How it Works Part 15

A lens which has been corrected for colour is still imperfect. If rays pa.s.s 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 pa.s.s 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.

[Ill.u.s.tration: FIG. 113.]

[Ill.u.s.tration: FIG. 114.]

DISTORTION OF IMAGE.

[Ill.u.s.tration: FIG. 115.--Section of a rectilinear lens.]

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-cus.h.i.+on_ 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 pa.s.s 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, h.o.r.n.y 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?

[Ill.u.s.tration: FIG. 116.--Section of the human eye.]

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 princ.i.p.al 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.

[Ill.u.s.tration: FIG. 117_a_.]

[Ill.u.s.tration: FIG. 117_b_.]

[Ill.u.s.tration: FIG. 118_a_.]

[Ill.u.s.tration: FIG. 118_b_.]

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 117_a_, 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. 117_b_) 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. 118_a_ 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. 118_b_, 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.

THE MICROSCOPE, THE TELESCOPE, AND THE MAGIC-LANTERN.

The simple microscope--Use of the simple microscope in the telescope--The terrestrial telescope--The Galilean telescope--The prismatic telescope--The reflecting telescope--The parabolic mirror--The compound microscope--The magic-lantern--The bioscope--The plane mirror.

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_.

[Ill.u.s.tration: FIG. 119.]

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.

[Ill.u.s.tration: FIG. 120.]

A magnifying gla.s.s comes in useful when we want to examine an object very closely. The gla.s.s is a lens of short focus, held at a distance somewhat less than its princ.i.p.al 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 gla.s.s 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 gla.s.s, 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 princ.i.p.al focus, F. We have already seen (Fig. 109) that rays coming from a point in the princ.i.p.al 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 gla.s.s a bit nearer than F to get full advantage of proximity. If we had the object _outside_ the princ.i.p.al 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.

[Ill.u.s.tration: FIG. 121.]

[Ill.u.s.tration: FIG. 122.]

USE OF THE SIMPLE MICROSCOPE IN THE TELESCOPE.

[Ill.u.s.tration: FIG. 123.]

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:--

Magnification = focal length of lens -------------------- _d_

[Ill.u.s.tration: FIG. 124.]

In Fig. 124 we have interposed between the eye and the object a small magnifying gla.s.s of 2-1/2-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-gla.s.s of a telescope) by the focus of the eye-piece, thus:--

20 ____ = 8 2-1/2

The ordinary astronomical telescope has a very long focus object-gla.s.s 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-gla.s.s.

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.