, and be absorbed.

R

FIG. 69.

(97) Reflection.-If a ray of light fall obliquely upon a flat, polished surface, a large portion of the incident rays, or rays which fall upon the surface, is reflected or thrown off obliquely, at an angle formed on the other side of a perpendicular to the point of incidence, equal to that formed between the incident ray and the perpendicular. Fig. 69 is intended to illustrate the law of reflection. If in this figure, I N represent the incident ray, м м the mirror, P N a perpendicular to the mirror at the point of incidence, P N I will be the angle of incidence, N R the reflected ray, and

M

A

PNB the angle of reflection formed between the same perpendicular and the reflected ray.

The law which regulates the reflection of light is expressed by saying that the angle of reflection is equal to the angle of incidence': the incidence and the reflected ray are always in the same plane, and that plane is perpendicular to the reflecting surface. When the incident ray is perpendicular to the surface, the reflected ray is therefore also perpendicular, and coincides with the incident ray, but it does so in no other position.

In fig. 69, the angle of reflection, P N R, is equal to the angle of incidence, P N I, but they are on opposite sides of the perpen

168

REFLECTION-SCATTERING OF LIGHT.

[97.

dicular. An eye at R looking into the mirror, would see the candle behind the mirror, and at the same distance behind it as the candle flame is in front. An object always appears to lie in the direction of the line which the ray last traversed when it reaches the eye.

The power of reflecting light varies very greatly in different bodies. In some, as in the metals, reflection is almost perfect; in others, as in charcoal, or in black velvet, it is almost wanting; but whenever light passes out of one medium or transparent body into another, no matter how perfect the transparency of such media may be, reflection more or less complete takes place at their common surface, and the greater the difference in refractive power of the two media, the more complete is the reflection.

Except in the case of the metals, in which reflection is most complete at the smaller angle of incidence, it is found that the greater the angle of incidence the more complete is the reflection; so that the surface of a smooth body, such as plaster of Paris, or hot-pressed writing-paper, may thus afford a tolerably perfect image of a luminous object, if the reflection be effected under a great angle.

Bodies in general do not possess surfaces actually flat; to common observation they may be flat, but when optically examined, their surface is found to consist of an indefinite number of minute planes inclined to each other at all possible angles, and therefore receiving and reflecting light in all possible directions. When by the operation of polishing they are so much reduced as not to be elevated or depressed more than about the millionth of an inch, they appear to become incapable of acting separately, and produce the effect of a uniform surface. (Young.) If a beam of light admitted into a dark room fall upon a bright metallic surface, a brilliant spot of light will be perceived in one particular position, the direction of which can be varied by altering the inclination of the mirror to the ray, but the mirror will be nearly invisible in all other directions, and the room will remain dark; but if for the mirror a sheet of white paper be substituted, the paper will be visible in every direction almost equally, and a general though slight illumination of the apartment will be perceived. It is this irregular reflection or scattering of the light in all directions, which renders non-luminous objects distinguishable in the light. The light of the moon and of the planetary bodies furnish instances of this kind. A further evidence of the value of this scattering or secondary radiation, is afforded by the difference between the mild. and softened light which is reflected from the heavens when par