The wonders of optics/Lenses
LENSES.
The word lens is derived from the Latin name of the seed of the Ervum lens, or ordinary lentil. When eating this wholesome vegetable, almost every one has noticed that its shape is exactly that of a double convex lens, as represented in the following figure:—
Fig. 26.—Double Convex Lens.
Perhaps it would be more correct if we were to say that a double convex lens is like a lentil, rather than turn the comparison the other way, seeing that this little seed has given its name not only to the particular-shaped glass depicted above, but also to some five others more or less analogous to it.
In fig. 27 we have the different forms of lenses shown in section. The first is the double convex lens, the second the plano-convex, the third and sixth the concavo-convex, the fourth the double concave, and the
Fig. 27.—Forms of Lenses.
fifth the plano-concave. A crossed lens is a double convex lens whose one side is more convex than the other. The third lens is also called meniscus.
The properties of the first, second, and third are similar; that is to say, they cause parallel rays of light passing through them to converge at a certain point, called their focus; while the three others have a divergent action on rays passing through them. By examining the path of the rays through these lenses, we shall find that the first three magnify objects seen through them, while the latter have the contrary effect.
As in the case of the curved mirrors, the rays falling on the surface of a convex lens may be either parallel, divergent, or convergent. In the case of parallel rays, as depicted in the following figure, they are represented as meeting at a point beyond the lens, which is called the sidereal focus, or the focus for parallel rays. It is generally found by causing the image of the sun or of some distant object to be thrown by the lens upon a screen, or by knowing the curvature of the faces, and the refractive power of the glass.
Every ray on striking the surface of the lens is refracted inwards, until it meets with its companions at the focus F, in accordance with the law of refraction, by which a ray of light passing from one transparent medium, such as air, to another which in this instance is glass, becomes refracted or bent in proportion to the
Fig. 28.—Path of a Ray through a Convex Lens.
relative density of the two mediæ. The nearer the ray passes to the edge of the lens, the more it is refracted, the angle of incidence being greater; the ray through the exact centre being uninfluenced by the form of the glass. Hence they all meet in a single point. Figs. 29 and 30 show the path of the rays when they are divergent and convergent.
Fig. 29.—Path of divergent Rays through a Convex Lens.
If the rays of light are not parallel, as in the case of the source of light being near the lens, they do not converge so rapidly as when they proceed from a distant object, consequently the focus for near objects is longer in proportion to their distance. In fig. 29 for instance, if a candle be placed as shown, and a screen on the other side of the lens, a point will be found where the image of the candle is seen upon it in a reversed position. The distance between these two points is always relative, and they are called conjugate foci. Thus, the candle may change places with the screen with a similar effect, as long as the exact position of the two points is preserved. If the candle is placed
Fig. 30.—Conjugate Foci.
farther off, we must diminish the distance between the screen and the lens, and vice versâ. In fact, the nearer the object, the longer the focus; the farther it is off, the shorter the focus. Half an hour's experiment with a double convex lens, a piece of white card-board, and a small candle, will teach the student more about the properties of convex lenses than a chapter of explanation. A common magnifying glass, or even an old spectacle lens, will serve the purpose of more expensive instruments.
We now proceed to speak of the images formed by lenses. In fig. 31 we have a flower placed on one side of a lens. As it is not at an infinite distance, the rays sent out by its various parts are convergent, and not parallel, consequently they do not meet at the sidereal focus, but at a point beyond it, according to the rule already laid down. The rays proceeding from the exact centre of the flower striking the lens exactly in the middle at right angles, suffer no change, the others being refracted in proportion to their angles of incidence.
Fig. 31.—Images formed by Convex Lenses.
The rays proceeding from the flower cross each other at a certain point: hence the image on the screen is reversed. The dimensions of the image will depend on the distance of the object from the lens. This is a fact we meet with every day, when using an opera-glass or a telescope. Images formed by convex lenses upon a screen are called by opticians real images, in contradistinction to those which are the result of mere reflection, as in the case of plane mirrors. These latter are known as virtual images and are produced by convex lenses as well as by plain reflecting surfaces. In fig. 32, for instance, the unreversed image of the insect seen by the eye is not a real image, but a virtual one,—a fact that might be easily proved by placing a screen in the position of the eye, when it would be found that no image would be formed.
When using an ordinary magnifying-glass we see the virtual image of the object we are looking at, but in the case of a telescope or opera-glass we see the real image of the object, formed by the large lens in front, and reversed again by the arrangement of small lenses next to the eye.
Fig. 32.—Magnifying Property of Convex Lenses.
