Light is a third form of that energy of which we have already treated two manifestations—heat and electricity. The distinguishing characteristic of ether light-waves is their extreme rapidity of vibration, which has been calculated to range from 700 billion movements per second for violet rays to 400 billion for red rays.

If a beam of white light be passed through a prism it is resolved into the seven visible colours of the spectrum—violet, indigo, blue, green, yellow, orange, and red—in this order. The human eye is most sensitive to the yellow-red rays, a photographic plate to the green-violet rays.

All bodies fall into one of two classes—(1) Luminous—that is, those which are a source of light, such as the sun, a candle flame, or a red-hot coal; and (2) non-luminous, which become visible only by virtue of light which they receive from other bodies and reflect to our eyes.

THE PROPAGATION OF LIGHT.

Light naturally travels in a straight line. It is deflected only when it passes from one transparent medium into another—for example, from air to water—and the mediums are of different densities. We may regard the surface of a visible object as made up of countless points, from each of which a diverging pencil of rays is sent off through the ether.

LENSES.

If a beam of light encounters a transparent glass body with non-parallel sides, the rays are deflected. The direction they take depends on the shape of the body, but it may be laid down as a rule that they are bent toward the thicker part of the glass. The common burning-glass is well known to us. We hold it up facing the sun to concentrate all the heat rays that fall upon it into one intensely brilliant spot, which speedily ignites any inflammable substance on which it may fall (Fig. 103). We may imagine that one ray passes from the centre of the sun through the centre of the glass. This is undeflected; but all the others are bent towards it, as they pass through the thinner parts of the lens.

It should be noted here that sunlight, as we call it, is accompanied by heat. A burning-glass is used to concentrate the heat rays, not the light rays, which, though they are collected too, have no igniting effect.

In photography we use a lens to concentrate light rays only. Such heat rays as may pass through the lens with them are not wanted, and as they have no practical effect are not taken any notice of. To be of real value, a lens must be quite symmetrical—that is, the curve from the centre to the circumference must be the same in all directions.

There are six forms of simple lenses, as given in Fig. 104. Nos. 1 and 2 have one flat and one spherical surface. Nos. 3, 4, 5, 6 have two spherical surfaces. When a lens is thicker at the middle than at the sides it is called a convex lens; when thinner, a concave lens. The names of the various shapes are as follows:—No. 1, plano-convex; No. 2, plano-concave; No. 3, double convex; No. 4, double concave; No. 5, meniscus; No. 6, concavo-convex. The thick-centre lenses, as we may term them (Nos. 1, 3, 5), concentrate a pencil of rays passing through them; while the thin-centre lenses (Nos. 2, 4, 6) scatter the rays (see Fig. 105).

THE CAMERA.

We said above that light is propagated in straight lines. To prove this is easy. Get a piece of cardboard and prick a hole in it. Set this up some distance away from a candle flame, and hold behind it a piece of tissue paper. You will at once perceive a faint, upside-down image of the flame on the tissue. Why is this? Turn for a moment to Fig. 106, which shows a "pinhole" camera in section. At the rear is a ground-glass screen, B, to catch the image. Suppose that A is the lowest point of the flame. A pencil of rays diverging from it strikes the front of the camera, which stops them all except the one which passes through the hole and makes a tiny luminous spot on B, above the centre of the screen, though A is below the axis of the camera. Similarly the tip of the flame (above the axis) would be represented by a dot on the screen below its centre. And so on for all the millions of points of the flame. If we were to enlarge the hole we should get a brighter image, but it would have less sharp outlines, because a number of rays from every point of the candle would reach the screen and be jumbled up with the rays of neighbouring pencils. Now, though a good, sharp photograph may be taken through a pinhole, the time required is so long that photography of this sort has little practical value. What we want is a large hole for the light to enter the camera by, and yet to secure a distinct image. If we place a lens in the hole we can fulfil our wish. Fig. 107 shows a lens in position, gathering up a number of rays from a point, A, and focussing them on a point, B. If the lens has 1,000 times the area of the pinhole, it will pass 1,000 times as many rays, and the image of A will be impressed on a sensitized photographic plate 1,000 times more quickly.

THE IMAGE CAST BY A CONVEX LENS.

