Intensity of Illumination as depending on the Distance of the Source and the Obliquity of the Rays. Brightness and Intrinsic Brightness.

Photometry.

Velocity of Light.

Behaviour of Light at the Common Surface of Two Homogeneous Media.

Reflexion. Plane, Spherical, and Cylindrical Mirrors. Real and Virtual Images.

Single Refraction. Composite Nature of White Light. Refractive Index. Dispersion. Prisms; Fraunhofer’s Lines. Irrationality of Dispersion. Achromatism. Lenses. Telescope, Microscope. Pure Spectrum. Refraction by Cylinder. Rainbow.

Refraction in a Non-homogeneous Medium. Hamilton’s Characteristic Function. Mirage.

Absorption, Abnormal Dispersion, Fluorescence, Phosphorescence.

Physical Optics. Undulatory Theory.

Nature and Propagation of Waves. Huygens’s Principle. Explanation of Reflexion and Single Refraction. Disproof of the Corpuscular Theory.

Sketch of the History of the Undulatory Theory. Young’s Discovery of Interference.

Interference Bands. Spectrum formed by Grating. Measure of Wave-Length. Loss of Semiundulatiom Newton’s Rings. Colours of Thin Plates and of Grooved Surfaces.

Relation between Wave-Length and Refractive Index.

Double Refraction. Wave-Surface in Iceland Spar.

Polarization. Transverse Vibrations. Nature of Unpolarized Light.

Plane, Circularly, and Elliptically Polarized Light. Nicol’s Prism. Depolarization by Doubly-Refracting Plate. Fresnel’s Rhomb.

Doppler’s Principle. Measurement of the Relative Velocity of Luminous Source and Spectator.

Under Optics (Geometrical, Physical, and Physiological) further developments will be given; and the connexion between light and radiant heat will be discussed under Radiation. Early History of the Subject. —It is to sight that we are mainly indebted for our knowledge of external things. All our other senses together, except under very special conditions, do not furnish us with a tithe of the information we gain by a single glance. And sight is also that one of our senses which we are able most effectively and extensively to aid by the help uf proper apparatus— not merely (as by spectacles, invented circa 1300) for the cure of natural defects, but (as by the telescope and microscope) for the examination of bodies either too distant or too minute to be studied by the unassisted eye.

It is very remarkable, under these circumstances, to find how slowly men have reached some even of the simplest facts of optics. We can easily understand how constant experience must have forced on them the conviction that light usually moves in straight lines,— i.e., that we see an object in the direction in which it really lies. But how they could have believed for ages that objects are rendered visible by something projected from the eye itself—so that the organ of sight was supposed to be analogous to the tentacula of insects, and sight itself a mere species of touch —is most puzzling. They seem not till about 350 b.c. tc have even raised·the question—If this is how we see, why cannot we see in the dark? or, more simply,—What it darkness? The former of these questions seems to have been first put by Aristotle.

The nature and laws of reflexion were, of course, forced on the ancients by the images seen in still water; and the geometers of the Platonic school were well acquainted with these laws. To Hero of Alexandria we owe the important deduction from them that the course of a reflected ray is the shortest possible.

The general nature of refraction also was known, with some of its special applications, such as, for instance, to burning-glasses and to magnifiers. These were probably either spherical glass shells filled with water (Pliny, 2Z.A r ., xxxvi. 67 [25]; Lact., De Ira Dei, c. 10) or balls of rock crystal (Pliny, xxxvii. 10).

In the first century of our era Cleomedes pointed out how a coin at the bottom of an empty cup, where the eye cannot see it, can be made visible by filling the cup with water; and he showed that, in a similar way, the air may render the sun visible to us while it is still under the horizon. Shortly after this date Ptolemy (the celebrated astronomer) published his great work on Optics. He treats of vision, reflexion, the theory of plane and concave mirrors, and refraction. He measured, with considerable accuracy, the angles of incidence and refraction, for rays passing from air into water and into glass, and from water into glass; it was not, however, till more than fifteen hundred years had passed that the true relation between these angles was discovered. In addition to what has just been mentioned, the ancients’ knowledge of optics was limited to a very superficial acquaintance with some of the properties of rainbows, halos, mirage, Ä’c. But it was fragmentary in the extreme—though it far surpassed in amount as well as in accuracy their knowledge of the other branches of physical science.

It is not easy to understand the ideas of the ancients about colour. That it is a property of a body—just as its density, its hardness, or its smell is a property—was probably held by them. But they also imagined that a body could communicate its colour to light; thus, for instance, the clouds were, bv some of them, sunoosed to communicate their colours to the sunbeams which form a rainbow.

Our next glimpse of real progress dates from the 11th or 12th century, when Alhazen (9.v.) wrote a treatise on optics in Arabic, which for five hundred years or more was a recognized authority on the subject. It was, in many parts, founded on the work of Ptolemy, but with considerable additions and improvements. Alhazen gives an anatomical description of the eye, and points out, fairly enough, how with two eyes we see only one image. But he also points out that we see each object, however small, ∖yya.pencil of diverging rays,—not (as the ancients imagined) by a single ray. Alhazen accounts for twilight, and shows how by it to measure the height of the atmosphere. He also gives the now generally received explanation of the curious fact that the sun and moon appear larger when rising or setting than when they are high in the heavens.