Double concave lenses produce effects which are just the reverse of those we have been considering. Instead of increasing in thickness from the edges to the centre, they follow the contrary plan, and increase from the centre to the edges. Consequently, instead of the rays meeting at the focus, they diverge from each other, and gradually spread out, as shown in fig. 33.
Fig. 33.—Diminishing Effect of Concave Lenses
The above figure shows the path of the rays proceeding from the vase, and meeting the eye at such an angle
Fig. 34.—Cannon of the Palais Royal.
lenses, as the student has no doubt already guessed, do not give real images.
The effects produced by the action of concave mirrors may be produced with just as much facility by convex lenses. If a body is placed in a focus of a lens which receives the direct rays of the sun, the heat as well as the light will be concentrated at one point; and if the object is combustible, it will take fire sooner or later, according to the size of the lens. All the experiments mentioned by Buffon as being produced by a concave mirror are equally obtainable with a concave lens. When of sufficient diameter, the most refractory metals, such as platinum or iridium, may be melted and dissipated into vapour. Before lucifer matches and vesuvians were as common as they are now, it was not at all unusual to find smokers carrying a small burning-glass and a piece of tinder, for the purpose of lighting their pipes or cigars; and there hardly exists a boy who has not lighted a bonfire in the fields or playground by means of an old spectacle lens or telescope glass.
Amongst other applications of this property of lenses may be mentioned that of causing guns to fire at a certain time, by arranging a small burning-glass above the touch-hole. In the Gardens of the Palais Royal, at Paris, there is such a gun, so arranged that on sunny days it fires exactly at noon, or, in other words, at the moment the sun comes to the meridian. Every fine day towards twelve o'clock, crowds of Parisians who have nothing to do may be seen bending their steps towards the Palais Royal to set their watches by the gun, which they believe to be superior as a time-keeper to the finest chronometer in the world. There they stand, most of them old fellows with a scar or two about their faces, showing that they have nobly won the rest they appear to enjoy so innocently and calmly with watch in hand, leaning against the railings, and waiting with impatience the moment when true solar noon is indicated by the sharp report of the little piece. Their belief in the correctness of solar time is something astonishing; and if a bystander were to insinuate, no matter how delicately, that solar time varied slightly every now and then, he would either receive a smile of pitying contempt, or else he would be called out upon the spot. Fig. 34 gives a pretty view of the celebrated cannon of the Palais Royal.
We now come to another application of the refracting power of lenses, in the way of concentrating rays, which is infinitely more valuable to humanity than
Fig. 35.—Fresnel's Lighthouse Apparatus.
either of those we have just mentioned; we mean the construction of enormous refracting apparatuses for lighthouse purposes. The first lighthouse of which we have any record is that which was erected on the island
of Pharos, by Ptolemy Philadelphus, in the year 470
of the foundation of Rome. This was merely a tower,
upon the top of which fires were kept burning at night;
but as the world progressed, the blazing tar-barrel or
wood fire gave place to the carefully-constructed lamp
and silvered reflector apparatus, which are fast disappearing
in their turn before the electric or Drummond light
and the refracting apparatus constructed by Fresnel,
who was the first to endeavour to abolish the old-fashioned
and inefficient metallic mirror from the
lanterns of lighthouses. Fig. 35 shows a section of
Fresnel's apparatus. A is a plano-convex lens of about
a foot in diameter, whose focus corresponds with those
of the concentric lenticular rings of glass which surround
it, and which are seen more plainly in fig. 36.
These rings, which are ground and polished with the
greatest accuracy, are somewhat in the shape of an
ordinary quoit, and are equivalent to a plano-convex
lens with the centre portion cut out. This arrangement
is so powerful that the distance at which a light provided
with it can be seen is only limited by bad weather,
the state of the atmosphere and the distance of the
horizon. It is common for such lights to be seen at a
distance of between fifty and sixty miles. The apparatus
is mostly arranged in the form of an octagon,
and is generally provided with additional reflecting
mirrors at those parts above the light which are out of
the range of the lenses. The light shining fully in eight
directions at one time, can scarcely be missed by any
ship within range; but in order to guard against any
possibility of accident, the optical apparatus is often
made to revolve by clockwork, so that every point of
the ocean is illuminated in turn. By using coloured
glasses, or by causing the light to disappear at distinct
intervals, different lighthouses may be identified by ships that are out of their reckoning. Fig. 36 represents the interior of the lantern of a first class lighthouse, showing the arrangement of the lenticular rings round the central lens. If ever the student should pass through Havre, he should not miss the opportunity of seeing this noble apparatus, which is one of the finest ever manufactured.
Fig. 36.—Lantern of a First-class Lighthouse.