Fig. 108 shows diagrammatically how a convex lens forms an image. From A and B, the extremities of the object, a simple ray is considered to pass through the centre of the lens. This is not deflected at all. Two other rays from the same points strike the lens above and below the centre respectively. These are bent inwards and meet the central rays, or come to a focus with them at A¹ and B¹. In reality a countless number of rays would be transmitted from every point of the object and collected to form the image.

FOCUS.

We must now take special notice of that word heard so often in photographic talk—"focus." What is meant by the focus or focal length of a lens? Well, it merely signifies the distance between the optical centre of the lens and the plane in which the image is formed.

We must here digress a moment to draw attention to the three simple diagrams of Fig. 109. The object, O, in each case is assumed to be to the right of the lens. In the topmost diagram the object is so far away from the lens that all rays coming from a single point in it are practically parallel. These converge to a focus at F. If the distance between F and the centre of the lens is six inches, we say that the lens has a six-inch focal length. The focal length of a lens is judged by the distance between lens and image when the object is far away. To avoid confusion, this focal length is known as the principal focus, and is denoted by the symbol f. In the middle diagram the object is quite near the lens, which has to deal with rays striking its nearer surface at an acuter angle than before (reckoning from the centre). As the lens can only deflect their path to a fixed degree, they will not, after passing the lens, come together until they have reached a point, F¹, further from the lens than F. The nearer we approach O to the lens, the further away on the other side is the focal point, until a distance equal to that of F from the lens is reached, when the rays emerge from the glass in a parallel pencil. The rays now come to a focus no longer, and there can be no image. If O be brought nearer than the focal distance, the rays would diverge after passing through the lens.

RELATIVE POSITIONS OF OBJECT AND IMAGE.

From what has been said above we deduce two main conclusions—(1.) The nearer an object is brought to the lens, the further away from the lens will the image be. (2.) If the object approaches within the principal focal distance of the lens, no image will be cast by the lens. To make this plainer we append a diagram (Fig. 110), which shows five positions of an object and the relative positions of the image (in dotted lines). First, we note that the line A B, or A B¹, denotes the principal focal length of the lens, and A C, or A C¹, denotes twice the focal length. We will take the positions in order:—

Position I. Object further away than 2f. Inverted image smaller than object, at distance somewhat exceeding f.

Position II. Object at distance = 2f. Inverted image at distance = 2f, and of size equal to that of object.

Position III Object nearer than 2f. Inverted image further away than 2f; larger than the object.

Position IV. Object at distance = f. As rays are parallel after passing the lens no image is cast.

Position V. Object at distance less than f. No real image—that is, one that can be caught on a focussing screen—is now given by the lens, but a magnified, erect, virtual image exists on the same side of the lens as the object.

We shall refer to virtual images at greater length presently. It is hoped that any reader who practises photography will now understand why it is necessary to rack his camera out beyond the ordinary focal distance when taking objects at close quarters. From Fig. 110 he may gather one practically useful hint—namely, that to copy a diagram, etc., full size, both it and the plate must be exactly 2f from the optical centre of the lens. And it follows from this that the further he can rack his camera out beyond 2f the greater will be the possible enlargement of the original.

CORRECTION OF LENSES FOR COLOUR.

We have referred to the separation of the spectrum colours of white light by a prism. Now, a lens is one form of prism, and therefore sorts out the colours. In Fig. 111 we assume that two parallel red rays and two parallel violet rays from a distant object pass through a lens. A lens has most bending effect on violet rays and least on red, and the other colours of the spectrum are intermediately influenced. For the sake of simplicity we have taken the two extremes only. You observe that the point R, in which the red rays meet, is much further from the lens than is V, the meeting-point of the violet rays. A photographer very seldom has to take a subject in which there are not objects of several different colours, and it is obvious that if he used a simple lens like that in Fig. 111 and got his red objects in good focus, the blue and green portions of his picture would necessarily be more or less out of focus.