The farther progress of the subject we need not now trace. From the end of 16th century that progress has been extremely rapid. The dates of the more important steps, and the names of their authors, will be given when we treat of these, in their turn, in the course of the article; and we will give them the additional interest of being presented, when this can readily be done, in the author’s own words.

Preliminary Statements. —Before we commence a more rigorous treatment of the subject, it may be well to make a few preliminary statements as to the nature of vision and the conditions for distinct vision. Properly speaking, these belong to Optics (Physiological) (g.v.), but it is impossible to treat intelligibly any part of our subject without presupposing some, generally very slight, knowledge of other parts. And the few preliminary statements we have now to make are in no respect theoretical, while they are so simple that any one may at once test their truth for himself.

Except in the case of a very abnormal eye (extremely short-sighted or long-sighted as the case may be) there is a distance from it—usually somewhere about 10 inches— at which if an object be placed it is seen more distinctly than if placed at any other distance. Almost every one, perhaps without knowing it, habitually places at or about that distance from his eye an object which he wishes to examine carefully. When he.places it at a smaller distance he becomes conscious of the effort required to see it distinctly. He has, in fact, to alter the form of the optical machinery of the eye, by a muscular effort, so that it may become capable of bringing to a focus on the retina rays more divergent than those for which the parts were in their unstrained state adapted. A corresponding effort, but usually much more slight, is commonly felt to be required if the object be at a distance greater than 10 inches.

Hence we arrive at the conclusion that, for the minimum of strain on the eye, rays should fall on it diverging as if they came from a peint about 10 inches distant. But for all ordinary eyes any divergence from double of this Ci.e., divergence as if from a distance of 5 inches) to zero (i.e., parallel rays) is consistent with the possibility of distinct vision. Rays either more divergent than the former limit, or convergent, are unfit to produce distinct vision. Hence every optical instrument, whatever be the reflexions or refractions to which light has been subjected in passing through it, must finally allow the light to escape either in parallel rays or with a divergence within the above specified limits, if it is to be employed by an ordinary eye. The comparatively slight differences which exist among ordinary eyes are easily compensated by the rack-work, or screw adjustment, which is invariably attached to the eye-piece of a good telescope and to the body of a good microscope. Every motion of this rack-work alters the divergence of the rays as they finally escape from the instrument Any eye, however abnormal, if it be capable of producing distinct vision at all, has only to be furnished with suitable spectacles in order that it may behave exactly as does a normal eye. This statement, however, refers only to sharpness of definition, not in any degree to colour. The deficiency which causes colour-blindness cannot be supplied by any conceivable process. A definite part of the ordinary organ of vision is wanting (or inactive) in such cases— while the merely optical parts of the eye are usually in perfect order.

Another fact which must be stated here is that, to produce vision of a body in its natural position, the image on the retina, as seen from the back, must be inverted—not merely as regards up and down, but also as regards right and left. Thus, in the ordinary astronomical telescope, the image on the retina is not inverted, and we therefore see an inverted image.

A third is that our judgment of the relative distances of objects is formed mainly by the use of the two eyes simultaneously. One eye, kept still, can inform us only of relative distance in virtue of the greater or less effort to see distinctly (already spoken of). With both eyes, or with one eye moved from side to side, parallax comes in, and gives us the stereoscopic effect, as it is called. This power of judging distance is, of course, greater as the eyes are set more widely apart. There is, practically, no limit to the effective distance between the eyes when the proper instrumental methods (as with the telestereoscope) are employed.

It is also necessary to premise a few words about colour. The various homogeneous rays of the solar spectrum have each a colour of its own which no refraction can modify. But what about the many colours which do not occur in the spectrum? To such a question as “What is yellow” 1 the answer is, “Each particular kind of yellow may be any one of an infinite number of different combinations of homogeneous rays.” And the same is true, in general, of all other colours. Clerk Maxwell found that a yellow equivalent to that of the spectrum can be obtained by mixing in proper proportions certain homogeneous red and green rays. This single example is sufficient to show that the coloursense is of a very singular nature. This question will be fully treated in Optics (Physiological) ; but for our present purpose it is only necessary to say that we now know (after Wünsch and Young) that the normal eye has only three colour-sensations— a red, a green, and a violet,—and that the apparent colour of any light which falls on it depends merely on the relative intensities of the excitement produced by the light on the three organs of sense corresponding to these sensations. This is true, however, only within certain limits of intensity; for extremely bright light, whatever be its real colour, seems to excite all the three sensations simultaneously, much as white light does; and with very feeble light (as, for instance, that of an ordinary aurora or of a lunar rainbow) we are sometimes scarcely conscious of colours. lu colour-blindness one or more of these organs of sense is wanting, or imperfect. The most common form, Daltonism, depends on the absence of the red sense. Great additions to our knowledge of this subject, if only in confirmation of results already deduced from theory, have been obtained in the last few years by Holmgren; who has experimented on two persons, each of whom was found to have one colour-blind eye, the other being nearly normal. In this way was obtained, what could otherwise have been matter of conjecture only, a description of colour-blind vision in terms of (at least approximately) normal vision.

