Chapter XII.

OPTICS.

Lenses--The image cast by a convex lens--Focus--Relative position of object and lens--Correction of lenses for colour--Spherical aberration--Distortion of image--The human eye--The use of spectacles--The blind spot.

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 pa.s.sed 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 cla.s.ses--(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 pa.s.ses 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 gla.s.s 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 gla.s.s. The common burning-gla.s.s 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 pa.s.ses from the centre of the sun through the centre of the gla.s.s. This is undeflected; but all the others are bent towards it, as they pa.s.s through the thinner parts of the lens.

[Ill.u.s.tration: FIG. 103.--Showing how a burning-gla.s.s concentrates the heat rays which fall upon it.]

It should be noted here that _sunlight_, as we call it, is accompanied by heat. A burning-gla.s.s 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 pa.s.s 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 circ.u.mference 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 pa.s.sing through them; while the thin-centre lenses (Nos. 2, 4, 6) _scatter_ the rays (see Fig. 105).

[Ill.u.s.tration: FIG. 104.--Six forms of lenses.]

THE CAMERA.

[Ill.u.s.tration: FIG. 105.]

[Ill.u.s.tration: FIG. 106.]

We said above that light is propagated in straight lines. To prove this is easy. Get a piece of cardboard and p.r.i.c.k 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-gla.s.s 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 pa.s.ses 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 pa.s.s 1,000 times as many rays, and the image of A will be impressed on a sensitized photographic plate 1,000 times more quickly.

[Ill.u.s.tration: FIG. 107.]

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 pa.s.s 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 A^1 and B^1. In reality a countless number of rays would be transmitted from every point of the object and collected to form the image.

[Ill.u.s.tration: FIG. 108.--Showing how an image is cast by a convex lens.]

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.

[Ill.u.s.tration: FIG. 109.]

We must here digress a moment to draw attention to the three simple diagrams of Fig. 109. The object, O, in each case is a.s.sumed 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 _princ.i.p.al_ 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 pa.s.sing the lens, come together until they have reached a point, F^1, 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 gla.s.s 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 pa.s.sing through the lens.

RELATIVE POSITIONS OF OBJECT AND IMAGE.

[Ill.u.s.tration: FIG. 110.--Showing how the position of the image alters relatively to the position of the object.]

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 princ.i.p.al 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 B^1, denotes the princ.i.p.al focal length of the lens, and A C, or A C^1, denotes twice the focal length. We will take the positions in order:--

_Position I._ Object further away than 2_f_. Inverted image _smaller_ than object, at distance somewhat exceeding _f_.

_Position II._ Object at distance = 2_f_. Inverted image at distance = 2_f_, and of size equal to that of object.

_Position III_ Object nearer than 2_f_. Inverted image further away than 2_f_; _larger_ than the object.

_Position IV._ Object at distance = _f_. As rays are parallel after pa.s.sing 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 2_f_ from the optical centre of the lens. And it follows from this that the further he can rack his camera out beyond 2_f_ 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 a.s.sume that two parallel red rays and two parallel violet rays from a distant object pa.s.s 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.

[Ill.u.s.tration: FIG. 111.]

[Ill.u.s.tration: FIG. 112.]

This defect can fortunately be corrected by the method shown in Fig.

112. A _compound_ lens is needed, made up of a _crown_ gla.s.s convex element, B, and a concave element, A, of _flint_ gla.s.s. For the sake of ill.u.s.tration 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 pa.s.sed through two similar prisms, one of flint gla.s.s the other of crown gla.s.s, 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-gla.s.s prism.

Look at Fig. 112. The red rays pa.s.sing through the flint gla.s.s 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-gla.s.s 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.