This defect can fortunately be corrected by the method shown in Fig. 112. A compound lens is needed, made up of a crown glass convex element, B, and a concave element, A, of flint glass. For the sake of illustration the two parts are shown separated; in practice they would be cemented together, forming one optical body, thicker in the centre than at the edges—a meniscus lens in fact, since A is not so concave as B is convex. Now, it was discovered by a Mr. Hall many years ago that if white light passed through two similar prisms, one of flint glass the other of crown glass, the former had the greater effect in separating the spectrum colours—that is, violet rays were bent aside more suddenly compared with the red rays than happened with the crown-glass prism. Look at Fig. 112. The red rays passing through the flint glass are but little deflected, while the violet rays turn suddenly outwards. This is just what is wanted, for it counteracts the unequal inward refraction by B, and both sets of rays come to a focus in the same plane. Such a lens is called achromatic, or colourless. If you hold a common reading-glass some distance away from large print you will see that the letters are edged with coloured bands, proving that the lens is not achromatic. A properly corrected photographic lens would not show these pretty edgings. Colour correction is necessary also for lenses used in telescopes and microscopes.

SPHERICAL ABERRATION.

A lens which has been corrected for colour is still imperfect. If rays pass through all parts of it, those which strike it near the edge will be refracted more than those near the centre, and a blurred focus results. This is termed spherical aberration. You will be able to understand the reason from Figs. 113 and 114. Two rays, A, are parallel to the axis and enter the lens near the centre (Fig. 113). These meet in one plane. Two other rays, B, strike the lens very obliquely near the edge, and on that account are both turned sharply upwards, coming to a focus in a plane nearer the lens than A. If this happened in a camera the results would be very bad. Either A or B would be out of focus. The trouble is minimized by placing in front of the lens a plate with a central circular opening in it (denoted by the thick, dark line in Fig. 114). The rays B of Fig. 113 are stopped by this plate, which is therefore called a stop. But other rays from the same point pass through the hole. These, however, strike the lens much more squarely above the centre, and are not unduly refracted, so that they are brought to a focus in the same plane as rays A.

DISTORTION OF IMAGE.

The lens we have been considering is a single meniscus, such as is used in landscape photography, mounted with the convex side turned towards the inside of the camera, and having the stop in front of it. If you possess a lens of this sort, try the following experiment with it. Draw a large square on a sheet of white paper and focus it on the screen. The sides instead of being straight bow outwards: this is called barrel distortion. Now turn the lens mount round so that the lens is outwards and the stop inwards. The sides of the square will appear to bow towards the centre: this is pin-cushion distortion. For a long time opticians were unable to find a remedy. Then Mr. George S. Cundell suggested that two meniscus lenses should be used in combination, one on either side of the stop, as in Fig 115. Each produces distortion, but it is counteracted by the opposite distortion of the other, and a square is represented as a square. Lenses of this kind are called rectilinear, or straight-line producing.

We have now reviewed the three chief defects of a lens—chromatic aberration, spherical aberration, and distortion—and have seen how they may be remedied. So we will now pass on to the most perfect of cameras,

THE HUMAN EYE.

The eye (Fig. 116) is nearly spherical in form, and is surrounded outside, except in front, by a hard, horny coat called the sclerotica (S). In front is the cornea (A), which bulges outwards, and acts as a transparent window to admit light to the lens of the eye (C). Inside the sclerotica, and next to it, comes the choroid coat; and inside that again is the retina, or curved focussing screen of the eye, which may best be described as a network of fibres ramifying from the optic nerve, which carries sight sensations to the brain. The hollow of the ball is full of a jelly-like substance called the vitreous humour; and the cavity between the lens and the cornea is full of water.

We have already seen that, in focussing, the distance between lens and image depends on the distance between object and lens. Now, the retina cannot be pushed nearer to or pulled further away from its lens, like the focussing screen of a camera. How, then, is the eye able to focus sharply objects at distances varying from a foot to many miles?

As a preliminary to the answer we must observe that the more convex a lens is, the shorter is its focus. We will suppose that we have a box camera with a lens of six-inch focus fixed rigidly in the position necessary for obtaining a sharp image of distant objects. It so happens that we want to take with it a portrait of a person only a few feet from the lens. If it were a bellows camera, we should rack out the back or front. But we cannot do this here. So we place in front of our lens a second convex lens which shortens its principal focus; so that in effect the box has been racked out sufficiently.