Finally, the sensation of sight is not limited to the duration of the mechanical action on the eye. It is known that we do not see a sudden flash (an electric spark for instance) until a measurable, though very short, period has elapsed. This depends on the rate at which an excitation is propagated along the optic nerve. But the familiar experiment of whirling a red-hot stick in a dark room shows that the sensation of sight lasts for a short period after the mechanical action which produced it has ceased. This period is probably different for different eyes, and for different amounts of excitement even in the same eye. (If the light be very intense the effect lasts much longer, but completely changes its character.) For our present purpose it may be assumed that the duration is somewhere about ⅜th of a second. Thus, if the end of the red-hot stick describes a circle once in γth of a second, we see the complete circle; if in a longer period, we only see at once such a part of it as was described in 4∙th of a second. Connected with this is the remarkable result obtained experimentally by Swan, that the amount of sensation is, for flashes of short duration, directly proportional, not only to the brightness of the flash, but also to its duration. A flash which lasts for τ 1 σ th of a second produces the full effect on the eye; but an electric spark, as a flash of lightning, which certainly does not endure for more than i 0 ⅛0 000 th of a second, produces at most only τστπππr t ħ °f the effect it would produce if it lasted τ ⅛th of a second. On this short duration of visual impressions depends the action of the thaumatrope, the wheel of life, <fcc, By various kinds of machinery a succession of views of an object in different positions or forms is presented to the eye, each for a brief interval The result is that we fancy we see one and the same object going through a species of continuous motion, or of change of form, which would present it to the eye in these successive positions or forms. Thus, a tadpole may be represented as wriggling about, or as developing continuously into a frog, &c.

Sources of Light. —This subject will be fully treated in other parts of this work under various heads: from the purely scientific point of view under Radiation ; from the more practical side under Lighting (Electric), àc. For our present purpose a very brief summary of the question will suffice; and we do not require to investigate the process by which, in any case, the light is produced.

1. The main source of light is incandescence. (It is usually understood that to be incandescent a body must be at a high temperature.) This may be due to any of a number of causes, such as the following :—

(a) The Potential Energy of Gravitation of Scattered Fragments of Matter.— When these fall together, as in the formation of the sun and stars, heat enough is generated by impact to render the whole vividly incandescent. It is probable that the light of nebulae, and the proper light of comets, is due to this cause. The proximate cause, in all these cases, is the kinetic energy of the fragments before impact. To this class, therefore, can be reduced the light given out when a target is struck by a cannon shot.

(δ) The Kinetic Energy of Cutrent Electricity or of an Electric Discharge.— Here we have lightning, the electric light, and probably also the light of the aurora.

(c) The Potential Energy of Chemical Affinity.— The lime-light, gas-light, candle and lamp-light, fire-light, the magnesium light, &c.; also phosphorus, dead fish (1), <fcc., glowing in the dark.

(<7) Friction, as in the trains of sparks from a grindstone or brake; though here, in general, chemical affinity also has a share.

(e) Sudden great Compression of a Gas, as of air by meteoric stones and falling stars.

2. Another very curious source, not (so far as is known) reducible to incandescence, is the giving out (^usually in an altered form') of light previously absorbed :—fluorescence, phosphorescence, <fcc.

3. A third source is physiological :—fire-flies, glowworms, Medusae, dead fish (?), <fcc., the eye of a cat.

Any not black and not transparent body, exposed to any of these sources of light, becomes in its turn what may for our purpose also be treated as a source.

As will be shown in Radiation, the only bodies which, when incandescent, give every constituent of white light are bodies which are black in the sense of absorbing each and every ray which falls upon them. Such bodies are not necessarily solids—though the best examples we have of them are lamp-black, and (somewhat less perfect) charcoal and gas-coke.

Newton’s speculations on these subjects, taken from the “Queries” at the end of his Optics, give an exceedingly interesting sketch of the state of this subject in his time. We quote a few of the more curious. There is a strange admixture of errors, but a still more strange anticipation of some of the most important of modern discoveries.

“Query 6. Do not Black bodies conceive heat more easily from light than those of other colours do, by reason that the light falling on them is not reflected outwards; but enters the bodies, and is often reflected and refracted within them, until it be stifled and lost?

“Query 8. Do not all Fixed bodies, when heated beyond a certain degree, emit light and shine; and is not this emission performed by the vibrating motions of their Parts. And do not all bodies, which abound with Terrestrial parts, and especially with Sulphureous ones, emit light, as often as those Parts are sufficiently agitated; whether that agitation be made by heat, or by friction, or percussion, or putrefaction, or by any vital motion, or any other cause? . . . .

“Query 9. Is not Fire a body heated so hot, as to emit light copiously? For what else is a red hot iron than fire? And what else is a burning coal than red hot wood?

“Query 10. Is not Flame a vapour,...