Nature, however, employs a much more perfect method than this. The eye lens is plastic, like a piece of india-rubber. Its edges are attached to ligaments (L L), which pull outwards and tend to flatten the curve of its surfaces. The normal focus is for distant objects. When we read a book the eye adapts itself to the work. The ligaments relax and the lens decreases in diameter while thickening at the centre, until its curvature is such as to focus all rays from the book sharply on the retina. If we suddenly look through the window at something outside, the ligaments pull on the lens envelope and flatten the curves.

This wonderful lens is achromatic, and free from spherical aberration and distortion of image. Nor must we forget that it is aided by an automatic "stop," the iris, the central hole of which is named the pupil. We say that a person has black, blue, or gray eyes according to the colour of the iris. Like the lens, the iris adapts itself to all conditions, contracting when the light is strong, and opening when the light is weak, so that as uniform an amount of light as conditions allow may be admitted to the eye. Most modern camera lenses are fitted with adjustable stops which can be made larger or smaller by twisting a ring on the mount, and are named "iris" stops. The image of anything seen is thrown on the retina upside down, and the brain reverses the position again, so that we get a correct impression of things.

THE USE OF SPECTACLES.

The reader will now be able to understand without much trouble the function of a pair of spectacles. A great many people of all ages suffer from short-sight. For one reason or another the distance between lens and retina becomes too great for a person to distinguish distant objects clearly. The lens, as shown in Fig 117a, is too convex—has its minimum focus too short—and the rays meet and cross before they reach the retina, causing general confusion of outline. This defect is simply remedied by placing in front of the eye (Fig. 117b) a concave lens, to disperse the rays somewhat before they enter the eye, so that they come to a focus on the retina. If a person's sight is thus corrected for distant objects, he can still see near objects quite plainly, as the lens will accommodate its convexity for them. The scientific term for short-sight is myopia. Long-sight, or hypermetropia, signifies that the eyeball is too short or the lens too flat. Fig. 118a represents the normal condition of a long-sighted eye. When looking at a distant object the eye thickens slightly and brings the focus forward into the retina. But its thickening power in such an eye is very limited, and consequently the rays from a near object focus behind the retina. It is therefore necessary for a long-sighted person to use convex spectacles for reading the newspaper. As seen in Fig. 118b, the spectacle lens concentrates the rays before they enter the eye, and so does part of the eye's work for it.

Returning for a moment to the diagram of the eye (Fig. 116), we notice a black patch on the retina near the optic nerve. This is the "yellow spot." Vision is most distinct when the image of the object looked at is formed on this part of the retina. The "blind spot" is that point at which the optic nerve enters the retina, being so called from the fact that it is quite insensitive to light. The finding of the blind spot is an interesting little experiment. On a card make a large and a small spot three inches apart, the one an eighth, the other half an inch in diameter. Bring the card near the face so that an eye is exactly opposite to each spot, and close the eye opposite to the smaller. Now direct the other eye to this spot and you will find, if the card be moved backwards and forwards, that at a certain distance the large spot, though many times larger than its fellow, has completely vanished, because the rays from it enter the open eye obliquely and fall on the "blind spot."

Chapter XIII.

In Fig. 119 is represented an eye looking at a vase, three inches high, situated at A, a foot away. If we were to place another vase, B, six inches high, at a distance of two feet; or C, nine inches high, at three feet; or D, a foot high, at four feet, the image on the retina would in every case be of the same size as that cast by A. We can therefore lay down the rule that the apparent size of an object depends on the angle that it subtends at the eye.

To see a thing more plainly, we go nearer to it; and if it be very small, we hold it close to the eye. There is, however, a limit to the nearness to which it can be brought with advantage. The normal eye is unable to adapt its focus to an object less than about ten inches away, termed the "least distance of distinct vision."

THE SIMPLE MICROSCOPE.

A magnifying glass comes in useful when we want to examine an object very closely. The glass is a lens of short focus, held at a distance somewhat less than its principal focal length, F (see Fig. 120), from the object. The rays from the head and tip of the pin which enter the eye are denoted by continuous lines. As they are deflected by the glass the eye gets the impression that a much longer pin is situated a considerable distance behind the real object in the plane in which the refracted rays would meet if produced backwards (shown by the dotted lines). The effect of the glass, practically, is to remove it (the object) to beyond the least distance of distinct vision, and at the same time to retain undiminished the angle it subtends at the eye, or, what amounts to the same thing, the actual size of the image formed on the retina.[22] It follows, therefore, that if a lens be of such short focus that it allows us to see an object clearly at a distance of two inches—that is, one-fifth of the least distance of distinct vision—we shall get an image on the retina five times larger in diameter than would be possible without the lens.

The two simple diagrams (Figs. 121 and 122) show why the image to be magnified should be nearer to the lens than the principal focus, F. We have already seen (Fig. 109) that rays coming from a point in the principal focal plane emerge as a parallel pencil. These the eye can bring to a focus, because it normally has a curvature for focussing parallel rays. But, owing to the power of "accommodation," it can also focus diverging rays (Fig. 121), the eye lens thickening the necessary amount, and we therefore put our magnifying glass a bit nearer than F to get full advantage of proximity. If we had the object outside the principal focus, as in Fig. 122, the rays from it would converge, and these could not be gathered to a sharp point by the eye lens, as it cannot flatten more than is required for focussing parallel rays.

USE OF THE SIMPLE MICROSCOPE IN THE TELESCOPE.

Let us now turn to Fig. 123. At A is a distant object, say, a hundred yards away. B is a double convex lens, which has a focal length of twenty inches. We may suppose that it is a lens in a camera. An inverted image of the object is cast by the lens at C. If the eye were placed at C, it would distinguish nothing. But if withdrawn to D, the least distance of distinct vision,[23] behind C, the image is seen clearly. That the image really is at C is proved by letting down the focussing screen, which at once catches it. Now, as the focus of the lens is twice d, the image will be twice as large as the object would appear if viewed directly without the lens. We may put this into a very simple formula:—

In Fig. 124 we have interposed between the eye and the object a small magnifying glass of 2½-inch focus, so that the eye can now clearly see the image when one-quarter d away from it. B already magnifies the image twice; the eye-piece again magnifies it four times; so that the total magnification is 2 × 4 = 8 times. This result is arrived at quickly by dividing the focus of B (which corresponds to the object-glass of a telescope) by the focus of the eye-piece, thus:—

The ordinary astronomical telescope has a very long focus object-glass at one end of the tube, and a very short focus eye-piece at the other. To see an object clearly one merely has to push in or pull out the eye-piece until its focus exactly corresponds with that of the object-glass.

THE TERRESTRIAL TELESCOPE.

An astronomical telescope inverts images. This inversion is inconvenient for other purposes. So the terrestrial telescope (such as is commonly used by sailors) has an eye-piece compounded of four convex lenses which erect as well as magnify the image. Fig. 125 shows the simplest form of compound erecting eye-piece.

THE GALILEAN TELESCOPE.

A third form of telescope is that invented by the great Italian astronomer, Galileo,[24] in 1609. Its principle is shown in Fig. 126. The rays transmitted by the object-glass are caught, before coming to a focus, on a concave lens which separates them so that they appear to meet in the paths of convergence denoted by the dotted lines. The image is erect. Opera-glasses are constructed on the Galilean principle.

THE PRISMATIC TELESCOPE.

In order to be able to use a long-focus object-glass without a long focussing-tube, a system of glass reflecting prisms is sometimes employed, as in Fig. 127. A ray passing through the object-glass is reflected from one posterior surface of prism A on to the other posterior surface, and by it out through the front on to a second prism arranged at right angles to it, which passes the ray on to the compound eye-piece. The distance between object-glass and eye-piece is thus practically trebled. The best-known prismatic telescopes are the Zeiss field-glasses.

THE REFLECTING TELESCOPE.

We must not omit reference to the reflecting telescope, so largely used by astronomers. The front end of the telescope is open, there being no object-glass. Rays from the object fall on a parabolic mirror situated in the rear end of the tube. This reflects them forwards to a focus. In the Newtonian reflector a plane mirror or prism is situated in the axis of the tube, at the focus, to reflect the rays through an eye-piece projecting through the side of the tube. Herschel's form of reflector has the mirror set at an angle to the axis, so that the rays are reflected direct into an eye-piece pointing through the side of the tube towards the mirror.

THE PARABOLIC MIRROR.

This mirror (Fig. 128) is of such a shape that all rays parallel to the axis are reflected to a common point. In the marine searchlight a powerful arc lamp is arranged with the arc at the focus of a parabolic reflector, which sends all reflected light forward in a pencil of parallel rays. The most powerful searchlight in existence gives a light equal to that of 350 million candles.

THE COMPOUND MICROSCOPE.

We have already observed (Fig. 110) that the nearer an object approaches a lens the further off behind it is the real image formed, until the object has reached the focal distance, when no image at all is cast, as it is an infinite distance behind the lens. We will assume that a certain lens has a focus of six inches. We place a lighted candle four feet in front of it, and find that a sharp diminished image is cast on a ground-glass screen held seven inches behind it. If we now exchange the positions of the candle and the screen, we shall get an enlarged image of the candle. This is a simple demonstration of the law of conjugate foci—namely, that the distance between the lens and an object on one side and that between the lens and the corresponding image on the other bear a definite relation to each other; and an object placed at either focus will cast an image at the other. Whether the image is larger or smaller than the object depends on which focus it occupies. In the case of the object-glass of a telescope the image was at what we may call the short focus.

Now, a compound microscope is practically a telescope with the object at the long focus, very close to a short-focus lens. A greatly enlarged image is thrown (see Fig. 129) at the conjugate focus, and this is caught and still further magnified by the eye-piece. We may add that the object-glass, or objective, of a microscope is usually compounded of several lenses, as is also the eye-piece.

THE MAGIC-LANTERN.

The most essential features of a magic-lantern are:—(1) The source of light; (2) the condenser for concentrating the light rays on to the slide; (3) the lens for projecting a magnified image on to a screen.

Fig. 130 shows these diagrammatically. The illuminant is most commonly an oil-lamp, or an acetylene gas jet, or a cylinder of lime heated to intense luminosity by an oxy-hydrogen flame. The natural combustion of hydrogen is attended by a great heat, and when the supply of oxygen is artificially increased the temperature of the flame rises enormously. The nozzle of an oxy-hydrogen jet has an interior pipe connected with the cylinder holding one gas, and an exterior, and somewhat larger, pipe leading from that containing the other, the two being arranged concentrically at the nozzle. By means of valves the proportions of the gases can be regulated to give the best results.

The condenser is set somewhat further from the illuminant than the principal focal length of the lenses, so that the rays falling on them are bent inwards, or to the slide.

The objective, or object lens, stands in front of the slide. Its position is adjustable by means of a rack and a draw-tube. The nearer it is brought to the slide the further away is the conjugate focus (see p. 239), and consequently the image. The exhibitor first sets up his screen and lantern, and then finds the conjugate foci of slide and image by racking the lens in or out.

If a very short focus objective be used, subjects of microscopic proportions can be projected on the screen enormously magnified. During the siege of Paris in 1870–71 the Parisians established a balloon and pigeon post to carry letters which had been copied in a minute size by photography. These copies could be enclosed in a quill and attached to a pigeon's wing. On receipt, the copies were placed in a special lantern and thrown as large writing on the screen. Micro-photography has since then made great strides, and is now widely used for scientific purposes, one of the most important being the study of the crystalline formations of metals under different conditions.

THE BIOSCOPE.

"Living pictures" are the most recent improvement in magic-lantern entertainments. The negatives from which the lantern films are printed are made by passing a ribbon of sensitized celluloid through a special form of camera, which feeds the ribbon past the lens in a series of jerks, an exposure being made automatically by a revolving shutter during each rest. The positive film is placed in a lantern, and the intermittent movement is repeated; but now the source of illumination is behind the film, and light passes outwards through the shutter to the screen. In the Urban bioscope the film travels at the rate of fifteen miles an hour, upwards of one hundred exposures being made every second.

The impression of continuous movement arises from the fact that the eye cannot get rid of a visual impression in less than one-tenth of a second. So that if a series of impressions follow one another more rapidly than the eye can rid itself of them the impressions will overlap, and give one of motion, if the position of some of the objects, or parts of the objects, varies slightly in each succeeding picture.[25]

THE PLANE MIRROR.